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)
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 .
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 ...