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Exercise 22 Solve the following inhomogeneous differential equations. Give the general solution and then apply the conditions: a. ÿ- 4y + 3y = t; b. y - 4y = 2 cost; c. ÿ+ 4y+3y=4e-t; d. ÿ + 2y + 6y = 3t sin 2t ; y(0) = 1, y (0) = 0. y(0) = 0, y (0) = 0. y(0) = 0, y (0) = 2. y(0) = 1, y (0) = 2.

Exercise 22 Solve the following inhomogeneous differential equations. Give the general solution and then apply the conditions: a. ÿ- 4y + 3y = t; b. y - 4y = 2 cost; c. ÿ+ 4y+3y=4e-t; d. ÿ + 2y + 6y = 3t sin 2t ; y(0) = 1, y (0) = 0. y(0) = 0, y (0) = 0. y(0) = 0, y (0) = 2. y(0) = 1, y (0) = 2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Exercise 22** Solve the following inhomogeneous differential equations. Give the general solution and then apply the conditions: a. \( \ddot{y} - 4\dot{y} + 3y = t \); Initial conditions: \( y(0) = 1 \), \( \dot{y}(0) = 0 \). b. \( \ddot{y} - 4y = 2 \cos t \); Initial conditions: \( y(0) = 0 \), \( \dot{y}(0) = 0 \). c. \( \ddot{y} + 4\dot{y} + 3y = 4e^{-t} \); Initial conditions: \( y(0) = 0 \), \( \dot{y}(0) = 2 \). d. \( \ddot{y} + 2\dot{y} + 6y = 3t \sin 2t \); Initial conditions: \( y(0) = 1 \), \( \dot{y}(0) = 2 \).
Transcribed Image Text:**Exercise 22** Solve the following inhomogeneous differential equations. Give the general solution and then apply the conditions: a. \( \ddot{y} - 4\dot{y} + 3y = t \); Initial conditions: \( y(0) = 1 \), \( \dot{y}(0) = 0 \). b. \( \ddot{y} - 4y = 2 \cos t \); Initial conditions: \( y(0) = 0 \), \( \dot{y}(0) = 0 \). c. \( \ddot{y} + 4\dot{y} + 3y = 4e^{-t} \); Initial conditions: \( y(0) = 0 \), \( \dot{y}(0) = 2 \). d. \( \ddot{y} + 2\dot{y} + 6y = 3t \sin 2t \); Initial conditions: \( y(0) = 1 \), \( \dot{y}(0) = 2 \).
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