Questions in diff-equation

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Integrating factor of equation $({{x}^{2}}+1)\frac{dy}{dx}+2xy={{x}^{2}}-1$ is
The solution of $\frac{dy}{dx}+\frac{y}{3}=1$ is
$y+{{x}^{2}}=\frac{dy}{dx}$ has the solution
The solution of $\frac{dy}{dx}+p(x)y=0$ is
The solution of $\frac{dy}{dx}+y={{e}^{-x}},\,\,y(0)=0$, is
Integrating factor of the differential equation $\frac{dy}{dx}+P(x)y=Q(x)$ is
To reduce the differential equation $\frac{dy}{dx}+P(x)y=Q(x).{{y}^{n}}$ to the linear form, the substitution is
The solution of differential equation $\frac{dy}{dx}+y=1$ is
The solution of $dy=\cos x(2-y\cos \text{ec}x)dx$ where $y=2$ when $x=\frac{\pi }{2}$ is
An integrating factor of the differential equation $x\frac{dy}{dx}+y\log x=x{{e}^{x}}{{x}^{-\frac{1}{2}\log x}}$, $(x>0)$ is

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