Never mind, I figured it out. Here's the question: Find the general solution to the homogeneous differential equation https://webwork.math.uga.edu/webwork2_files/tmp/equations/59/540a7a16e5c4e841a098d9d2a72f0a1.png The solution has the form https://webwork.math.uga.edu/webwork2_files/tmp/equations/06/69c97d88bd2a92e464b45652c75c181.png enter your answers so that https://webwork.math.uga.edu/webwork2_files/tmp/equations/b6/bf0051fdc1775f5fe9263992f485f41.png I'm supposed to find f1(t) and f2(t). I know the form ar^2+br+c=0 but in this case it's only r^2=0 so r=0. Also y=c1f1(t)+c2f2(t)=c1e^(r1t)+c2e^(r2t) f1(t)=e^(r1t) and f1(0)=1 so f1(0)=e^(r1*0)=1 I know that's right I'm stuck on f2(t) f2(t)=e^(r2t) and f2(2)=0 so f2(2)=e^(r2*2)=2 I tried solving for r2 r2*2=ln(2) r2=ln(2)/2=.3466 and then plugged it into e^(rt), so it was e^(.3466*t) This isn't right. I don't know what else to try. Both r1 and r2 should be equal to 0 to satisfy r^2=0, but then f2(t)=e^(rt)=e^(0*t)=1 and that wouldn't satisfy f(2)=2. Can anyone tell me what else I can try? Thanks a lot.