- #1
cue928
- 130
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I am working on the following initial value problem:
y'' + 4y = 4, y(0) = 1, y'(0) = 1
The method they show is:
(1): y = A cos x + B sin x
A = 1, (2): y = 1 + A cos x + B sin x
y(0) = 1 + A = 0
y'(0) = B = 1
Final answer is y(x) = 1 + sin(x)
The problem I don't see is the first equation (1). I had y = A cos(2x) + B sin(2x) by solving the LHS. The, I am confused on how they proceed with writing the equation (2). I've done IVP's before without problems, so I am confused what I am missing here.
y'' + 4y = 4, y(0) = 1, y'(0) = 1
The method they show is:
(1): y = A cos x + B sin x
A = 1, (2): y = 1 + A cos x + B sin x
y(0) = 1 + A = 0
y'(0) = B = 1
Final answer is y(x) = 1 + sin(x)
The problem I don't see is the first equation (1). I had y = A cos(2x) + B sin(2x) by solving the LHS. The, I am confused on how they proceed with writing the equation (2). I've done IVP's before without problems, so I am confused what I am missing here.