# Introduction to Systems of Differential Equations: The Method of Elimination

• Aug 1st 2007, 02:00 PM
googoogaga
Introduction to Systems of Differential Equations: The Method of Elimination

-Find the General Solution to the system

{ x'' = -5x + 2y
{ y'' = 2x - 8y
• Aug 1st 2007, 02:24 PM
ThePerfectHacker
Quote:

Originally Posted by googoogaga

-Find the General Solution to the system

{ x'' = -5x + 2y
{ y'' = 2x - 8y

$2y = x''+5x\implies 2y''=x''''+5x''$
Substitute,
$x''''+5x'' = 4x - 8x'' - 40x$
$x'''' + 13 x'' +40 x = 0$
$x = C_1\sin (t\sqrt{5})+C_2\cos (t\sqrt{5})+C_3\sin (t\sqrt{8})+C_4\cos (t\sqrt{8})$

You do now "y".