Amit M Agarwal Solutions for Chapter: Differential Equations, Exercise 4: Work Book Exercise 12.4

An integrating factor of the differential equation $\left(1+y+x^{2}y\right)dx+\left(x+x^3\right)dy=0$ is

The solution of the differential equation $x\frac{dy}{dx}=2y+x^3{e}^x,$ where $y=0,$ when $x=1,$ is

The solution of the differential equation $\frac{dy}{dx}=\frac{x+y}{x}$ satisfying the condition $y\left(1\right)=1$ is

The solution of the differential equation $\left(e^{-2\sqrt{x}}-\frac{y}{\sqrt{x}}\right)\frac{dx}{dy}=1$ is given by

If ${\cos }^{2}x\frac{dy}{dx}-y\tan 2x={\cos }^{4}x,$ where $\left|x\right|<\frac{\pi }{4}$ and $y\left(\frac{\pi }{6}\right)=\frac{3\sqrt{3}}{8}$, then the constant term in the solution of the differential equation is

The solution of the equation $x^{2}y-x^3\frac{dy}{dx}=y^4\cos x,$ when $y\left(0\right)=1$ is

The solution of the differential equation $\frac{dy}{dx}+\frac{2x}{1+x^2}·y=\frac{1}{{\left(1+x^2\right)}^2}$ is

The solution of $(x+y+1)\frac{dy}{dx}=1$ is