Please Help mewith this problem, I am not really getting the double prime stuff...

-Find the General Solution to the system

{ x'' = -5x + 2y

{ y'' = 2x - 8y

- Aug 1st 2007, 02:00 PMgoogoogagaIntroduction to Systems of Differential Equations: The Method of Elimination
Please Help mewith this problem, I am not really getting the double prime stuff...

-Find the General Solution to the system

{ x'' = -5x + 2y

{ y'' = 2x - 8y - Aug 1st 2007, 02:24 PMThePerfectHacker
$\displaystyle 2y = x''+5x\implies 2y''=x''''+5x''$

Substitute,

$\displaystyle x''''+5x'' = 4x - 8x'' - 40x$

$\displaystyle x'''' + 13 x'' +40 x = 0$

$\displaystyle x = C_1\sin (t\sqrt{5})+C_2\cos (t\sqrt{5})+C_3\sin (t\sqrt{8})+C_4\cos (t\sqrt{8})$

You do now "y".