- #1
glid02
- 54
- 0
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.
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.
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