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Systems of Ordinary Differential Equations

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Solve the matrix differential equation X^'=AX where X= [x_1,〖 x〗_2 ]^T=[■(x_1@x_2 )] and A=[■(3&-1@-5&-1)].
Find the eigenvalue(s) of A by solving |λ-A|=0
Solve the linear equation (λ-A)u=0 to get the eigenvector(s) u= 〖[u_1,u_2]〗^2
Find the fundamental matrix Φ(t)
What is the Wronskian for Φ?
Use the result from a to c to express the general solution

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We solve systems of ordinary differential equations by using matrices.

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Solve the matrix differential equation X^'=AX where X= [x_1,〖 x〗_2 ]^T=[■(x_1@x_2 )] and A=[■(3&-1@-5&-1)].
Find the eigenvalue(s) of A by solving |λ-A|=0
We have

whence the ...

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