Question

Particular Integral of (D2+4)y=sin 3x
is​

Answer 1

SOLUTION

TO DETERMINE

The particular integral of ( D² + 4 )y + sin 3x

EVALUATION

Here the given differential equation is

( D² + 4 )y + sin 3x

Now the required particular integral

= P.I.

$\displaystyle \sf{ = \frac{1}{ {D}^{2} + 4} \sin 3x}$

$\displaystyle \sf{ = \frac{1}{ - {(3)}^{2} + 4} \sin 3x}$

$\displaystyle \sf{ = \frac{1}{ - 9 + 4} \sin 3x}$

$\displaystyle \sf{ = \frac{1}{ -5} \sin 3x}$

$\displaystyle \sf{ = - \frac{1}{5} \sin 3x}$

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