Sandoval Moreno
09/12/2023 · Elementary School
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to \( t \). \[ \begin{aligned} 2 x^{\prime}+y^{\prime}-9 x-9 y & =e^{-4 t} \\ x^{\prime}+y^{\prime}+8 x+4 y & =e^{9 t}\end{aligned} \]
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The general solution for the given system of differential equations involves finding the homogeneous solution and a particular solution. The homogeneous solution is derived from the eigenvalues and eigenvectors of the coefficient matrix, while the particular solution is found by assuming a form that matches the non-homogeneous terms and solving for the coefficients.
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