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Question

The solution of the differential equation xdydx+2y=x2logx is

A
x216(4logx1)+Cx2
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B
x216(2logx1)+Cx2
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C
x24(4logx1)+Cx2
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D
None of the above
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Solution

The correct option is B x216(4logx1)+Cx2
Given differential equation can be written as
dydx+2yx=xlogx
Here, P=2x and Q=xlogx
IF=ePdx=e21xdx
=e2logx=elogx2=x2
The general solution is
y×IF=Q×IF
y×x2=×logx×x2dx+C
=x3logxdx
=logx×x44[1x×x44]dx+C
=x44logxx34dx+C
x2y=x44logxx416+C
y=x216(4logx1)+Cx2.

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