-y'(x) \left(\frac{2 f'(x)}{f(x)}-\frac{g'(x)}{g(x)}+\frac{g''(x)}{g'(x)}\right)+y(x) \left(-\frac{f''(x)}{f(x)}+\frac{f'(x) \left(\frac{2 f'(x)}{f(x)}-\frac{g'(x)}{g(x)}+\frac{g''(x)}{g'(x)}\right)}{f(x)}-\frac{v^2 g'(x)^2}{g(x)^2}+g'(x)^2\right)+y''(x)=0