Particular integral of \(\frac{{{d^2}y}}{{d{x^2}}} + 3\frac{{dy}}{{dx}} + 2y = {e^{ - 2x}} + \sin x\) is

\( - x{e^{ - 2x}} + \frac{1}{{10}}\left( {\cos x - 3\sin x} \right)\)

\(x{e^{ - 2x}} + \frac{1}{{10}}\left( {\sin x + 3\cos x} \right)\)

\( - x{e^{ - 2x}} + \frac{1}{{10}}\left( {\sin x - 3\cos x} \right)\)

\( - x{e^{ - 2x}} + \frac{1}{{10}}\left( {\sin x + 3\cos x} \right)\)

Particular integral of \(\frac{{{d^2}y}}{{d{x^2}}} + 3\frac{{dy}}{{dx}

1.	Particular integral of \(\frac{{{d^2}y}}{{d{x^2}}} + 3\frac{{dy}}{{dx}} + 2y = {e^{ - 2x}} + \sin x\) is
A.	\(x{e^{ - 2x}} + \frac{1}{{10}}\left( {\sin x + 3\cos x} \right)\)
B.	\( - x{e^{ - 2x}} + \frac{1}{{10}}\left( {\sin x - 3\cos x} \right)\)
C.	\( - x{e^{ - 2x}} + \frac{1}{{10}}\left( {\cos x - 3\sin x} \right)\)
D.	\( - x{e^{ - 2x}} + \frac{1}{{10}}\left( {\sin x + 3\cos x} \right)\)
Answer» C. \( - x{e^{ - 2x}} + \frac{1}{{10}}\left( {\cos x - 3\sin x} \right)\)

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