SOLUTION: 1). Find the constant A and B such limit the function y=Asinx+Bcosx satisfies the equation y^“+y^'-2y=sinx.

Algebra ->  Trigonometry-basics -> SOLUTION: 1). Find the constant A and B such limit the function y=Asinx+Bcosx satisfies the equation y^“+y^'-2y=sinx.       Log On


   

Question 862271: 1). Find the constant A and B such limit the function y=Asinx+Bcosx satisfies the equation y^“+y^'-2y=sinx.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=Asinx%2BBcosx+
dy%2Fdx=Acos%28x%29-Bsin%28x%29
d%28dy%2Fdx%29%2Fdx=-Asin%28x%29-Bcos%28x%29
So then,

%28-A-B-2A%29sin%28x%29%2B%28-B%2BA-2B%29cos%28x%29=sin%28x%29
%28-B-3A%29sin%28x%29%2B%28A-3B%29cos%28x%29=sin%28x%29
So comparing both sides,
1.-B-3A=1
2.A-3B=0
From eq. 2,
A=3B
Substitute into eq. 1,
-B-3%283B%29=1
-B-9B=1
-10B=1
B=-1%2F10
and
A=-3%2F10