How to Solve This Differential Equation Analytically?

[SantiagoCR]

TL;DR

calculate integral of a differential equation

Hello,

can someone help me to solve the following differential equation analitically:

$$\frac{2 y''}{y'} - \frac{y'}{y} = \frac{x'}{x}$$

where $y = y(t)$ and $x = x(t)$

br

Santiago

 

[renormalize]

Hint: $$\frac{2y''}{y'}=2\log\left(y'\right)',\quad\frac{y'}{y}=\log\left(y\right)',\quad\frac{x'}{x}=\log\left(x\right)'$$

 

[SantiagoCR]

Hint: $$\frac{2y''}{y'}=2\log\left(y'\right)',\quad\frac{y'}{y}=\log\left(y\right)',\quad\frac{x'}{x}=\log\left(x\right)'$$

cool, thank you very much!