Find the particular solution of the following differential equation : $(x\ +1){\frac{d y}{d x}}=2e^{-y}-1;$ y = 0 when x = 0.

Find the particular solution of the following differential equation : $x y{\frac{d y}{d x}}\,=(x+2)\,(y+2);y=-1,{\mathrm{when}}\,x=1.$

Find the particular solution of the following differential equation : $x\left(x^{2}-1\right){\frac{d y}{d x}}\ =1;$ y = 0, when x = 2.

Solve the differential equation : $3e^{x}\tan y\,d x\ +(2-e^{x})\,\mathrm{sec}^{2}\,y\,d y=0,$ given that when x = 0, y = ${\frac{\pi}{4}}.$ 

Solve the following differential equation. (1 + y²) (1 + log |x|) dx + x dy = 0

Find the particular solution of the differential equation $(1+e^{2x})d y+(1+y^{2})e^{x}d x=0,$ given that y = 1, when x = 0.

Find the particular solution of the differential equation satisfying the given condition ${\frac{d y}{d x}}=y\tan x,$ given that y = 1, when x = 0.

Solve the following differential equation. $(x^{3}+x^{2}+x+1){\frac{d y}{d x}}=2x^{2}+x.$

Find the particular solution of the differential equation ${\frac{d y}{d x}}={\frac{x\left(2\log x+1\right)}{\sin y+y\cos y}}$ given that $y={\frac{\pi}{2}}$ where x = 1.

Solve the differential equation: $x\,{\frac{d y}{d x}}\ +y=x\cos x+\sin x,$ given $y\left({\frac{\pi}{2}}\right)=1.$

Solve the following differential equation : $(x^{2}-1){\frac{d y}{d x}}~+2x y={\frac{2}{x^{2}-1}},~~x\neq{\bf1}$

Solve the differential equation : $(1+x^{2}){\frac{d y}{d x}}\ +y=e^{\tan^{-1}x}.$

Solve the differential equation ${\frac{d y}{d x}}\ +\ y\ \cot\ x$= 2 cos x, given that y = 0 when $x={\frac{\pi}{3}}\,.$

Find the particular solution of the differential equation $\frac{d y}{d x}\ \ +\ 2y\ \tan\ x\ =\ \sin\ x,$ given that y = 0 when $x={\frac{\pi}{3}}\,.$

Solve the differential equation $x\log x\ {\frac{d y}{d x}}+y\ =$${\frac{2}{x}}\mathrm{log}\,x.$