I want to solve the following differential equation:
$$y''=e^{x}(y')^2$$
then I substitute $y''=u'u$,$y'=u$ so I got:
$u'=e^{x}u$
But then I don't know how to solve this, may be separate variables or what can be done, Can you help me to solve this please? (In fact I don't know have to solve non-linear differential equations but the substitution was like a hint, so If can you help to clarify the substitution I appreciate it :) )