Question

Consider the differential equation y''-y'-12y=0

a) Solve the linear second order homogeneous differential equation with constant coefficients
b) Rewrite the differential equation as a first order system
c) Find the matrix A so the system is written as x'=Ax
d) Solve the system x '=Ax

Answer 1

solve the characteristic equation

r^2 -r -12 = 0

--> r = 4, -3

y(t) = c1*e^4t + c2*e^-3t

Answer 2

Not sure about the other parts