Differential Equation System: Laplace

**cith** · May 20th 2009, 04:46 AM

I want to solve this system using the Laplace transform $(y_1=y_1(t),y_2=y_2(t))$

$y_1=-y_1+y_2 \hspace{0.5cm} y_1(0)=0$
$y_2=2y_1 \hspace{1.5cm} y_2(0)=1$

Probably not the hardest of problems, but I'm not even sure where to start :P

**Danny** · May 20th 2009, 05:07 AM

Originally Posted by cith

I want to solve this system using the Laplace transform $(y_1=y_1(t),y_2=y_2(t))$

$y_1=-y_1+y_2 \hspace{0.5cm} y_1(0)=0$
$y_2=2y_1 \hspace{1.5cm} y_2(0)=1$

Probably not the hardest of problems, but I'm not even sure where to start :P

First I'm assuming that you have differential equations

$y'_1=-y_1+y_2 \hspace{0.5cm} y_1(0)=0$
$y'_2=2y_1 \hspace{1.5cm} y_2(0)=1$

Let $L(y_1) = Y_1$ and $L(y_2) = Y_2$ so

$sY_1-0 = -Y_1 +Y_2$ and $sY_2 -1 = 2Y_2$ . Solve for $Y_1$ and $Y_2$ and then take the Laplace inverses of each.

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