Hi,I need to solve this equationf''(x) + a*f'(x)^2 +b* f'(x)=0.Any clue?Thanks a lot,Isatis
First to simplify the notation I will use $\displaystyle f(x)=y$
While harder for this problem, in general, any 2nd order ODE can be reduced to a first order ODE by the substitution $\displaystyle u=y'$
By the chain rule we get
$\displaystyle \frac{d}{dx}y'=\frac{du}{dy}\underbrace{\frac{dy}{ dx}}_{y'=u} \iff y''=u\frac{du}{dy}$
This will change $\displaystyle y$ from the dependent variable to the independent variable of a new function u.
This gives
$\displaystyle u\frac{du}{dy}+au^2+bu=0 \iff \frac{du}{dy}+au=-b$
This can be solved by an integrating factor.