4. Solve the initial-value problem y + 4y = sin(2t), y(0) = 0, y'(0) = 0....

 

 

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4. Solve the initial-value problem y" + 4y = sin(2t), y(0) = 0, y'(0) = 0. Answer: Apply the Laplace transform to the equation: 2 2 s2Y(s) + 4Y (s) = = Y(s) s2 +4 (s + 4)2 Using Example 1.55 from the textbook (see the problem above) with a = 2, we obtain y(t) = L-1 2.23. 11/13 (s2+22)2 8 [sin(2t) - 2t cos(2t)]. 4. Solve the initial-value problem y" + 4y = sin(2t), y(0) = 0, y'(0) = 0. Answer: Apply the Laplace transform to the equation: 2 2 s2Y(s) + 4Y (s) = = Y(s) s2 +4 (s + 4)2 Using Example 1.55 from the textbook (see the problem above) with a = 2, we obtain y(t) = L-1 2.23. 11/13 (s2+22)2 8 [sin(2t) - 2t cos(2t)].