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Question

The particular integral of d2ydx2+dydx=x2+2x+4 is

A
x33+x2+4x+C
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B
x33+x2+C
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C
x33+4x+C
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D
x2+4x+C
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Solution

The correct option is C x33+4x+C
Given equation is of the form

(D2+D)y=x2+2x+4

P.I.=1D(D+1)(x2+2x+4)

=1D(1+D)1(x2+2x+4)

=1D(1D+D2...)(x2+2x+4)

=1D[x2+2x+4(2x+2)+2]

=(x2+4)dx=x33+4x+C

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