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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.3 Growth and Decay in Science and Economics, #38 · Differential Equations · Applications

Solve … from … by Method 2, where the deposit … at…

Solve $y^{'} = y + e^{t}$ from $y_{0} = 0$ by Method 2, where the deposit $e^{T}$ at time $T$ is multiplied by $e^{t - T}$ . The total output at time $t$ is $y (t) = \int_{0}^{t} e^{T} e^{t - T} d T =$ ______. Substitute back to check $y^{'} = y + e^{t}$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.3 Growth and Decay in Science and Economics, #38

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