## anonymous 4 years ago 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

1. TuringTest

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

2. TuringTest

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

3. anonymous

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

4. TuringTest

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

5. anonymous

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)

6. Mr.Math

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.