Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
solve the differential equation. assume x,y,t>0
dy/dt=yln(y/2). y(0)=1
 4 months ago
 4 months ago
solve the differential equation. assume x,y,t>0 dy/dt=yln(y/2). y(0)=1
 4 months ago
 4 months ago

This Question is Closed

megannicole51Best ResponseYou've already chosen the best response.0
so i think im doing this right so far but I'm not really sure can someone work through the steps with me?
 4 months ago

ddog1437Best ResponseYou've already chosen the best response.0
are you taking calculus though?
 4 months ago

megannicole51Best ResponseYou've already chosen the best response.0
\[\frac{ dy }{ ylny } = \frac{ 1 }{ 2 }dt\]
 4 months ago

megannicole51Best ResponseYou've already chosen the best response.0
ill show the steps i have so far and can u tell me if im right or not?
 4 months ago

megannicole51Best ResponseYou've already chosen the best response.0
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
 4 months ago

megannicole51Best ResponseYou've already chosen the best response.0
@SithsAndGiggles
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
\[\frac{1}{y \ln (\frac{y}{2})} dy= dt \]
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
He is doing separation of variables.
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
I think he meant to divide yln(y/2) on both sides.
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
and then he multiplied both sides by dt
 4 months ago

SithsAndGigglesBest ResponseYou've already chosen the best response.1
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? \(\color{blue}{\text{End of Quote}}\)
 4 months ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.