Question

5. By applying Laplace transform, find the solution of the following system of differential equations $3\frac{dy}{dt} - \frac{dx}{dt} - y + 2x = e^{2x}$, $\frac{dy}{dt} - 2\frac{dx}{dt} + 2y - x = e^{-x}$, x(0) = 3, y(0) = 1;

          5. By applying Laplace transform, find the solution of the following system of differential equations
$3\frac{dy}{dt} - \frac{dx}{dt} - y + 2x = e^{2x}$,
$\frac{dy}{dt} - 2\frac{dx}{dt} + 2y - x = e^{-x}$,
x(0) = 3, y(0) = 1;

5. By applying Laplace transform, find the solution of the following system of differential equations
3(dy)/(dt) - (dx)/(dt) - y + 2x = e^2x,
(dy)/(dt) - 2(dx)/(dt) + 2y - x = e^-x,
x(0) = 3, y(0) = 1;

Added by Teresa Y.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Adi S

05/23/2023

Step 1

The Laplace transform of the first equation gives: 3(sY - y(0)) - (sX - x(0)) - Y + 2X = 1/(s-2) The Laplace transform of the second equation gives: (sY - y(0)) - 2(sX - x(0)) + 2Y - X = 1/(s+1) Show more…

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By applying Laplace transform, find the solution of the following system of differential equations 3(dy)/(dt)-(dx)/(dt)-y+2x=e^(2x) (dy)/(dt)-2(dx)/(dt)+2y-x=e^(-x) x(0)=3,y(0)=1 of differential equations dy dx 3 y+2x=e2x dt dt dy dx 2u dt dt x0=3.0=1