not able to find solution for a system of differential equation

Questions
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1

Hi,
Mathematica 10 not giving any output to the following system of equation and returns the input as output Help required

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2

these are nonlinear coupled second order ODE. Most non-linear ode’s do not have closed form solution. (the ticks on your screen shot look strange. But may be this is copy/paste. It is better to post plain text code here. not screen shot assuming you want someone to copy and try what you have there. You might want to try numerical solution.

3

Here is the equation I typed

DSolve[{((x''[t])/(2*x[t]))+((y[t])/(4*(x[t])^3))+(((x'[t])^2)/(4*(x[t])^2))-
                                       ((y''[t])/(2*y[t]))-(((y'[t])^2)/(4*(y[t]^2)))==0, 
   ((3*x''[t])/(2*x[t]))-(((x'[t])^2)/(4*(x[t])^2))-((y[t])/(2*(x[t])^3))+((y''[t])/(2*y[t]))- 
  ((3*((y'[t])^2))/(4*(y[t]^2)))+((2)/(x[t]*y[t]))-((x'[t]*y'[t])/(x[t]*y[t]))==0},{x,y},t]
4

It would be better to put your code in a “code sample” block, using the first icon under “reply to this discussion”. Putting code in as text can result in errors. I speak from experience.

5

Dsolve[{((x’‘[t])/(2x[t]))+((y[t])/(4(x[t])^3))+(((x’[t])^2)/(4*(x[t])^2))-((y’‘[t])/(2y[t]))-(((y’[t])^2)/(4(y[t]^2)))==0,((3x’'[t])/(2x[t]))-(((x’[t])^2)/(4*(x[t])^2))-((y[t])/(2*(x[t])^3))+((y’‘[t])/(2y[t]))-((3((y’[t])^2))/(4*(y[t]^2)))+((2)/(x[t]*y[t]))-((x’[t]*y’[t])/(x[t]*y[t]))==0},{x,y},t]

6

Looks like Mathematica can’t solve it symbolically. Complex differential equations frequently don’t have symbolic solutions.