The particular solution of $$e^{\frac{d y}{d x}}=2 x+1$$ given that $$y=1$$ when $$x=0$$ is

The general solution of the differential equation $$\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y$$

The solution of the differential equation $$\frac{d y}{d x}+y \cos x=\frac{1}{2} \sin 2 x$$

The sum of the degree and order of the following differential equation $$\left[1-\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}=k x \frac{d^2 y}{d x^2}$$