Question

need help solving system of differential equations
x'1=4*x1+x2
x'2=6*x1-x2

Answer 1

my attempt
x2=x'1-4x1
x'2=x''1-4x'1
sub back into second equation and I ended up with
x''1=3x'1+10x1 or r^2-3r-10=0
so I ended up with r=-2 and 5 so solutions= e^-2t, e^5t

Answer 2

i need to solve it by transforming it into a second order D.E.