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megannicole51
 one year ago
solve the differential equation. assume x,y,t>0
dy/dt=yln(y/2). y(0)=1
megannicole51
 one year ago
solve the differential equation. assume x,y,t>0 dy/dt=yln(y/2). y(0)=1

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megannicole51
 one year ago
Best ResponseYou've already chosen the best response.0so i think im doing this right so far but I'm not really sure can someone work through the steps with me?

ddog1437
 one year ago
Best ResponseYou've already chosen the best response.0are you taking calculus though?

megannicole51
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ dy }{ ylny } = \frac{ 1 }{ 2 }dt\]

megannicole51
 one year ago
Best ResponseYou've already chosen the best response.0ill show the steps i have so far and can u tell me if im right or not?

megannicole51
 one year ago
Best ResponseYou've already chosen the best response.0ive 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
 one year ago
Best ResponseYou've already chosen the best response.0@SithsAndGiggles

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{y \ln (\frac{y}{2})} dy= dt \]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1He is doing separation of variables.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1I think he meant to divide yln(y/2) on both sides.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1and then he multiplied both sides by dt

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.1Thanks 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? \(\color{blue}{\text{End of Quote}}\)
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