54 3. Consider the differential equation x' = Ax where A = (2 I) and xt) = CH\") . Find the solutiOn x(t) as follows: \"1 (a) Look for solutions of the form x(t} = e'uv where A. and v = (1:2) are to be determined: substitute this Ansatz into xi = Ax and show that A and v must satisfy AV 2 Av (h) Explain why1 if there is to be a nonzero solution if to the above equation, it must he that (mm m = 0. (c) Find the eigenvalues A and eigenvectors v of A. Then list the corresponding two solutions x103}. Kg\"). A A {(1) Write the general solution to the differential equation in the form x(t) = {:16 \"V; + 52:: 2'V2 (0) Sketch several solutions in the phase plane and classify the equilibrium