# Solution of the differential equation $\large\frac{dy}{dx}+\frac{y}{x}$$=\sin x is: (A)\;x(y+\cos x)=\sin x+c \\ (B)\;x(y-\cos x)=\sin x+c \\ (C)\;xy\cos x=\sin x+c \\ (D)\;x(y+\cos x)=\cos x+c ## 1 Answer Toolbox: • A linear differential equation of the form \large\frac{dy}{dx}$$+Py=Q$ has general solution as $ye^{\int pdx}=\int Qe^{\int pdx}dx+c$
• $\int udv=uv-\int vdu$
Step 1:
Given $\large\frac{dy}{dx}+\frac{y}{x}$$=\sin x Clearly this is a linear differential equation of the form \large\frac{dy}{dx}$$+Py=Q$. where $P=\large\frac{1}{x}$ and $Q= \sin x$