5.2 Solution by Elimination
In this method, unknown functions and their derivatives are successively eliminated until one arrives at a single higher order differential equation containing only one unknown function and its derivatives.
Solution.
From \(1^{\text {st}}\) equation we get \(y = x' + 2x\) substitute in second equation \begin {align*} (x' + 2x)' & = -4x + 3(x' + 2x) + 10\cos t\\\\ x'' + 2x' & = -4x + 3x' + 6x + 10\cos t \end {align*}
\[x'' - x' 2x = 10\cos t\hspace {2cm} *\]
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