## anonymous one year ago 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

1. anonymous

its a diffrential equation

2. anonymous

tr to move all like terms to one side

3. anonymous

t(dx/dt)=2x

4. anonymous

so you will have t/dt=2x/dx

5. 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??

6. anonymous

OOOh okay cool. thanks so much;)

7. anonymous

now you can take the integral of both sides

8. triciaal

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9. Michele_Laino

hint: if we make the separation of variable, we can write: $\Large \frac{{dx}}{x} = 2\frac{{dt}}{t}$

10. anonymous

LOL YES DEFINITELY!! quick question, how would i do that? I'm new to this site lol

11. Michele_Laino

please, in order to integrate that ODE, we can use this identity: $\Large \int {\frac{{d\xi }}{\xi }} = \ln \xi + C,\quad C \in \mathbb{R}$

12. Michele_Laino

providing that x>0 and t>0

13. anonymous

sorry about that @michele_laino, the last message i sent was meant for an earlier post. but thanks so much :D

14. Michele_Laino

ok!

15. anonymous

tell me quickly, before i go, the, there are like 3 different answers here?

16. Michele_Laino

I'm sorry I can not give the answer directly, since it is against the Code of Conduct

17. anonymous

There are no different answers, @Michele_Laino is just telling you a formula for your question your job is as simple as $\frac{1}{2}\int\limits \frac{dx}{x}=\int\limits \frac{dt}{t}$

18. anonymous

don't forget the constant of integration

19. anonymous

oh okay sorry about that. thanks again:)