Question: Verify a solution of a nonlinear ODE


I am trying to verify the general solution to the nonlinear ode

diff(y(x), x, x) = 1/y(x) - x*diff(y(x), x)/y(x)^2  (1)

Maple says this expression is invalid when I try to enter it using the button.  I can copy and paste this expression into maple, however, and it works fine.


I take the second derivative of the general solution, then use the solve(solution, diff(y(x),x,x) command to try to put the second derivative in the form of (1).  The result from this command does not match the original ode, but the odetest( ) funtion returns a value of zero. 


How do I "manually" verify this solution with maple?  I am investigating a certain type of equation, and my solution technique so far involves rewriting the equation into a different form (nonlinear PDE) and then solving the PDE.  I am building up maple skills to eventually do that.


For your reference, this equation is from a maple help page:


I would really appreciate some help with this,

Steve :)

Please Wait...