anonymous
  • anonymous
hi guys, quick question, im busy with differential equations. My question is, if i have dx/dt=2x/t, how could i manipulate this equation so that i get 2x, thats in the numerator, across the equal sign. i need to have x one side and t on the opposite side. Silly question but a little help would be much appreciated. BIG THANKS IN ADVANCE:D
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
its a diffrential equation
anonymous
  • anonymous
tr to move all like terms to one side
anonymous
  • anonymous
t(dx/dt)=2x

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anonymous
  • anonymous
so you will have t/dt=2x/dx
anonymous
  • anonymous
lol thanks, i got that much yes. my problem is, its a little algebra problem, how do i get something out the numerator. like if it were in the denominator, i'd multiply both sides by what ever is in the denominator. here the variable sits in the numerator??
anonymous
  • anonymous
OOOh okay cool. thanks so much;)
anonymous
  • anonymous
now you can take the integral of both sides
triciaal
  • triciaal
|dw:1439920322980:dw|
Michele_Laino
  • Michele_Laino
hint: if we make the separation of variable, we can write: \[\Large \frac{{dx}}{x} = 2\frac{{dt}}{t}\]
anonymous
  • anonymous
LOL YES DEFINITELY!! quick question, how would i do that? I'm new to this site lol
Michele_Laino
  • Michele_Laino
please, in order to integrate that ODE, we can use this identity: \[\Large \int {\frac{{d\xi }}{\xi }} = \ln \xi + C,\quad C \in \mathbb{R}\]
Michele_Laino
  • Michele_Laino
providing that x>0 and t>0
anonymous
  • anonymous
sorry about that @michele_laino, the last message i sent was meant for an earlier post. but thanks so much :D
Michele_Laino
  • Michele_Laino
ok!
anonymous
  • anonymous
tell me quickly, before i go, the, there are like 3 different answers here?
Michele_Laino
  • Michele_Laino
I'm sorry I can not give the answer directly, since it is against the Code of Conduct
anonymous
  • anonymous
There are no different answers, @Michele_Laino is just telling you a formula for your question your job is as simple as \[\frac{1}{2}\int\limits \frac{dx}{x}=\int\limits \frac{dt}{t}\]
anonymous
  • anonymous
don't forget the constant of integration
anonymous
  • anonymous
oh okay sorry about that. thanks again:)

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