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Q4. (Initial Value Problems - IVPs) Solve the following initial value problems (IVPs) by the Laplace transform. (i) $y' + 5y = 10 \sin 2t$; $y(0) = 0$ (ii) $y'' + 16y = 2e^{-2t}$; $y(0) = 0$, $y'(0) = 0$ (iii) $y'' + 3y' + 2y = 0$; $y(0) = 3$, $y'(0) = -2$ (iv) $y'' + 4y' + 4y = 8t^3 + 12$; $y(0) = 1$, $y'(0) = 3$

          Q4. (Initial Value Problems - IVPs) Solve the following initial value problems (IVPs) by the Laplace transform.
(i) $y' + 5y = 10 \sin 2t$; $y(0) = 0$
(ii) $y'' + 16y = 2e^{-2t}$; $y(0) = 0$, $y'(0) = 0$
(iii) $y'' + 3y' + 2y = 0$; $y(0) = 3$, $y'(0) = -2$
(iv) $y'' + 4y' + 4y = 8t^3 + 12$; $y(0) = 1$, $y'(0) = 3$

Q4. (Initial Value Problems - IVPs) Solve the following initial value problems (IVPs) by the Laplace transform.
(i) y' + 5y = 10 sin 2t; y(0) = 0
(ii) y” + 16y = 2e^-2t; y(0) = 0, y'(0) = 0
(iii) y” + 3y' + 2y = 0; y(0) = 3, y'(0) = -2
(iv) y” + 4y' + 4y = 8t^3 + 12; y(0) = 1, y'(0) = 3

Added by Christine C.

Calculus: Early Transcendentals

James Stewart 8th Edition

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05/01/2023

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(i) y'' + 5y = 10sin(2t) Taking the Laplace transform of both sides: s^2Y(s) - sy(0) - y'(0) + 5Y(s) = 10/(s^2 + 4) s^2Y(s) - 5 + 5Y(s) = 10/(s^2 + 4) (ii) y'' + 16y = 2e^(-2t) Taking the Laplace transform of both sides: s^2Y(s) - sy(0) - y'(0) + 16Y(s) = Show more…

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Q4. (Initial Value Problems - IVPs) Solve the following initial value problems (IVPs) by the Laplace transform. (i) y'' + 5y = 10sin(2t); y(0) = 0 (ii) y'' + 16y = 2e^(-2t); y(0) = 0, y'(0) = 0 (iii) y'' + 3y' + 2y = 0; y(0) = 3, y'(0) = 2 (iv) y'' + 4y' + 4y = 8t^3 + 12; y(0) = 1, y'(0) = 3

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