Can you help me with this system of linear equations, to find the general solution??

dx_{1}/dt=2x_{1}-5x_{2 }

dx_{2}/dt=x_{1}-2x_{2}+cos(t)

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- February 26th 2013, 12:17 PMejenanonhomogeneous linear system
Can you help me with this system of linear equations, to find the general solution??

dx_{1}/dt=2x_{1}-5x_{2 }

dx_{2}/dt=x_{1}-2x_{2}+cos(t) - February 26th 2013, 05:03 PMProve ItRe: nonhomogeneous linear system

Differentiating the second equation, we get

This is a second order linear constant coefficient nonhomogeneous ODE. Solve as you normally would for .

Differentiating the first function, we have

This is another second order linear constant coefficient nonhomogeneous ODE. Solve as you normally would for . - February 27th 2013, 05:41 AMejenaRe: nonhomogeneous linear system
thanks a lot for the answer , but in fact I should solve it by using the eigenvalues and eigenvectors ... I have found the eigenvalues λ1 = i λ2=-i and the eigenvectors from

(A-λ1)α=0 ( where α is the eigenvector , and A is the matrix ( {2 , -5 } { 1 , -2} ) , but I have difficulties finding a particular solution , so i can find the general solution in the end ... :)