DE with initial conditions with repeated rootsplease check work thanks

[fufufu]

Homework Statement

4y'' - 4y' + y = 0
y(1) = -4
y'(1) = 0

Homework Equations

getting the coeff's gets messier and messier.. am i doing something wrong?

The Attempt at a Solution

4y'' - 4y' + y = 0
y'' - y' - (1/4)y = 0

r_1 = r_2 = 1/2

general soln:
y(t) = c_1e^(t/2) + c_2te^(t/2)
y'(t) = (1/2)c_1e^(t/2) + [(e^(t/2) + (1/2)te^(t/2)]c_2

now applying init cond...

-4 = c_1e^(1/2) + c_2e^(1/2)
0 = (1/2)c_1e^(1/2) + [(e^(1/2) + (1/2)e^(1/2)]c_2

after trying to solve for c_2 I am ending up with c_1 = -4/e^(1/2) - (4/3)/e
but i stopped here because it looks completely wrong... please help any help is really appreciated ...thanks

 

[alanlu]

y'' - y' - (1/4)y = 0

Should be y'' - y' + (1/4)y = 0.