Question

Find a particular solution to y" - y' + 9y = 3 sin 3x

Answer 1

Answer:

cos3x

Step-by-step explanation:

y" - y' + 9y = 3 sin 3x

$D^{2}y-Dy+9y=3 sin3x$

$y=\frac{3 sin 3x}{(D^{2} -D+9}=3 sin 3x$

here $D^2$ will be replaced by  $\alpha^2$ where $\alpha$ is coefficient of x

$y=\frac{3 sin 3x}{-3^{2} -D+9}$

$y=-3\frac{sin 3x}{D}$

$y=-3\int\ {sin 3x} \, dx$

$y=-3\frac{cos3x}{-3}$

y=cos3x

hence Particular solution is cos3x