Differential Eq...

Find general solution of  $$\sqrt{1 + 4x^{2}} dy = y^{3} xdx$$.

The solution of the differential equation $$\displaystyle \left( 1+\cos { x }  \right) \frac { dy }{ dx } =1-\cos { x } $$ is

The equation of the curve in which sub-normal varies as the square of the ordinate is ($$k$$ is constant of proportionality)

Solve : $$(\tan y)\displaystyle \frac{dy}{dx} = \sin(x + y) + \sin(x - y)$$

Find general solution of $$\displaystyle \frac{2dy}{dx} = \frac{y(x + 1)}{x}$$.

A solution of the differential equation, $$\left ( \displaystyle \dfrac {dy}{dx} \right ) ^2\, -\,x\, \displaystyle \dfrac {dy}{dx}\, +\, y\, =\, 0$$ is

Find the equation of the curve for which the normal at any point (x, y) passes through the origin. The curve represents a :

Which one of the following curves represents the solution of the initial value problem $$Dy = 100- y$$, where $$y(0) = 50$$

Find general solution of $$y-x\, \cfrac {dy}{dx}\, =\, b(1+x^2\cfrac {dy}{dx})$$ is:

The solution to the differential equation $$y\ln y \, +\, xy'\, =\, 0\,$$ where$$\, y(1)\, =\, e$$, is: