Verify whether y(t) = e^t + t is a solution of the differential equation y' + 2y = e^2t + 2t. Reminder: calculators or CAS are not allowed!
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y(t) = t * e^{2t} + 1 Using the product rule, we get: y'(t) = (1) * e^{2t} + t * (2 * e^{2t}) = e^{2t} + 2t * e^{2t} Now, let's plug y(t) and y'(t) into the given differential equation: y'(t) - 2y(t) = e^{2t} + 2t * e^{2t} - 2(t * e^{2t} + 1) Show more…
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