Question

solve this nonlinear differential equation:
xy''=y'+(y'^3)
I have the solution but it does not match up with wolfram and please do this step by step!

Answer 1

hint is that this is a y dependent equation so u have to let u=y' to reduce it to first order and then solve.

Answer 2

\[\left\{y[x]\to -i e^{-C[1]} \sqrt{-1+e^{2 C[1]} x^2}+C[2]\right\} \],\[\left\{y[x]\to i e^{-C[1]} \sqrt{-1+e^{2 C[1]} x^2}+C[2]\right\} \]

Answer 3

thats the solution from wolfram...how did they get the imaginary and e terms?

Answer 4

my answer includes everything except those terms

Answer 5

The solutions came from Mathematica 8 processing the following statement:\[\text{DSolve}[x y\text{''}[x]\text{==}y'[x]+(y'[x]{}^{\wedge}3),y[x],x] \]I have no idea how they came up with their answer.

Answer 6

sir my question is to solve the problem step by step i had already mentioned i have the solution i know the answer and i don't need that i need the process to get to that answer