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)