1. The integrating factor of the D. Equation Cos x $\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)$ +Y sin x = 1 is

2. The solution of x dy / dx + y = $x^3$ given y = 1 when x = 1, is given by

3. The complete solution of dy/dx+y = Cos 2x is given by

4. The solution $\frac{\mathrm{dy}}{\mathrm{dx}}$+y = $e^{-x};$ y(0) = 0 is

5.  The solution of $\frac{\mathrm{dy}}{\mathrm{dx}}$ + P(x) Y = 0 is

6.  The solution of $\frac{\mathrm{dy}}{\mathrm{dx}}$ = $\frac{\mathrm{xy}+y}{\mathrm{xy}+x}$ is given by

7.  If m is the order and n is the degree of the D.Equation ${\left(\frac{dy}{\mathrm{dx}}\right)}^3$- ${\left(\frac{d^{2}y}{\mathrm{dx}2}\right)}^{3/2}+8=0$

8.  The order of differential equation ${\left(\frac{d^{2}y}{{\mathrm{dx}}^2}\right)}^3$ = ${[1+\frac{\mathrm{dy}}{\mathrm{dx}}]}^{1/2}$ is