If the differential equation having $y=A e^x+B \sin x$ as its general solution is $f(x) \frac{d^2 y}{d x^2}+g(x) \frac{d y}{d x}+h(x) y=0$, then $f(x)+g(x)+h(x)=$

The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2 x$ and eccentricity is $\sqrt{3}$ is

The general solution of the differential equation $\left(x^3-y^3\right) d x=\left(x^2 y-x y^2\right) d y$ is

The substitution required to reduce the differential equation $t^2 d x+\left(x^2-t x+t^2\right) d t=0$ to a differential equation which can be solved by variables separable method is