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Question

If y1(x) is a solution of the differential equation dydx+f(x)y=0, then a solution of differential equation dydx+f(x)y=r(x) is
  1. 1y(x)y1(x)dx
  2. y1(x)r(x)y1(x)dx+c
  3. intr(x)y1(x)dx
  4. none of these


Solution

The correct option is B y1(x)r(x)y1(x)dx+c
i)dydx+f(x)y1=0f(x)=1y1dy1dxii)dydx1y1dy1dx.y=r(x)e1y1dydxdx=edy1dx=1y1ddx(yy1)=r(x)y1yy1=r(x)dx+cy1y=y1r(x)dxy1+cy1

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