Solving an Initial Value Problem: 9r^2-12r+4=0

[Punchlinegirl]

Solve the given initial value problem.
9y"-12y'+4y=0 y(0)=2 y'(0)=-1

9r^2-12r +4=0
(3r-2)^2
so r=2/3
so my general solution would be y(t)=c_1e^2/3t +c_2e^2/3t
Whenever I try to use the initial conditions I can't get them to work. One disappears.
Is my general solution even right?

 

[StatusX]

You only have one linearly independent solution there. When you get a double root like that, the other solution is given by, in this case, [itex]t e^{2/3 t} [/tex]. You can verify this by plugging it into the DE.[/itex]

 

[Punchlinegirl]

I get it.. thanks a lot!