Thread: Is this non-linear equation solvable?

Hi,I need to solve this equationf''(x) + a*f'(x)^2 +b* f'(x)=0.Any clue?Thanks a lot,Isatis

Hey isatis55.

Consider u = f'(x), then:

du/dx + a*u^2 + b*u = 0 or
du/dx = -a*u^2 - b*u which is separable.

Originally Posted by isatis55

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

While harder for this problem, in general, any 2nd order ODE can be reduced to a first order ODE by the substitution

By the chain rule we get



This will change from the dependent variable to the independent variable of a new function u.

This gives



This can be solved by an integrating factor.