Question

Find the particular solution of the differential equation x (1 + y²) dx – y (1 + x²) dy = 0, given that y = 1, when x =0.

Solve the following differential equation : $\mathrm{cosec}\,x\,\mathrm{log}\,y\,\frac{d y}{d x}+x^{2}y^{2}=0\,.$

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

Solve the following differential equation : ${\frac{d y}{d x}}={\frac{y}{x}}+{\frac{\sqrt{x^{2}+y^{2}}}{x}},\,x>0\,.$

Find the particular solution of the differential equation $\log\left(\frac{d y}{d x}\right)=3x+4y,$ given that y = 0, when x = 0.

Evaluate : $\large\textstyle\int$$\large{\frac{x}{(x-1)^{2}(x+2)}}d x\ .$

Find the particular solution of differential equation : ${\frac{d y}{d x}}=-{\frac{x+y\cos x}{1+\sin x}}$ given that y = 1 when x = 0.