# Second order nonlinear differential equation

1. Jan 15, 2009

### vashistha

hi,
i am facing problem in solving the following differential equation. help me.
y''+ayy'+b=0, where y is a function of x, 'a' & 'b' are constants.

i have tried substituting y'=u, which implies u'=u*dy/dx, these substitution change the equation to first order but i found no way ahead.

Last edited: Jan 15, 2009
2. Jan 15, 2009

### Mute

To do this, recognize that you can reverse the chain rule on the term yy' to get (y^2/2)'. You can then directly integrate the equation to get a first order equation. (Don't forget the arbitrary constant that comes from doing so).

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