Question

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

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.

Find the particular solution of the differential equation $e^{x}{\sqrt{1-y^{2}}}d x+\left({\frac{y}{x}}\right)d x=0$ given that y = 1 when x = 0.

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

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

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