Idealist10
  • Idealist10
Find a particular solution of y"+3y'+2y=7cosx-sinx.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Idealist10
  • Idealist10
@Compassionate @sammixboo @thomaster @zepdrix
zepdrix
  • zepdrix
Particular? It will have the "form" of the right side, ya?\[\large\rm y_p=A \cos x+ B \sin x\]
zepdrix
  • zepdrix
\[\large\rm y_p'=-A \sin x+ B \cos x\]\[\large\rm y_p''=-A \cos x- B \sin x\]

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zepdrix
  • zepdrix
And then ummm, substitute that stuff back into the original equation. Ya? :o
Idealist10
  • Idealist10
Let me try.
zepdrix
  • zepdrix
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
Idealist10
  • Idealist10
So I got Acosx+3Bcosx=7cosx and Bsinx-3Asinx=-sinx, how to find A and B?
zepdrix
  • zepdrix
\[\large\rm A \cos x+3B \cos x=7\cos x\]Factor a cosine out of each term,\[\large\rm (A+3B)\cos x=7\cos x\]Divide out the cosines,\[\large\rm A+3B=7\]
zepdrix
  • zepdrix
Understand those steps? Try it with the sines :)
Idealist10
  • Idealist10
I was stupid. Thanks.

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