kailoon889 Group Title 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 2 years ago 2 years ago

1. TuringTest Group Title

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

2. TuringTest Group Title

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

3. kailoon889 Group Title

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

4. TuringTest Group Title

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

5. exraven Group Title

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 Group Title

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.