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

64y''+144y'=0

y1(0)=1 y'1(0)=0

and

y2(0)=0 and y'2(0)=1

2. Relevant equations

y1=c1*e^(r1*t) + c2*e^(r2*t)

3. The attempt at a solution

I start by finding the characteristic equation:

64r^2+144r=0

r1=-9/4 and r2=0

y1=c1e(r1*t) + c2e(r2*t)

so I get

y1=c1e^(-9/4 *t) + c2e^(0*t)

e^(0*t) = 1 will always = 0, which gives

y1=c1e^(-9/4 *t) + c2(1)

so I suppose I am asking if I started this wrong or if not, because I need y'1.

With these values I would have:

y'1=(-9/4)c1e^(-9/4 *t) + 0(c2)

?? because the derivative of 1 is zero

Is this correct or have I gone about the problem in the wrong way?

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# Homework Help: Finding a fundamental set of solutions for a 2nd order differential equation

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