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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

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  1. anonymous
    • one year ago
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    its a diffrential equation

  2. anonymous
    • one year ago
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    tr to move all like terms to one side

  3. anonymous
    • one year ago
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    t(dx/dt)=2x

  4. anonymous
    • one year ago
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    so you will have t/dt=2x/dx

  5. anonymous
    • one year ago
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    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
    • one year ago
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    OOOh okay cool. thanks so much;)

  7. anonymous
    • one year ago
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    now you can take the integral of both sides

  8. triciaal
    • one year ago
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    |dw:1439920322980:dw|

  9. Michele_Laino
    • one year ago
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    hint: if we make the separation of variable, we can write: \[\Large \frac{{dx}}{x} = 2\frac{{dt}}{t}\]

  10. anonymous
    • one year ago
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    LOL YES DEFINITELY!! quick question, how would i do that? I'm new to this site lol

  11. Michele_Laino
    • one year ago
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    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
    • one year ago
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    providing that x>0 and t>0

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

  14. Michele_Laino
    • one year ago
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    ok!

  15. anonymous
    • one year ago
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    tell me quickly, before i go, the, there are like 3 different answers here?

  16. Michele_Laino
    • one year ago
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    I'm sorry I can not give the answer directly, since it is against the Code of Conduct

  17. anonymous
    • one year ago
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    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
    • one year ago
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    don't forget the constant of integration

  19. anonymous
    • one year ago
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    oh okay sorry about that. thanks again:)

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