The general solution to the inhomogeneous equation \( y'' + y = \sec^2(t) \) is confirmed to be \( y(t) = C_1 \cos(t) + C_2 \sin(t) + Y_p \), where \( Y_p = -\sec(t) \cos(t) + \ln|\sec(t) + \tan(t)| \sin(t) \) is the particular solution. This conclusion is reached through the method of undetermined coefficients and the superposition principle. The discussion emphasizes the importance of verifying solutions through examples, particularly in the context of complex numbers.
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giacomh said:Homework Statement
Find the general solution to:
yii +y=sec2(t)
The Attempt at a Solution
I found the particular solution, which is
Yp=-sec(t)cos(t)+ln|sec(t)+tan(t)|sin(t)
Is the general solution just y(t)=C1cos(t)+C2sin(t)+Yp?
I just can't find an example of an inhomogeneous problem with complex numbers to verify this.