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Question

# The solution y(x) of the differential equation d2ydx2=sin 3x+ex+x2 when y1(0)=1 and y(0) = 0 is

A
sin 3x9+ex+x412+13x1
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B
sin 3x9+ex+x412+13x
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C
cos 3x3+ex+x412+13x+1
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D
None of these
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Solution

## The correct option is A −sin 3x9+ex+x412+13x−1Integrating the given differential equation, we have dydx=−cos 3x3+ex+x33+C1 but y1(0) 1 so 1=−13+1+C1⇒C1=13 Again integrating, we get y=−sin 3x9+ex+x412+13x+C2 but y(0)=0 so 0=1+C2⇒C2=−1. Thus y=−sin 3x9+ex+x412+13x−1

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