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) is1y(x)∫y1(x)dxy1(x)∫r(x)y1(x)dx+cintr(x)y1(x)dxnone of these

Solution

The correct option is B y1(x)∫r(x)y1(x)dx+ci)dydx+f(x)y1=0⇒f(x)=−1y1dy1dxii)dydx−1y1dy1dx.y=r(x)e−∫1y1dydxdx=e−∫dy1dx=1y1ddx(yy1)=r(x)y1⇒yy1=∫r(x)dx+cy1y=y1∫r(x)dxy1+cy1

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