Question

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

Answer 1

cos3x

Explanation:

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

`D^(2)y-Dy+9y=3 sin3x`

`y=(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=(3 sin 3x)/(-3^(2) -D+9)`

`y=-3(sin 3x)/(D)`

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

`y=-3(cos3x)/(-3)`

y=cos3x

hence Particular solution is cos3x