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salim-barzani

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1 years, 74 days
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These are questions asked by salim-barzani

How can we generate solutions for an ODE...

salim-barzani 1640 Maple 2024
ode parameters dsolve
October 26 2024
2 4

In many papers, I've noticed that the solution to an ODE (ordinary differential equation) often emerges directly when there's only a single function involved. My question is: is there a way to generate solutions to an ODE by producing specific parameters?

 

> 

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)
> 

NULL
> 

S := diff(F(xi), xi) = sqrt(P*F(xi)^4+Q*F(xi)^2+R)

diff(F(xi), xi) = (P*F(xi)^4+Q*F(xi)^2+R)^(1/2)

 (2)
> 

S1 := dsolve(S, F(xi))

xi-Intat(1/(P*_a^4+Q*_a^2+R)^(1/2), _a = F(xi))+c__1 = 0

 (3)
> 

S2 := (diff(F(xi), xi))^2 = P*F(xi)^4+Q*F(xi)^2+R

(diff(F(xi), xi))^2 = P*F(xi)^4+Q*F(xi)^2+R

 (4)
> 

S3 := dsolve(S2, F(xi))

F(xi) = -(1/2)*(-2*P*(Q+(-4*P*R+Q^2)^(1/2)))^(1/2)/P, F(xi) = (1/2)*(-2*P*(Q+(-4*P*R+Q^2)^(1/2)))^(1/2)/P, F(xi) = -(1/2)*2^(1/2)*(P*(-Q+(-4*P*R+Q^2)^(1/2)))^(1/2)/P, F(xi) = (1/2)*2^(1/2)*(P*(-Q+(-4*P*R+Q^2)^(1/2)))^(1/2)/P, F(xi) = JacobiSN((1/2)*(2*(-4*P*R+Q^2)^(1/2)-2*Q)^(1/2)*xi+c__1, (-2*(Q*(-4*P*R+Q^2)^(1/2)+2*R*P-Q^2)*R*P)^(1/2)/(Q*(-4*P*R+Q^2)^(1/2)+2*R*P-Q^2))*R*2^(1/2)/(R*(-Q+(-4*P*R+Q^2)^(1/2)))^(1/2)

 (5)
 

NULL

Download get_all_solution_of_ode_by_generation.mw

How i can give assumption to a ODE equat...

salim-barzani 1640 Maple 2024
ode assumptions dsolve
October 25 2024
2 20

i can do one by one for all case but i am intrested for this idea how we can do that for each equation automatically calculate all case without use one by one case ?
there is any other shorter way for get solution of this mw

all_case.mw

> 

restart
> 

with(PDEtools)
> 

undeclare(prime)

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

 (1)
> 

with(DEtools)
> 

S := diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

 (2)
> 

S1 := dsolve(S, G(xi))

G(xi) = -(1/2)*A-(1/2)*tanh((1/2)*(A^2-4*B)^(1/2)*(c__1+xi))*(A^2-4*B)^(1/2)

 (3)
> 

A := 0

0

 (4)
> 

S

diff(G(xi), xi) = G(xi)^2+B

 (5)
> 

dsolve(S, G(xi))

G(xi) = tan(B^(1/2)*(c__1+xi))*B^(1/2)

 (6)
> 

restart
> 

NULL
> 

with(PDEtools)
> 

undeclare(prime)

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

 (7)
> 

with(DEtools)
> 

S := diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

 (8)
> 

B := 0

0

 (9)
> 

S1 := dsolve(S, G(xi))

G(xi) = A/(-1+exp(-A*xi)*c__1*A)

 (10)
> 

NULL
> 

restart
> 

NULL
> 

with(PDEtools)
> 

undeclare(prime)

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

 (11)
> 

with(DEtools)
> 

S := diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

diff(G(xi), xi) = G(xi)^2+A*G(xi)+B

 (12)
> 

B := 0; A := 0

0

  

0

 (13)
> 

S1 := dsolve(S, G(xi))

G(xi) = 1/(-xi+c__1)

 (14)
 

NULL

Download find_all_case_solution_of_ode_.mw

Why equation not run ?...

salim-barzani 1640 Maple 2024
syntax procedure 2dmath
October 23 2024
1 1

i did all the time like that and don't have any issue but i don't know why not take derivative by x and t have a problem when i remove t is ok but when i take duble derivative by x and t not run and did't give me error too what is problem with this?

> 

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)
> 

tr := {t = tau, x = xi+delta*(tau+1), u(x, t) = U(xi)*exp(I*(-kx+w*(t+1)))}

{t = tau, x = xi+delta*(tau+1), u(x, t) = U(xi)*exp(I*(-kx+w*(t+1)))}

 (2)
> 

pde := I*(diff(u(x, t), t))+alpha*(diff(u(x, t), `$`(x, 2)))+beta*(diff(u(x, t), x, t))+gamma*u(x, t)*V(xi) = 0
 

NULL

Download non_sense.mw

why not do cancelation at 2024 version...

salim-barzani 1640 Maple 2024
radical simplification automatic-simplification
October 21 2024
0 1

every time i have a small problem 2  why not cancel number 2 in denominator , i don't want see a number with fraction like 1/3  3/4 how i fix this

> 

restart
> 

K := (1/2)*sqrt(2*sqrt(2)*sqrt(lambda*a[5]/a[4])+2*sqrt(-2*a[5]/a[4])*(B[1]*sqrt(-lambda)*sinh(sigma)+B[2]*sqrt(-lambda)*cosh(sigma))/(B[1]*cosh(sigma)+B[2]*sinh(sigma)+mu/lambda)+2*sqrt(-(2*(lambda^2*B[1]^2*a[5]-lambda^2*B[2]^2*a[5]-mu^2*a[5]))/(lambda*a[4]))/(B[1]*cosh(sigma)+B[2]*sinh(sigma)+mu/lambda))*e^(i*psi(x, t))

Warning, if e is meant to be the exponential e, use command/symbol completion or palettes to enter this special symbol, or use the exp function

  

(1/2)*(2*2^(1/2)*(lambda*a[5]/a[4])^(1/2)+2*(-2*a[5]/a[4])^(1/2)*(B[1]*(-lambda)^(1/2)*sinh(sigma)+B[2]*(-lambda)^(1/2)*cosh(sigma))/(B[1]*cosh(sigma)+B[2]*sinh(sigma)+mu/lambda)+2*(-2*(lambda^2*B[1]^2*a[5]-lambda^2*B[2]^2*a[5]-mu^2*a[5])/(lambda*a[4]))^(1/2)/(B[1]*cosh(sigma)+B[2]*sinh(sigma)+mu/lambda))^(1/2)*e^(i*psi(x, t))

 (1)
> 

B[1] := 0; mu := 0

0

  

0

 (2)
> 

simplify(eval(K))

(1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t))

 (3)
> 

simplify((1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t)), 'trig')

(1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t))

 (4)
> 

simplify((1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t)))

(1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t))

 (5)
> 

simplify((1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t)), 'constant')

(1/2)*2^(3/4)*(((coth(sigma)*(-lambda)^(1/2)*(-a[5]/a[4])^(1/2)+(lambda*a[5]/a[4])^(1/2))*B[2]+csch(sigma)*(lambda*a[5]*B[2]^2/a[4])^(1/2))/B[2])^(1/2)*e^(i*psi(x, t))

 (6)
 

 

 

NULL

Download cancelation.mw

How change trigonometry to shorter trigo...

salim-barzani 1640 Maple 2021
simplification trig
October 20 2024
2 7

How we can change identity like 1/sin(x)=csc(x) or 1/cos(x)=sec(x) sometime our function is beger than this and radical come in how i can do thus simplification?

> 

restart
> 

M := sin(x)/cos(x)

sin(x)/cos(x)

 (1)
> 

convert(M, trig)

sin(x)/cos(x)

 (2)
> 

tan(x)

tan(x)

 (3)
> 

simplify(M)

sin(x)/cos(x)

 (4)
> 

K := 1/sinh(x)

1/sinh(x)

 (5)
> 

simplify(convert(K, trig))

1/sinh(x)

 (6)
> 

csch(x)

csch(x)

 (7)
> 

Q := sqrt(beta[0]/(B[1]*cosh(xi*sqrt(-lambda))))

(beta[0]/(B[1]*cosh(xi*(-lambda)^(1/2))))^(1/2)

 (8)

(beta[0]/(B[1]*cosh(xi*(-lambda)^(1/2))))^(1/2)

 (9)
> 

simplify((beta[0]/(B[1]*cosh(xi*(-lambda)^(1/2))))^(1/2), 'trig')

(beta[0]/(B[1]*cosh(xi*(-lambda)^(1/2))))^(1/2)

 (10)
 

NULL

Download identity_change.mw

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