Answer:
cos3x
Step-by-step explanation:
y" - y' + 9y = 3 sin 3x
[tex]D^{2}y-Dy+9y=3 sin3x[/tex]
[tex]y=\frac{3 sin 3x}{(D^{2} -D+9}=3 sin 3x[/tex]
here [tex]D^2[/tex] will be replaced by [tex]\alpha^2[/tex] where [tex]\alpha[/tex] is coefficient of x
[tex]y=\frac{3 sin 3x}{-3^{2} -D+9}[/tex]
[tex]y=-3\frac{sin 3x}{D}[/tex]
[tex]y=-3\int\ {sin 3x} \, dx[/tex]
[tex]y=-3\frac{cos3x}{-3}[/tex]
y=cos3x
hence Particular solution is cos3x
