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## Homework Statement

Hi

I am trying to solve the following system of ODE's by Laplace transforming:

[tex]

x' = 1 + 21y - 6x \\

y' = 6x-53y

[/tex]

with the initial conditions x(0)=y(0)=0. Laplace transforming gives me (X and Y denote the Laplace transformed variables)

[tex]

sX = 1 + 21y-6x \\

sY = 6x-53y

[/tex]

From these I find

[tex]

X(s) = \frac{1}{6+s-126/(s+53)}

[/tex]

The inverse Laplace transform is (I have checked this with Mathematica)

[tex]

x(t) = \frac{e^{-\frac{1}{2} \left(59+\sqrt{2713}\right) t} \left(-47+\sqrt{2713}+\left(47+\sqrt{2713}\right) e^{\sqrt{2713} t}\right)}{2 \sqrt{2713}}

[/tex]

When I take t=0, then I get x(0)=1, not x(0)=0. I not quite sure where I have gone wrong, I have double-checked everything by doing it numerically too.

Is there something that I have forgotten to do?

Best,

Niles.