Question

Solve the following differential equations using Laplace transforms. Assume zero initial conditions and that the forcing functions are zero prior to t=0-.a. x(t) +7x (t) =5cos2tb. x(t) + 8 x(t) + 25x (t) =10u (t )

Answer 1

Answer:

(A) $X(S)=\frac{1.25}{S^2+4}$

(B) $X(S)=\frac{0.2941}{S}$

Step-by-step explanation:

We have to find the Laplace transform

(a) x(t) + 7 x(t) = 5 cos2t

Taking Laplace of both side

$X(X)+7X(S)=5\times \frac{2}{S^2+4}$

$8X(S)=\frac{10}{S^2+4}$

$X(S)=\frac{1.25}{S^2+4}$

(B) $x(t)+8x(t)+25x(t)=10u(t)$

Taking Laplace transform of both side

$X(S)+8X(S)+25X(S)=10\times \frac{1}{S}$

$34X(S)=\frac{10}{S}$

$X(S)=\frac{0.2941}{S}$