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I would like some help solving the following differential equation:

[tex] \frac{d^2 y(t)}{dt^2} + \lambda ^2 y(t) = F(t)[/tex]

In my document, it is solved in this form, but I do not understand how or why:

[tex] y(t) = A cos(\lambda t) + B sin(\lambda t) + \int_0^t F(t) sin\lambda (t-\tau ) \,d\tau. [/tex]

I can understand how to solve for the first two terms (A and B), using the initial conditions. But where in the world is the third term from? In fact in the text they write,

[tex] \frac{F(t) \ast sin\lambda }{\lambda} [/tex] where the asterisk, I suppose, means the integration??

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# Homework Help: 2nd-Order Non-homogeneous Differential Equations

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