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Question

The general solution of the differential equation xdydx+2y=x2 is y= .

A
x24+Cx2
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B
x24
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C
x24+C
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D
x24+Cx2
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Solution

The correct option is A x24+Cx2
xdydx+2y=x2dydx+2yx=x
I.F=ePdx=e2xdx=e2log x=elog x2=x2
The solution of the differential equation is y.x2=x.x2dx
y.x2=x3dxy.x2=x44+Cy=x24+Cx2

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