mew55
  • mew55
i need help. a differential equation problem. Find the general solution of the first order linear differential equation and use it to determine how solutions behave as t>infinity
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
theEric
  • theEric
Hi! I'm just staring to learn about ordinary differential equations, so I probably can't help. But you'd need to have your equation so we can see how it behaves. If you need help putting it into the fancy \(m+a+t+h\) writing, I can \(\dfrac{h\ e\ \quad\ }{\ \ \quad l\ p}\) because I am used to \(\large_i^{\quad t}\).... I hope you see what I mean about the fancy math writing.
theEric
  • theEric
\(y''=5y+6+\dots\) Or whatever.
ybarrap
  • ybarrap
The simplest type of 1st order linear diff equation is something like $$ \Large y'(t)+by(t)=c\\ $$ With solution: $$ \Large y=e^{-a(t)}\left (\int c e^{a(t)} dt+\kappa\right )\\ $$ where $$ \Large a(t)=\int b~ dt=bt\\ $$ So, $$ \Large y=e^{-bt}\left ({e^{bt}\over b}+\kappa\right )\\ \Large ~~~={1\over b}+e^{-bt}\kappa $$ So, as \(\Large t\to\infty,~y(t)\to\dfrac 1 b\) if \(\Large b>0\). Otherwise, it diverges.

Looking for something else?

Not the answer you are looking for? Search for more explanations.