Now let so that so that
where
where
where
.
Being a physicist, I rarely encountered a nonlinear ODE. Accordingly, I have no idea how to solve the following equation:
y(x) * y''(x) + y'(x)^2 = 0
with y(0) = C, y'(x) = 0.
It's fairly obvious that one of the solutions is y(x) = C. But, how to find the other solution? I don't even know enough about general ODE to know is there another solution being the equation is not linear?
Thanks
*** I now see I should've posted this under the Differential Equations. Sorry! ***
Another way: the function
satisfies:
that is, it is homogeneous. Using the substitution:
the new equation is a first order equation.
Fernando Revilla