The differential equation formed by eliminating $a$ and $b$ from the equation $y=a e^{2 x}+b x e^{2 x}$ is

If $y=a^3 e^{y^2 x+c}$ is the general solution of a differential equation, where $a$ and $c$ are arbitrary constants and $b$ is fixed constant, then the order of differential equation is

The solution of differential equation $\left(x+2 y^3\right) \frac{d y}{d x}=y$ ls

Order and degree of the differential equation $\frac{d^3 y}{d x^3}=\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{5}{2}}$, respectively are