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find A and B so that y= A sin 3x + b cos 3x satisfies the equation d2y/dx2 + 4(dy/dx) +3y = 10 cos 3x.

find A and B so that y= A sin 3x + b cos 3x satisfies the equation d2y/dx2 + 4(dy/dx) +3y = 10 cos 3x.

Grade:12

2 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
dy/dx=3Acos3x-3bsin3x
d2y/dx2= -9Asin3x-9bcos3x
-9Asin3x-9bcos3x+4(3Acos3x-3bsin3x)+3(Asin3x+bcos3x)=10cos3x
-9A-12b+3A=0=>-6A-12b=0=>A=-2b
-9b+12A+3b=10=> -6b+12A=10=>-6b-24b=10=>-30b=10=>b=-10/30=-1/2
so a= 2/3
Ans a=2/3, b=-1/3
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hi


you can find a

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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