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Question

The integrating factor of the first order differential equation
x2(x21)dydx+x(x2+1)y=x21 is

A
ex
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B
x1x
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C
x+1x
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D
1x2
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Solution

The correct option is B x1x
x2(x21)dydx+x(x2+1)y=x21dydx+x2+1x(x21)y=1x2dydx+(2x2(x21)x(x21))y=1x2dydx+(2xx211x)y=1x2

I.F.=exp((2x(x21)1x)dx) =exp(log(x21)log(x)) =exp(logx21x)=x1x

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