Mathematics : Differential Equations

Solve the following differential equation:

${\cos }^2 \mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}} + \mathrm{y} = \mathrm{tanx}$

Solve the following differential equation:

$\left( 1 + {\mathrm{x}}^2 \right) \frac{\mathrm{dy}}{\mathrm{dx}} + \mathrm{y} = {\tan }^{-1} \mathrm{x}$

Find the particular solution, satisfying the given condition, for the following differential equation:

$\frac{\mathrm{dy}}{\mathrm{dx}} - \frac{\mathrm{y}}{\mathrm{x}} + \mathrm{cosec} \left(\frac{\mathrm{y}}{\mathrm{x}}\right) = 0 ; \mathrm{y} = 0 \mathrm{when} \mathrm{x} = 1$

What is the degree of the following differential equation?

5x $5\mathrm{x} {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2 - \frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} - 6\mathrm{y} = \log \mathrm{x}$

Find the particular solution of the differential equation satisfying the given conditions: x² dy + (xy + y² )dx = 0; y = 1 when x = 1.

Find the general solution of the differential equation,

$\mathrm{x} \log \mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}} + \mathrm{y} = \frac{2}{\mathrm{x}} \log \mathrm{x}$

Find the particular solution of the differential equation satisfying the given conditions:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \mathrm{y} \tan \mathrm{x}$,    given that   y = 1  when   x= 0.

Solve the following differential equation:

e^x tan y dx + ( 1 - e^x ) sec² y dy  = 0

Solve the following differential equation:

${\cos }^2 \mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}} + \mathrm{y} = \tan \mathrm{x}$

Solve the following differential equation:

$2 {\mathrm{x}}^2 \frac{\mathrm{dy}}{\mathrm{dx}} - 2 \mathrm{x} \mathrm{y} + {\mathrm{y}}^2 = 0$