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mm391
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Homework Statement
Find the general solution to d2y/dx2 +4y=cos(2x)
Homework Equations
The Attempt at a Solution
I have woked out what I think is the Complementary function C1sin(2x)+C2cos(2x) the reason it is cos and sin is because the roots are 2i and therefore the exponential and imaginary number turn it into a cos or sin.
Particular Integral:
y = a cos(2x) + b sin(2x)
y' = -2a sin(2x) + 2b cos(2x)
y'' = 4a cos(2x) - 4b sin(2x)
∴ -4a cos(2x) + 4b sin(2x) + 4a cos(2x) - 4b sin(2x) = cos(2x)
but it all cancels out to give 0=cos(2x) which surely can't be right. Have I been staring at this so long that I cannot see the obvious answer?