Question

y(t) is INCORRECT
but
x(t) is CORRECT

7.10.4 Question Help Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y' denote differentiation with respect to t x(O) = 0 x' - 6x + 2y = sint 29 2x-y'- 4y = cost y(0) = 0 Click the icon to view information on Laplace transforms. 1 1 X(t) = cost + 2 sint+det sin 2t - e' cos 21 get sin 2 3 11 11 y(t) = cost ecos 2t et 4 4 (Type exact answers in terms of e.) 2 sint+ Fl-

DIFFERENTIAL EQUATIONS / Linear Algebra

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example

Answer 1

Here x - 6x + 2y - Sint X (0) 20 29 x - y - 4y = cost Now, – e sim 2t - e Cosat 4 X(t) = cost & sint & correct solution. WR fina Jow, + t t ne cos at 2 е + cos at -Sint + - cost the sight 1 +ge Sinat 2 - sint of cost + esionat - ecuat put x '(t), X (H value in i Now SO) t t - sint to last + 2 Sinat - e cos at -6 (cost to simt + e sinat - e cos 2t) of 2y = sint 4 t fe sinat - simt - 3 simt I cost 6 cast t. e Sinat - 4 t the cosat +2y = Sant R eos 2t 2 t + II e cos at + 2y = sint + TO -4 sint - cost & 2 e sinat & 2y = simt + 4 simt + 1 cost-3 e simat the cost y = 5 sint + 1 cost So, y(t) = 5 sint the cost of + e simat + e as at 8 4 e sim at e Cosat