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 following differential equation. ${\sqrt{1+x^{2}+y^{2}+x^{2}y^{2}}}+x y{\frac{d y}{d x}}\,=0$

Write the integrating factor of the differential equations ${\sqrt{x}}{\frac{d y}{d x}}+y=e^{-2{\sqrt{x}}}\,.$

Find the integrating factor of the differential equation

Write the integrating factor of the following differential equation. $(1+y^{2})+(2x y-\mathrm{cot}\;y){\frac{d y}{d x}}\;=0$

Find the general solution of the differential equation ${\frac{d y}{d x}}+2y=e^{3x}$

Find the general solution of the differential equation ${\frac{d y}{d x}}+{\frac{2}{x}}y=x$

Find the integrating factor of the differential equation ${\frac{d y}{d x}}+y\ =\ {\frac{1+y}{x}}$

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