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

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- November 2nd 2012, 02:38 AMisatis55Is 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

- November 2nd 2012, 03:20 AMchiroRe: Is this non-linear equation solvable?
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. - November 2nd 2012, 05:42 AMTheEmptySetRe: Is this non-linear equation solvable?
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.