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
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
$\displaystyle 2y = x''+5x\implies 2y''=x''''+5x''$Quote:
Originally Posted by googoogaga
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".
