# Systems of Ordinary Differential Equations

Not what you're looking for? Search our solutions OR ask your own Custom question.

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

Please see the attachment.

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.

$2.49