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First-order linear IVP: y' + 2y = e^-t, y(0)=1. μ = e^2t, (e^2t y)' = e^t. Integrate: e^2t y = e^t + C. Use y(0)=1 → 1 = 1 + C → C=0. So y = e^-t. ordinary differential equations titas pdf
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