Differential Equation Test

Degree of $$\left[1+\left(\frac{\text{d}y}{\text{d}x}\right)^2\right]^3=\left(\frac{\text{d}^2y}{\text{d}x^2}\right)^2$$ is ______

The order of $$x\frac{\text{d}^2y}{\text{d}x^2}-\left(2x-1\right)\frac{\text{d}y}{\text{d}x}+\left(x-1\right)y=e^x$$ is ______

The complimentary solution of $$\left(D^3-D^2-4D+4\right)y=0$$

Find the general solution of $$\frac{\text{d}y}{\text{d}x}=e^{\left(x+y\right)}$$

Find the Integrating Factor of $$\frac{\text{d}u}{\text{d}x}-\frac{u}{x}=\frac{1}{x^2}$$

Find the particular Integral of $$\left(D^2+D+1\right)y=\sin x$$

The solution of clairaut's equation $$y=xp+\frac{2}{p}$$ where $$p=\frac{\text{d}y}{\text{d}x}$$ is______

The Differential equation $$x\left(1+y^2\right)dx+y\left(1+x^2\right)dy=0$$ is

Form a differential equation whose solution is $$y=Ae^{2x}+Be^{-2x}$$ where A ,B are arbitary constants

The Integrating Factor of Homogeneous equation Mdx+Ndy=0 is___