(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

4y'' - 4y' + y = 0

y(1) = -4

y'(1) = 0

2. Relevant equations

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

3. 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

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: DE with initial conditions with repeated rootsplease check work thanks

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