For my thesis I need to solve many differential equations non linear, second order by using maple....

For example figure adjoint

using dsolve command, the solutions are very extensives and very bad.

 

there is a suggest for to solve the differential equations by using maple?

 

there is some methods in maple to find the aproximate solution?

 

thanks

It would be helpful if you could include the Maple code rather than leaving us to transpose it. I figured it was something like:

(
 -2*exp( -3*f(t))*Diff(f(t),t)^2
 +2*exp( -3*f(t))*Diff(f(t),t,t)
 +3*exp( -2*f(t))*Diff(f(t),t)^4
 +2*sqrt( (-1+ exp(f(t))*(Diff(f(t),t)^2 ))*exp(-4*f(t))  )
 *sqrt( -(exp(-f(t)) - Diff(f(t),t)^2*exp(-f(t)) ))
 *exp(-f(t))
)/
(
 (exp(-f(t)) - (Diff(f(t),t))^2 )
 *sqrt( (-1 + Diff(f(t),t)^2 )*exp(-4*f(t)) )
 *sqrt(-(exp(f(t)) - Diff(f(t),t)^2 ) * exp(-3*f(t))  )
)
= 0;

Which could easily be wrong.

From there I would suggest manually simplifying the expression (simple things like [imath]\sqrt{a}\sqrt{b}=\sqrt{ab}[/imath]) and maybe replacing the [imath]e^{-n f(t))}[/imath] with a new function, then letting Maple solve the pair of them as a system of equations.

you say this?

if exp(-f(t))=c(t) then

 

a := (-2*c(t)^3*(Diff(f(t), t))^2
+2*c(t)^3*(Diff(f(t), t, t))
+3*c(t)^2*(Diff(f(t), t))^4
+2*sqrt((-1+c(t)^(-1)*(Diff(f(t), t))^2)*c(t)^4*(-c(t))
+(Diff(f(t), t))^2*c(t)))*c(t)/((c(t)
-(Diff(f(t), t))^2)*sqrt(((-1+(Diff(f(t), t))^2)*c(t)^4)
*(-(c(t))-(Diff(f(t), t))^2)*c(t)^3)) = 0;

 

but

    dsolve(a,c(t)); maple says error... 

    dsolve(a,f(t)); maple shows a bas solution and extensive... 

 

sorry for not understanding. I'm starting to use maple