$$y=A e^x+B e^{-2 x}$$ satisfies which of the following differential equations?

If $$y=\sin (\sin x)$$ and $$y^{\prime \prime}+f(x) \cdot y^{\prime}+g(x) \cdot y=0$$, then $$f(x) \cdot g(x)$$ is equal to

The equation of the curve passing through the point $$\left(0, \frac{\pi}{4}\right)$$ and satisfying the differential equation $$\left(e^x \tan y\right) d x\left.+\left(1+e^x\right) \sec ^2 y\right) d y=0$$ is given by

The solution of the differential equation $$2x\left(\frac{dy}{dx}\right)-y=4$$ represents a family of