-\frac{f'(x) y'(x)}{f(x)}+y(x) \left(-\frac{f''(x)}{2 f(x)}+\frac{3 f'(x)^2}{4 f(x)^2}+\frac{\left(\frac{1}{4}-v^2\right) g'(x)^2}{g(x)^2}+g'(x)^2+\frac{g^3(x)}{2 g'(x)}-\frac{3 g''(x)^2}{4 g'(x)^2}\right)+y''(x)=0