## 100 Reputation

6 years, 155 days

## exact solution of differential equation...

Maple

Hello guys,

I want to find exact form of a(t) in following differential equation:

-diff(a(t), t)^2*_C1*6^(-1/(-1 + 2*alpha))*((diff(a(t), t, t)*a(t) + diff(a(t), t)^2)/a(t)^2)^(-1/(-1 + 2*alpha))/(4*(diff(a(t), t, t)*a(t) + diff(a(t), t)^2)*(-1/2 + alpha)) = (6*diff(a(t), t, t)*a(t)^2*alpha + 6*a(t)*diff(a(t), t)^2*alpha + k^2)/a(t)^3

## plot two depending equation in maple...

Maple

Hello guys,

I want to plot two functions such as x(t) and y(t) in a unique diagram as a function of each other. In a routine way, one needs to solve one of these functions as t and then input its results in others. for example, solving x(t) to find t and then input this t(x) into y(t) to have y(x). but here problem is that I cannot solve x(t) to find t and so this routine solution is not accelssible.

x(t):=1 + (3*n*(v - 1)^2*A*(t^v)^2*(1 + alpha*(v - 1)^2*A^2*(t^v)^2*ln(m^2*t^2/((v - 1)^2*A^2*(t^v)^2))/(3*n^2*m^2*t^2) + A^2*beta*(v - 1)^2*(t^v)^2/(3*n^2*m^2*t^2))*((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))*(1 + ((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))))/(2*v^2*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)) - (3*n^2*(v - 1)^2*A^2*(t^v)^2*(1 + alpha*(v - 1)^2*A^2*(t^v)^2*ln(m^2*t^2/((v - 1)^2*A^2*(t^v)^2))/(3*n^2*m^2*t^2) + A^2*beta*(v - 1)^2*(t^v)^2/(3*n^2*m^2*t^2))*(((4*A^2*alpha*t^v*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + 4*A^2*alpha*t^v*(v - 1)^2*(2 - 2*v)/t + 6*t^(-v + 2)*(-v + 2)*m^2*n^2/t + 4*t^v*v*(beta - alpha/2)*A^2*(v - 1)^2/t)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) + (4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*n^2*(v - 1)^2*A^2*t^(2*v)/(sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2)*v*t) - 3*n*A*(2*A^2*alpha*t^(2*v)*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + A^2*alpha*t^(2*v)*(v - 1)^2*(2 - 2*v)/t + 2*A^2*beta*(v - 1)^2*t^(2*v)*v/t + 6*n^2*m^2*t))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)) - (((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))*(2*A^2*alpha*t^(2*v)*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + A^2*alpha*t^(2*v)*(v - 1)^2*(2 - 2*v)/t + 2*A^2*beta*(v - 1)^2*t^(2*v)*v/t + 6*n^2*m^2*t))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)^2)))/(2*v^2):

y(t):=1 + ((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)) - (((4*A^2*alpha*t^v*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + 4*A^2*alpha*t^v*(v - 1)^2*(2 - 2*v)/t + 6*t^(-v + 2)*(-v + 2)*m^2*n^2/t + 4*t^v*v*(beta - alpha/2)*A^2*(v - 1)^2/t)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) + (4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*n^2*(v - 1)^2*A^2*t^(2*v)/(sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2)*v*t) - 3*n*A*(2*A^2*alpha*t^(2*v)*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + A^2*alpha*t^(2*v)*(v - 1)^2*(2 - 2*v)/t + 2*A^2*beta*(v - 1)^2*t^(2*v)*v/t + 6*n^2*m^2*t))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)) - (((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2))*(2*A^2*alpha*t^(2*v)*v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2))/t + A^2*alpha*t^(2*v)*(v - 1)^2*(2 - 2*v)/t + 2*A^2*beta*(v - 1)^2*t^(2*v)*v/t + 6*n^2*m^2*t))/(3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)^2))*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)/((4*A^2*alpha*t^v*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + 6*t^(-v + 2)*m^2*n^2 + 4*t^v*(beta - alpha/2)*A^2*(v - 1)^2)*sqrt(n^2*(v - 1)^2*A^2*t^(2*v)/v^2) - 3*n*A*(A^2*alpha*t^(2*v)*(v - 1)^2*ln(m^2*t^(2 - 2*v)/((v - 1)^2*A^2)) + A^2*beta*(v - 1)^2*t^(2*v) + 3*n^2*m^2*t^2)):

there are x(t) and y(t). I want to plot y as x, not t. so please help me.

with best

## how product Riemann tensor to itself...

Maple

hi guys,

I have a question about computing reimann tensor in general relativity.

suppose we have schwarzschidl metric: ds^2=-(1-2*m*(r^-1))*dt^2+(1-2*m*(r^-1))^(-1)*dr^2+r^2*dtheta^2+r^2*sin^2(theta)*dphi^2.

I want to caclulate R[alpha,beta,mu,nu]*R[~alpha,~beta,~mu,~nu] where R[alpha,beta,mu,nu] is covariant form of Reimann tensor and also R[~alpha,~beta,~mu,~nu] is the contravariant form of Riemann tensor. I also want to calculate same thing for weyl tensor. please guide me.

with best regards.

## Phase Plane between two functions...

Maple 2018

hello guys,

I want to plot the phase plane between F and m when:

F := 736*R^4/sqrt((-1380*Pi*R*m(r)^3 + 368*R^4 - 1587*m(r)^2*R^2 + 1280*m(r)^2*a)^2);
R := X^(1/3)/(-l^2 + 4*a) - 3*l^2*m(r)^2/X^(1/3);
X := m(r)*l^2*(sqrt((27*l^2*m(r)^4 - 16*a^2*l^2 + 64*a^3)/(-l^2 + 4*a)) + 4*a)*(-l^2 + 4*a)^2;

and

m := (l^2*r^2 + r^4 + a*l^2)/(2*l^2*r)

for positive constant a and l

thanks

## solve non-linear differential equation...

Maple 2018

Hi guys

I want to solve the following non-linear differential equation but by using dsolve(), the computer cannot solve it, so please guide me.

Q:=2*diff(a(t), t, t)*a(t)^3 - 3*diff(a(t), t)^4 + diff(a(t), t)^2*a(t)^2

with the best regards

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