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salim-barzani

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These are questions asked by salim-barzani

Clarifying and Solving a New ODE with Ex...

salim-barzani 1640 Maple 2024
ode differential-equations duplicate-question
May 03 2025
0 10

I am currently working with an ordinary differential equation (ODE) that I find difficult to express and solve accurately. In this ODE, the symbol f represents an exponential function rather than a typical variable, which adds to the confusion. Although I have followed the format used in related research papers, the results I obtain are not satisfactory.

Since this type of ODE is new and somewhat unfamiliar to me, I would greatly appreciate your guidance in:

  1. Properly formulating the ODE.

  2. Understanding the role of f in the context of exponential functions.

  3. Finding the correct and complete solutions.

  4. Learning how to clearly present each solution step by step.

Thank you in advance for your support.

AA.mw

Symbolic Factoring of Multiplicative Ter...

salim-barzani 1640 Maple 2024
factorization coefficients duplicate-question
May 02 2025
0 14

Manually factoring each equation in this system one by one is time-consuming and inefficient. Is there a way to automate the factoring of expressions into two multiplicative terms—some of which may be single-term factors—using code?

> 

restart
> 

with(PDEtools)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

G1 := 5*lambda^2*alpha[1]^4*alpha[0]*a[4]+lambda^2*alpha[1]^4*a[3]-10*lambda*alpha[1]^2*alpha[0]^3*a[4]+lambda*k^2*a[1]*alpha[1]^2-6*lambda*alpha[1]^2*alpha[0]^2*a[3]+alpha[0]^5*a[4]-k^2*a[1]*alpha[0]^2-3*lambda*alpha[1]^2*alpha[0]*a[2]+alpha[0]^4*a[3]+lambda*w*alpha[1]^2+alpha[0]^3*a[2]-w*alpha[0]^2+((lambda^2*a[4]*alpha[1]^5-10*lambda*a[4]*alpha[0]^2*alpha[1]^3-4*lambda*a[3]*alpha[0]*alpha[1]^3+5*a[4]*alpha[0]^4*alpha[1]-2*k^2*a[1]*alpha[0]*alpha[1]-lambda*a[2]*alpha[1]^3+4*a[3]*alpha[0]^3*alpha[1]+3*a[2]*alpha[0]^2*alpha[1]-2*w*alpha[0]*alpha[1])*(diff(G(xi), xi))+lambda^2*beta[0]*a[5]*alpha[1]^2-4*mu*lambda*alpha[1]^4*a[3]+5*lambda^2*beta[0]*alpha[1]^4*a[4]-3*lambda*beta[0]*alpha[1]^2*a[2]-lambda*beta[0]*a[5]*alpha[0]^2-(1/2)*lambda*a[1]*alpha[0]*beta[0]-2*k^2*a[1]*alpha[0]*beta[0]+12*mu*alpha[1]^2*alpha[0]^2*a[3]+6*mu*alpha[1]^2*alpha[0]*a[2]-2*mu*k^2*a[1]*alpha[1]^2-(1/2)*mu*lambda*alpha[1]^2*a[1]+20*mu*alpha[1]^2*alpha[0]^3*a[4]-20*mu*lambda*alpha[1]^4*alpha[0]*a[4]-2*mu*lambda*alpha[1]^2*a[5]*alpha[0]-30*lambda*beta[0]*alpha[1]^2*alpha[0]^2*a[4]-12*lambda*beta[0]*alpha[1]^2*alpha[0]*a[3]-2*w*alpha[0]*beta[0]+5*beta[0]*alpha[0]^4*a[4]+4*beta[0]*alpha[0]^3*a[3]+3*beta[0]*alpha[0]^2*a[2]-2*mu*w*alpha[1]^2)/G(xi)+((1/4)*(3*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[1]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^2*a[3]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]*a[2]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+3*mu*a[1]*alpha[0]*beta[0]*(1/2)+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]+3*beta[0]^2*alpha[0]*a[2]-k^2*a[1]*beta[0]^2+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^3*a[4]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^4*alpha[0]*a[4]+(4*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[5]*alpha[0]+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]-9*mu^2*alpha[1]^2*a[1]*(1/4)-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^4*a[3]-(1/4)*lambda*beta[0]^2*a[1]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*lambda*a[5]*alpha[0]-20*mu*lambda*beta[0]*alpha[1]^4*a[4]-7*mu*lambda*beta[0]*a[5]*alpha[1]^2+(2*mu*alpha[1]^3*a[2]-2*w*alpha[1]*beta[0]-4*lambda*beta[0]*alpha[1]^3*a[3]+8*mu*alpha[1]^3*alpha[0]*a[3]+mu*alpha[1]*a[5]*alpha[0]^2+(1/2)*mu*alpha[1]*alpha[0]*a[1]+20*mu*alpha[1]^3*alpha[0]^2*a[4]-4*mu*lambda*alpha[1]^5*a[4]-mu*lambda*alpha[1]^3*a[5]+20*beta[0]*alpha[1]*alpha[0]^3*a[4]+12*beta[0]*alpha[1]*alpha[0]^2*a[3]+6*beta[0]*alpha[1]*alpha[0]*a[2]-2*k^2*a[1]*alpha[1]*beta[0]-(1/2)*lambda*beta[0]*alpha[1]*a[1]-20*lambda*beta[0]*alpha[1]^3*alpha[0]*a[4]-2*lambda*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))-w*beta[0]^2)/G(xi)^2+(((lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^3*a[2]+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^5*a[4]+(2*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^3*a[5]+3*beta[0]^2*alpha[1]*a[2]+3*mu*beta[0]*alpha[1]*a[1]*(1/2)+8*mu*beta[0]*alpha[1]^3*a[3]-2*lambda*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]*alpha[0]*a[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*lambda*a[5]+30*beta[0]^2*alpha[1]*alpha[0]^2*a[4]+12*beta[0]^2*alpha[1]*alpha[0]*a[3]-6*mu^2*alpha[1]^3*a[5]-10*lambda*beta[0]^2*alpha[1]^3*a[4]+40*mu*beta[0]*alpha[1]^3*alpha[0]*a[4]+8*mu*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*a[3]+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*alpha[1]^4*a[4]+(6*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*a[5]*alpha[1]^2-10*lambda*beta[0]^3*alpha[1]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[1]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*a[2]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*a[1]*alpha[0]*beta[0]+12*mu*beta[0]^2*alpha[1]^2*a[3]+6*mu*beta[0]^2*a[5]*alpha[0]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[5]*alpha[0]+beta[0]^3*a[2]-14*mu^2*beta[0]*a[5]*alpha[1]^2+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*lambda*a[5]*alpha[1]^2+(12*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+mu*beta[0]^2*a[1]-lambda*beta[0]^3*a[5]+10*beta[0]^3*alpha[0]^2*a[4]+4*beta[0]^3*alpha[0]*a[3])/G(xi)^3+((4*beta[0]^3*alpha[1]*a[3]+(1/2)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]*a[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*a[3]+7*mu*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^5*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^3*a[5]+20*beta[0]^3*alpha[1]*alpha[0]*a[4]+20*mu*beta[0]^2*alpha[1]^3*a[4]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*alpha[0]*a[4]+(8*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))+20*mu*beta[0]^3*alpha[1]^2*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[0]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*alpha[0]*a[4]+4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[5]*alpha[0]+(17*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*beta[0]*a[5]*alpha[1]^2+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*beta[0]*alpha[1]^4*a[4]+beta[0]^4*a[3]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+(1/4)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[1]+3*mu*beta[0]^3*a[5]+5*beta[0]^4*alpha[0]*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*a[3]+3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[1]*(1/4))/G(xi)^4+(((lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^5*a[4]+2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^3*a[5]+5*beta[0]^4*alpha[1]*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^3*a[4])*(diff(G(xi), xi))+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*a[5]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*alpha[1]^2*a[4]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*alpha[1]^4*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*a[5]*alpha[1]^2+beta[0]^5*a[4])/G(xi)^5 = 0
> 

indets(G1)

{k, lambda, mu, w, xi, B[1], B[2], a[1], a[2], a[3], a[4], a[5], alpha[0], alpha[1], beta[0], G(xi), diff(G(xi), xi)}

 (2)

``

 (3)
> 

eq0 := 5*lambda^2*a[4]*alpha[0]*alpha[1]^4+lambda^2*a[3]*alpha[1]^4-10*lambda*a[4]*alpha[0]^3*alpha[1]^2+k^2*lambda*a[1]*alpha[1]^2-6*lambda*a[3]*alpha[0]^2*alpha[1]^2+a[4]*alpha[0]^5-k^2*a[1]*alpha[0]^2-3*lambda*a[2]*alpha[0]*alpha[1]^2+a[3]*alpha[0]^4+lambda*w*alpha[1]^2+a[2]*alpha[0]^3-w*alpha[0]^2 = 0
> 

``
> 

eq1 := lambda^2*a[4]*alpha[1]^5-10*lambda*a[4]*alpha[0]^2*alpha[1]^3-4*lambda*a[3]*alpha[0]*alpha[1]^3+5*a[4]*alpha[0]^4*alpha[1]-2*k^2*a[1]*alpha[0]*alpha[1]-lambda*a[2]*alpha[1]^3+4*a[3]*alpha[0]^3*alpha[1]+3*a[2]*alpha[0]^2*alpha[1]-2*w*alpha[0]*alpha[1] = 0
> 

eq2 := lambda^2*beta[0]*a[5]*alpha[1]^2+6*mu*alpha[1]^2*alpha[0]*a[2]-2*mu*k^2*a[1]*alpha[1]^2-(1/2)*mu*alpha[1]^2*lambda*a[1]+20*mu*alpha[1]^2*alpha[0]^3*a[4]+12*mu*alpha[1]^2*alpha[0]^2*a[3]-(1/2)*lambda*a[1]*alpha[0]*beta[0]-2*k^2*a[1]*alpha[0]*beta[0]-3*lambda*beta[0]*alpha[1]^2*a[2]-lambda*beta[0]*a[5]*alpha[0]^2+5*lambda^2*beta[0]*alpha[1]^4*a[4]-4*mu*lambda*alpha[1]^4*a[3]-2*mu*w*alpha[1]^2+5*beta[0]*alpha[0]^4*a[4]+4*beta[0]*alpha[0]^3*a[3]+3*beta[0]*alpha[0]^2*a[2]-2*w*alpha[0]*beta[0]-20*mu*lambda*alpha[1]^4*alpha[0]*a[4]-2*mu*alpha[1]^2*lambda*a[5]*alpha[0]-30*lambda*beta[0]*alpha[1]^2*alpha[0]^2*a[4]-12*lambda*beta[0]*alpha[1]^2*alpha[0]*a[3] = 0
> 

NULL
> 

eq3 := (1/4)*(3*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[1]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^3*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^2*a[3]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]+(4*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[5]*alpha[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]*a[2]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*lambda*a[5]*alpha[0]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]-9*mu^2*alpha[1]^2*a[1]*(1/4)-w*beta[0]^2+3*beta[0]^2*alpha[0]*a[2]-(1/4)*lambda*beta[0]^2*a[1]-k^2*a[1]*beta[0]^2+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2+3*mu*a[1]*alpha[0]*beta[0]*(1/2)+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^4*a[3]+3*mu*beta[0]*a[5]*alpha[0]^2-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+6*mu*beta[0]*alpha[1]^2*a[2]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4] = 0
> 

eq4 := 2*mu*alpha[1]^3*a[2]-2*w*alpha[1]*beta[0]-20*lambda*beta[0]*alpha[1]^3*alpha[0]*a[4]-2*lambda*beta[0]*a[5]*alpha[1]*alpha[0]-2*k^2*a[1]*alpha[1]*beta[0]+20*beta[0]*alpha[1]*alpha[0]^3*a[4]+12*beta[0]*alpha[1]*alpha[0]^2*a[3]+6*beta[0]*alpha[1]*alpha[0]*a[2]+8*mu*alpha[1]^3*alpha[0]*a[3]+mu*alpha[1]*a[5]*alpha[0]^2+(1/2)*mu*alpha[1]*alpha[0]*a[1]-4*lambda*beta[0]*alpha[1]^3*a[3]-lambda*alpha[1]^3*mu*a[5]-(1/2)*lambda*beta[0]*alpha[1]*a[1]+20*mu*alpha[1]^3*alpha[0]^2*a[4]-4*mu*lambda*alpha[1]^5*a[4] = 0
> 

eq5 := -6*mu^2*alpha[1]^3*a[5]+(2*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^3*a[5]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^3*a[2]+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^5*a[4]+3*beta[0]^2*alpha[1]*a[2]+40*mu*beta[0]*alpha[1]^3*alpha[0]*a[4]+8*mu*beta[0]*a[5]*alpha[1]*alpha[0]+30*beta[0]^2*alpha[1]*alpha[0]^2*a[4]+12*beta[0]^2*alpha[1]*alpha[0]*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]*alpha[0]*a[1]+8*mu*beta[0]*alpha[1]^3*a[3]+3*mu*beta[0]*alpha[1]*a[1]*(1/2)-10*lambda*beta[0]^2*alpha[1]^3*a[4]-2*lambda*beta[0]^2*a[5]*alpha[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*lambda*a[5] = 0
> 

eq6 := -14*mu^2*beta[0]*a[5]*alpha[1]^2+beta[0]^3*a[2]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*a[1]*alpha[0]*beta[0]+12*mu*beta[0]^2*alpha[1]^2*a[3]+6*mu*beta[0]^2*a[5]*alpha[0]-10*lambda*beta[0]^3*alpha[1]^2*a[4]+(6*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*a[5]*alpha[1]^2+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*a[2]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[0]^2+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*alpha[1]^4*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[1]+10*beta[0]^3*alpha[0]^2*a[4]+4*beta[0]^3*alpha[0]*a[3]-lambda*beta[0]^3*a[5]+mu*beta[0]^2*a[1]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[5]*alpha[0]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*lambda*a[5]*alpha[1]^2+(12*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]^2*alpha[1]^2*alpha[0]*a[4] = 0
> 

eq7 := 4*beta[0]^3*alpha[1]*a[3]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*alpha[0]*a[4]+(8*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[1]*alpha[0]+20*beta[0]^3*alpha[1]*alpha[0]*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*a[3]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*mu*a[5]+(1/2)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]*a[1]+20*mu*beta[0]^2*alpha[1]^3*a[4]+7*mu*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^5*a[4] = 0
> 

eq8 := 4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[5]*alpha[0]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*alpha[0]*a[4]+beta[0]^4*a[3]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[0]+20*mu*beta[0]^3*alpha[1]^2*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*a[3]+3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[1]*(1/4)+5*beta[0]^4*alpha[0]*a[4]+3*mu*beta[0]^3*a[5]+(1/4)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[1]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+(17*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*mu*a[5]*alpha[1]^2+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*mu*alpha[1]^4*a[4] = 0
> 

eq9 := (10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^3*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[1]+5*beta[0]^4*alpha[1]*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^5*a[4]+2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^3*a[5] = 0
> 

eq10 := (2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*a[5]+beta[0]^5*a[4]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*alpha[1]^4*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*a[5]*alpha[1]^2+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*alpha[1]^2*a[4] = 0
 
> 

with(LargeExpressions)
> 

COEFFS := solve({eq0, eq1, eq10, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {w, a[1], a[2], alpha[0], alpha[1], beta[0]})

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Verifying Exact Solutions of a Nonlinear...

salim-barzani 1640 Maple 2024
ode radical differential-equations
May 02 2025
1 1

Substituting the solutions into the ODE doesn't yield zero, despite the code appearing correct—suggesting either complexity, symbolic limits, or an implementation issue.

 

 

17-ode.mw

 

also in this ode why solution is like this how i can fixed this too

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

ode := diff(G(xi), xi) = sqrt(C*G(xi)^4+B*G(xi)^2+A)

diff(G(xi), xi) = (C*G(xi)^4+B*G(xi)^2+A)^(1/2)

 (2)
> 

dsolve(ode, G(xi))

xi-Intat(1/(C*_a^4+B*_a^2+A)^(1/2), _a = G(xi))+c__1 = 0

 (3)
 

NULL

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Can Maple Handle Fuzzy Derivatives and P...

salim-barzani 1640 Maple
derivative plotting
May 02 2025
0 1

This question is actually on behalf of a colleague who works with fuzzy mathematics. He typically computes things like fuzzy derivatives by hand, including for specific functions such as "function 14" (though I'm not familiar with the specific form of that function). He’s interested in whether Maple can symbolically and numerically handle tasks in fuzzy calculus — especially taking and plotting fuzzy derivatives.

I’m not experienced with fuzzy systems myself, but I’d like to recommend Maple to him if it supports these features. So my main questions are:

  1. Can Maple compute and plot fuzzy functions and their derivatives?

  2. Does Maple have built-in support or packages for fuzzy arithmetic or fuzzy calculus?

  3. If not natively, is there a workaround or external library that integrates with Maple to do this?

I’d really appreciate any insights or examples. It seems like a missed opportunity for my friend to be doing all this manually when such software might already handle it.

Thanks in advance!

 

Difficulty Collecting Coefficients...

salim-barzani 1640 Maple 2024
substitution differential-equations coefficients
May 02 2025
1 3

I'm trying to collect all terms involving the expression diff(G(xi), xi)/G(xi) in a symbolic equation using . While it's straightforward to do this by hand, I want to automate it in code — ideally by extracting the coefficient of this entire expression directly. However, when I use collect, Maple treats diff(G(xi), xi) and G(xi) separately, and I can't seem to group terms properly by the full ratio diff(G(xi), xi)/G(xi).

Is there a clean way or built-in Maple function to automatically collect or isolate the coefficient of diff(G(xi), xi)/G(xi) as a whole, without having to manually substitute or restructure the expression?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

L := (-6*f^3*g*a[2]+6*f*g^3*a[2]+6*f*g*a[2]^2)*(diff(G(xi), xi))^4/G(xi)^4+(f*g^3*(10*lambda*a[2]+2*a[1])-f^3*g*(10*lambda*a[2]+2*a[1])+12*f*g*a[1]*a[2])*(diff(G(xi), xi))^3/G(xi)^3+(f*g^3*(2*a[2]*lambda^2+3*lambda*a[1]+10*mu*a[2]+2*a[2]*(lambda^2-mu))-4*f*p*a[2]-6*k*l*a[2]-f^3*g*(2*a[2]*lambda^2+3*lambda*a[1]+10*mu*a[2]+2*a[2]*(lambda^2-mu))+6*f*g*(2*a[0]*a[2]+a[1]^2))*(diff(G(xi), xi))^2/G(xi)^2+(f*g^3*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*lambda*a[2]*mu)-4*f*p*a[1]-6*k*l*a[1]-f^3*g*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*lambda*a[2]*mu)+12*f*g*a[0]*a[1])*(diff(G(xi), xi))/G(xi)+f*g^3*(lambda*mu*a[1]+2*mu^2*a[2])-4*f*p*a[0]-6*k*l*a[0]-f^3*g*(lambda*mu*a[1]+2*mu^2*a[2])+6*f*g*a[0]^2 = 0

(-6*f^3*g*a[2]+6*f*g^3*a[2]+6*f*g*a[2]^2)*(diff(G(xi), xi))^4/G(xi)^4+(f*g^3*(10*lambda*a[2]+2*a[1])-f^3*g*(10*lambda*a[2]+2*a[1])+12*f*g*a[1]*a[2])*(diff(G(xi), xi))^3/G(xi)^3+(f*g^3*(3*lambda*a[1]+2*a[2]*lambda^2+10*mu*a[2]+2*a[2]*(lambda^2-mu))-4*f*p*a[2]-6*k*l*a[2]-f^3*g*(3*lambda*a[1]+2*a[2]*lambda^2+10*mu*a[2]+2*a[2]*(lambda^2-mu))+6*f*g*(2*a[0]*a[2]+a[1]^2))*(diff(G(xi), xi))^2/G(xi)^2+(f*g^3*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*a[2]*lambda*mu)-4*f*p*a[1]-6*k*l*a[1]-f^3*g*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*a[2]*lambda*mu)+12*f*g*a[0]*a[1])*(diff(G(xi), xi))/G(xi)+f*g^3*(lambda*mu*a[1]+2*mu^2*a[2])-4*f*p*a[0]-6*k*l*a[0]-f^3*g*(lambda*mu*a[1]+2*mu^2*a[2])+6*f*g*a[0]^2 = 0

 (2)

``

 (3)
> 

collect(%, {1/(diff(G(xi), xi)), G(xi)})

(-6*f^3*g*a[2]+6*f*g^3*a[2]+6*f*g*a[2]^2)*(diff(G(xi), xi))^4/G(xi)^4+(f*g^3*(10*lambda*a[2]+2*a[1])-f^3*g*(10*lambda*a[2]+2*a[1])+12*f*g*a[1]*a[2])*(diff(G(xi), xi))^3/G(xi)^3+(f*g^3*(3*lambda*a[1]+2*a[2]*lambda^2+10*mu*a[2]+2*a[2]*(lambda^2-mu))-4*f*p*a[2]-6*k*l*a[2]-f^3*g*(3*lambda*a[1]+2*a[2]*lambda^2+10*mu*a[2]+2*a[2]*(lambda^2-mu))+6*f*g*(2*a[0]*a[2]+a[1]^2))*(diff(G(xi), xi))^2/G(xi)^2+(f*g^3*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*a[2]*lambda*mu)-4*f*p*a[1]-6*k*l*a[1]-f^3*g*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*a[2]*lambda*mu)+12*f*g*a[0]*a[1])*(diff(G(xi), xi))/G(xi)+f*g^3*(lambda*mu*a[1]+2*mu^2*a[2])-4*f*p*a[0]-6*k*l*a[0]-f^3*g*(lambda*mu*a[1]+2*mu^2*a[2])+6*f*g*a[0]^2 = 0

 (4)
> 

L1 := %
> 

num := numer(lhs(L)); num := expand(num); num_collected := collect(num, [1/(diff(G(xi), xi)), G(xi)]); eqs := [seq(coeff(num_collected, {1/(diff(G(xi), xi)), G(xi)}, i) = 0, i = 0 .. 8)]

[(-6*f^3*g*a[2]+6*f*g^3*a[2]+6*f*g*a[2]^2)*(diff(G(xi), xi))^4+(-10*f^3*g*lambda*a[2]+10*f*g^3*lambda*a[2]-2*f^3*g*a[1]+2*f*g^3*a[1]+12*f*g*a[1]*a[2])*G(xi)*(diff(G(xi), xi))^3+(-4*f^3*g*lambda^2*a[2]+4*f*g^3*lambda^2*a[2]-3*f^3*g*lambda*a[1]-8*f^3*g*mu*a[2]+3*f*g^3*lambda*a[1]+8*f*g^3*mu*a[2]+12*f*g*a[0]*a[2]+6*f*g*a[1]^2-4*f*p*a[2]-6*k*l*a[2])*G(xi)^2*(diff(G(xi), xi))^2+(-f^3*g*lambda^2*a[1]-6*f^3*g*lambda*mu*a[2]+f*g^3*lambda^2*a[1]+6*f*g^3*lambda*mu*a[2]-2*f^3*g*mu*a[1]+2*f*g^3*mu*a[1]+12*f*g*a[0]*a[1]-4*f*p*a[1]-6*k*l*a[1])*G(xi)^3*(diff(G(xi), xi))+(-f^3*g*lambda*mu*a[1]-2*f^3*g*mu^2*a[2]+f*g^3*lambda*mu*a[1]+2*f*g^3*mu^2*a[2]+6*f*g*a[0]^2-4*f*p*a[0]-6*k*l*a[0])*G(xi)^4 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0]

 (5)

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