The solution of the differential equationxsinxdydx+(xcosx+sinx)y=s | Filo
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Calculus

Differential Equations

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

  1. xysinx=1−cosx
  2. xysinx+cosx=0
  3. xsinx+ycosx=0
  4. 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
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