1) Find a power series solution in powers of x for the following ODE. y"-y'+x²y=0 2) Solve the following second order differential equations by the Laplace transform. a) y-6y'+5y=29 cos 21, The initial conditions are: y(0) 3.2, y'(0)=6.2 b) y-4y+4y=0, The initial conditions are: y(0) = 8.1, y'(0) =3.9 3) Solve the following linear systems. The given matrices are the augmented matrices. 13 12 -6 a) -4 7-73 11-13 157 2 4 10] b) -1 1-2 0 4 0 60 [05 5-10 0] c) 2-3-3 62 4 11 -24