7. Given the particular solution $y_p(t) = t$, to $y'' + y' = 1$, find the general solution.
Added by Daniel S.
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The characteristic equation is r^2 + r = 0. Factoring out an r, we get r(r+1) = 0. So the roots are r = 0 and r = -1. Therefore, the complementary solution is y c (t) = c1e^0t + c2e^(-1t). Simplifying, we get y c (t) = c1 + c2e^(-t). Now, let's find the Show more…
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