Please help me to solve this problem:
Differential equation $y''+p(x)y=0$ has nonzero solution $f(x)$. Find the equation for function $z(x)=\frac{f'(x)}{f(x)}$.
My ideas:
I only see that $z(x) = \ln(y(x))'$. I tried to express this function in terms of $p(x)$, but failed.
Can you please help me with the problem? Thanks a lot!
Update: After the hint given by A.Γ. it was trivial to show that required equation is $z'+z^2+p=0$. Thanks a lot for your help, A.Γ.!
Hint: If $f'=z\cdot f$ then $f''=z'\cdot f+z\cdot f'=z'\cdot f+z^2\cdot f$ then $$ 0=f''+p\cdot f=\ldots $$