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