Differential Eq...

Find the solution of $$\displaystyle \left ( e^{y}+1 \right )\cos x dx+e^{y}\sin x dy=0$$

The order of the differential equation is

The order of differential equation of all parabola's having directrix parallel to $$x$$-axis is:

Find the solution of $$\displaystyle \left ( e^{x}+1 \right )y dy=\left ( y+1 \right )e^{x}dx$$.

A function $$y=f(x)$$ has a second order derivative $${f}''\left ( x \right )=6\left ( x-1 \right )$$. If its graph passes through tbe point $$(2, 1)$$ and at that point the tangent to the curve is $$y=3x-5$$, then the function is:

Find the solution of $$\displaystyle \left ( 1-x \right )dy-\left ( 3+y \right )dx=0$$

The solution of the equation $$\displaystyle \frac{d^{2}y}{dx^{2}}=e^{-2x}$$ is:

Find the solution of $$\displaystyle \left ( 1-x^{2} \right )\left ( 1-y \right )dx=xy\left ( 1+y \right )dy.$$

$$\displaystyle ydx-x dy=xy\:dx$$

Solve the given differential equation  $$\displaystyle \left ( xy^{2}+x \right )dx+\left ( yx^{2}+y \right )dy=0.$$