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Question

If dydx+ytanx=sin2x and y(0)=1, then y(π)=?

A
1
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B
1
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C
5
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D
5
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Solution

The correct option is C 5
I.F.=etanxdx
I.F.=elncosx
I.F.=1cosx
Multiplying with I.F. in the given equation,we get-
dycosxdx+ysinxcos2x=2sinx
d(ycosx)=2sinxdx
Integrating both sides, we get-
ycosx=2cosx+C
y(0)=1
1=2+C
C=3
For x=π we get
y1=2+3
y=5

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