The solution of differential equation `(dy)/(dx)+(y)/(x)=sin x` is

Options

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+cosx)=cos +C`

Answer

B

Explanation

Given differential equation is `(Dy)/(dx+y(1)/(x)=sinx`
which is linear differential equation.
Here, `P=(1)/(x)and Q=sin x`
`therefore IF=e^(int(1)/(x)dx)=e^(logx)=x`
The general solution is `y.x.=intx.sin xdx+C`
`"Take" I=intx sin xdx`
`-x cos x -f -cos xdx`
`-x cos x+sin x`
Put the value l in Eq. (i), we get
`xy=-x cos x+sin x+C`
`Rightarrow x(y+cos x)=sin x+C`