Solving first order systems using matrices 04/21/16
Suppose we have a first order system with equations x(t)’ =ax(t)+by(t)and y(t)’=cx(t)+dy(t). We can solve these equation by putting the equations into a matrix form. The matrix will end up with a, b, c, and din progressing order. By taking the determinant, we can find the eigenvalues. We then transform this in to what looks like a solution to a second order differential equation C1*e1t*V1+C2*e2t*V2. We then solve for x(t)and y(t), with the front and bottom rows for the vectors are correlated with the x(t)and y(t)respectfully.