1. The problem statement, all variables and given/known data Find all solutions to [dx/dt; dy/dt] = [1, 2; 0, 1]*[x; y] 2. Relevant equations the eigenvalue characteristic equation: det(A-λ*I)=0 3. The attempt at a solution This results in real, repeated eigen values: λ1,2 = 1 for λ1 = 1, (1-1)k1 + 2k2 = 0 choose k1 = 1 then k2 = 0 gives us the eigenvector K1 = [1, 0] this gives part of the general solution X1 = [1, 0]*e^t to get a second solution we create a new vector P to avoid duplication with K1 = [1,0] and P = [p1; p2] we solve (A-λ2*I)*P=K (1-1)*p1 + 2*p2 = 1 choose p1 = 0 then p2 = 1/2 this gives us the solution X2 = [1;0]*t*e^t + [0;1/2]*e^t putting it together X = X1 + X2 [x; y] = c1*[1, 0]*e^t + c2*([1;0]*t*e^t + [0;1/2]*e^t) or x = c1*e^t + c2*t*e^t y = (1/2)*c2*e^t Have I found all the solutions to this system? I think this is the general solution, is this all they are asking for? If we multiply an eigenvalue by some multiple to get a new eigenvalue, is it really possible to find all the solutions? It seems like there would be infinitely many..