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# Systems of Ordinary Differential Equations

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Solve the matrix differential equation X^'=AX where X= [x_1,ã€– xã€—_2 ]^T=[â– ([email protected]_2 )] and A=[â– (3&[email protected]&-1)].
Find the eigenvalue(s) of A by solving |Î»-A|=0
Solve the linear equation (Î»-A)u=0 to get the eigenvector(s) u= ã€–[u_1,u_2]ã€—^2
Find the fundamental matrix Î¦(t)
What is the Wronskian for Î¦?
Use the result from a to c to express the general solution

https://brainmass.com/math/ordinary-differential-equations/systems-ordinary-differential-equations-444172

#### Solution Preview

Solve the matrix differential equation X^'=AX where X= [x_1,ã€– xã€—_2 ]^T=[â– ([email protected]_2 )] and A=[â– (3&[email protected]&-1)].
Find the eigenvalue(s) of A by solving |Î»-A|=0
We have

whence the ...

#### Solution Summary

We solve systems of ordinary differential equations by using matrices.

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