megannicole51
  • megannicole51
solve the differential equation. assume x,y,t>0 dy/dt=-yln(y/2). y(0)=1
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.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
megannicole51
  • megannicole51
so i think im doing this right so far but I'm not really sure can someone work through the steps with me?
anonymous
  • anonymous
are you taking calculus though?
megannicole51
  • megannicole51
calc 2

Looking for something else?

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

More answers

megannicole51
  • megannicole51
\[\frac{ dy }{ -ylny } = \frac{ 1 }{ 2 }dt\]
megannicole51
  • megannicole51
ill show the steps i have so far and can u tell me if im right or not?
megannicole51
  • megannicole51
ive never seen it done like that actually....my professor hasnt really done any examples so i am trying to figure it out from our book which isnt helping either
megannicole51
  • megannicole51
@SithsAndGiggles
myininaya
  • myininaya
\[\frac{-1}{y \ln (\frac{y}{2})} dy= dt \]
myininaya
  • myininaya
He is doing separation of variables.
myininaya
  • myininaya
I think he meant to divide -yln(y/2) on both sides.
myininaya
  • myininaya
and then he multiplied both sides by dt
anonymous
  • anonymous
Thanks to @myininaya for pointing out my mistake: \(\color{blue}{\text{Originally Posted by}}\) @SithsAndGiggles \[\frac{dy}{dt}=-y\ln\left(\frac{y}{2}\right)\\ -\frac{1}{y\ln\left(\frac{y}{2}\right)}~dy=dt\] Integrate both sides: \[-\int\frac{1}{y\ln\left(\frac{y}{2}\right)}~dy=\int dt\] First, a substitution: \(u=\dfrac{y}{2}\), or \(2u=y\), so that \(2du=dy\): \[-\int\frac{1}{2u\ln u}~(2~du)=\int dt\\ -\int\frac{1}{u \ln u}~du=\int dt\] Got everything so far? \(\color{blue}{\text{End of Quote}}\)

Looking for something else?

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