TUT0101 Quiz3

[Mingdi Xie]

y’’-6y’+5y=0     y(0)=2    y’(0)=6
r^2-6r+5=0
(r-1)(r-5)=0
r=1   r=5
y(t)=c1e^-3t+c2e^-t
Since y(0)=2
y(0)=c1+c2=2
c2=2-c1                        (1)
y’(t)=c1e^t+5c2e^5t
y’(0)=-1
y’(0)=c1+5c2=6
c2=4
c1=-2
And Wronskian doesn't equal 0
y(t)=-2e^t+4e^5t