Use Laplace transform to solve the following system:
x''=x+3y
y''=4x-(4e^t)

x(0)=2; x'(0)=3 ;y(0)=1 ;y'(0)=2

Question

Use Laplace transform to solve the following system:
x''=x+3y
y''=4x-(4e^t)

x(0)=2; x'(0)=3 ;y(0)=1 ;y'(0)=2

turingtest · Answer

Laplace to solve a system?
new one on me, can't wait to see the soution

turingtest · Answer

...but you know how to take the laplace of these expressions, right?

anonymous · Answer

yeah but i have no idea how to solve this system D=

turingtest · Answer

me neither :(
let me call for reinforcements:
@JamesJ @Mr.Math @across @lalaly  help with a DE system

anonymous · Answer

transform both DEs$$s^{2} X(s) - sx(0) - x'(0) = X(s) + 3Y(s)$$$$s^{2}Y(s) - sy(0) - y'(0) = 4X(s)-\frac{4}{s-1}$$plug in the initial conditions, simplify and solve for X(s) and Y(s)

mr.math · Answer

It's easy if you already know how to do the laplace transform. You'll be left, as exraven explained, with two equations in two variables $X(s)$ and $Y(s)$, solve for them and then take the inverse laplace transform to each one separately.