Question

Use the Laplace transform to solve the following initial value problem:

x′=12x+3y

y′=−9x+e^(3t)

x(0)=0, y(0)=0

Let X(s)=L{x(t)}, and Y(s)=L{y(t)}.
Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s):

X(s)=

Y(s)=

Find the partial fraction decomposition of X(s)X(s) and Y(s)Y(s) and their inverse Laplace transforms to find the solution of the system of DEs:

x(t)

y(t)

Answer 1