Question

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 ${\frac{d y}{d x}}\ =1+x+y+x y$ given that y = 0 when x = 1.

Find the particular solution of the following differential equation : ${\frac{d y}{d x}}\;=1+x^{2}+y^{2}+x^{2}y^{2},$ given that y = 1, when x = 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 $\frac{d y}{d x}\ \ +\ 2y\ \tan\ x\ =\ \sin\ x,$ given that y = 0 when $x={\frac{\pi}{3}}\,.$

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 $2y e^{x/y}d x+(y-2x e^{x/y})d y=0$ given that x = 0 when y = 1.