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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, #62 · Differential Equations · Applications

True or false, when … and … both satisfy

These problems approach a steady state $y_{\infty}$ as $t \to \infty$ .

True or false, when $y_{1}$ and $y_{2}$ both satisfy $y^{'} = cy + s$ .
(a) The sum $y = y_{1} + y_{2}$ also satisfies this equation.
(b) The average $y = \frac{1}{2} (y_{1} + y_{2})$ satisfies the same equation.
(c) The derivative $y = y_{1}^{'}$ satisfies the same equation.

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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, #62

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