Differential Eq...

The solution of the differential equation $$ y(2x^{2}+y)\dfrac{dy}{dx}=(1-4xy^{2})x^{2} $$ is given by

The solution of the following differential equation $$ [1+x\sqrt{(x^{2}+y^{2})}]dx+[\sqrt{(x^{2}+y^{2})-1}]ydy=0 $$ is equal to

The solution of the differential equation $$\dfrac{dy}{dx}=\dfrac{3x^{2}y^{4}+2xy}{x^{2}-2x^{3}y^{3}} $$ is

Number of values of $$m\in N$$ for which $$y=e^{mx}$$ is a solution of the differential equation $$\dfrac{d^3y}{dx^3}-3\dfrac{d^2y}{dx^2}-4\dfrac{dy}{dx}+12y=0 $$

The solution of the differential equation $$ \dfrac{x+\dfrac{x^3}{3!}+\dfrac{x^5}{5!}+ \dots}{1+\dfrac{x^2}{2!}+\dfrac{x^4}{4!}+\dots}=\dfrac{dx-dy}{dx+dy} $$ is

The solution of the differential equation $$\dfrac {dy}{dx}=\dfrac {1+y^2}{1+x^2}$$ is :

Solution of the diffrential equation $$\dfrac{dy}{dx}+ \dfrac {1+y^2}{\sqrt {1-x^2}}=0$$ is

Which of the following is the general solution of $$\dfrac{d^2y}{dx^2}-2\dfrac{dy}{dx}+y=0$$?

Solution of $$\displaystyle \sqrt{1+x^{2}+y^{2}+x^{2}y^{2}}+xy\frac{dy}{dx}=0$$, is: