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

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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

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its a diffrential equation
tr to move all like terms to one side
t(dx/dt)=2x

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

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