Use the laplace transform to solve the given system of differential equations. dx dt + 3x + dy dt = 1 dx dt − x + dy dt − y = et
x(0) = 0, y(0) = 0
1 answer:
Let
and
denote the Laplace transforms of
and
.
Taking the Laplace transform of both sides of both equations, we have


Eliminating
, we get

Take the inverse transform of both sides to solve for
.

Solve for
.

Taking the inverse transform of both sides, we get

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