Class 12

Math

Calculus

Differential Equations

The solution of the differential equationxsinxdydx+(xcosx+sinx)y=sinx. When y(0)=0 is

- xysinx=1−cosx
- xysinx+cosx=0
- xsinx+ycosx=0
- xsinx+ycosx=1

**Correct Answer: ** Option(a)

**Solution: **[a] The equation is dydx+(xcosx+sinxxsinx)y=1x Integrating factor I.F. =e∫xcosx+sinxxsinxdx=elog(xsinx)=xsinx ∴ The solution is y(xsinx)=∫1x(xsinx)dx+c xysinx=−cosx+c when x=0,y=0⇒c=cos0=1 ∴ The particular solution is xysinx=1−cosx