Question

Find a particular solution of y"+3y'+2y=7cosx-sinx.

Answer 1

@Compassionate @sammixboo @thomaster @zepdrix

Answer 2

Particular?
It will have the "form" of the right side, ya?\[\large\rm y_p=A \cos x+ B \sin x\]

Answer 3

\[\large\rm y_p'=-A \sin x+ B \cos x\]\[\large\rm y_p''=-A \cos x- B \sin x\]

Answer 4

And then ummm, substitute that stuff back into the original equation.
Ya? :o

Answer 5

Let me try.

Answer 6

Recommendation: Call C=cos(x) and S=sin(x) for problems like this.
It's so tedious to rewrite sine and cosine over and over lol

Answer 7

So I got Acosx+3Bcosx=7cosx and Bsinx-3Asinx=-sinx, how to find A and B?

Answer 8

\[\large\rm A \cos x+3B \cos x=7\cos x\]Factor a cosine out of each term,\[\large\rm (A+3B)\cos x=7\cos x\]Divide out the cosines,\[\large\rm A+3B=7\]

Answer 9

Understand those steps?
Try it with the sines :)

Answer 10

I was stupid. Thanks.