Given that the eigenvalues of the matrix [2 5 -1 2] are λ = -3 and 4 with corresponding eigenvectors [2 -5] and [1 1], what is the general solution of the following system of differential equations? dx/dt = 2x + 2y dy/dt = 5x - y
Added by Lynn P.
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$$ Now, we want to find the general solution of the system of differential equations $$ \frac{d\mathbf{x}}{dt} = A\mathbf{x}, $$ where $\mathbf{x} = \begin{bmatrix} x \\ y \end{bmatrix}$. Show more…
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Determine the general solution to the linear system $\mathbf{x}^{\prime}=A \mathbf{x}$ for the given matrix $A$. $$\left[\begin{array}{rrr} 2 & -2 & 1 \\ 1 & -4 & 1 \\ 2 & 2 & -3 \end{array}\right]$$ [Hint: The eigenvalues of $A \text { are } \lambda=2,-2,-5 .]$
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