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awfawef

  • 2 years ago

*Solve the differential equation dy/dx=x/16y. *Find the equation of the solution through the point (x,y)=(−4,1). *Find the equation of the solution through the point (x,y)=(0,−4). Your answer should be of the form y=f(x)

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  1. awfawef
    • 2 years ago
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    I already solved the first part. C=8y^2 -(x^2/2)

  2. myininaya
    • 2 years ago
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    ok replace your x and y with -4 and 1 respectively to find the C so that your graph for your equation will go through that point

  3. awfawef
    • 2 years ago
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    so y=sqrt((x^2/16) + c) and i plugged in (-4,1) and got y=sqrt((x^2/16) is that correct?

  4. awfawef
    • 2 years ago
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    c= 0 for the second question?

  5. myininaya
    • 2 years ago
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    You have \[C=8y^2-\frac{x^2}{2}\] Replace x with -4 and y with 1 like this: \[C=8(1)^2-\frac{(-4)^2}{2}\] Is this what you did to solve for C?

  6. myininaya
    • 2 years ago
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    \[C=8-\frac{16}{2}=8-8=0\]

  7. awfawef
    • 2 years ago
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    yes that's what i did

  8. myininaya
    • 2 years ago
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    I can't do arithmetic somethings lol But you have \[0=8y^2-\frac{x^2}{2} \]

  9. myininaya
    • 2 years ago
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    that is the equation satisfying the point (-4,1)

  10. awfawef
    • 2 years ago
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    hmm it the system doesn't seem to accept it.. it says it isn't a linear equation

  11. awfawef
    • 2 years ago
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    doesn't that mean i have to solve for y=...

  12. myininaya
    • 2 years ago
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    Your differential equation was: \[\frac{dy}{dx}=\frac{x}{16y} \text{ \right ?} \]

  13. awfawef
    • 2 years ago
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    yup

  14. myininaya
    • 2 years ago
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    Ok solve for y make sure you keep in mind we want to go through the point (-4,1)

  15. awfawef
    • 2 years ago
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    ok so y=x/4

  16. awfawef
    • 2 years ago
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    but it still doesn't work??

  17. awfawef
    • 2 years ago
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    oh wait y=-x/4 works!!

  18. myininaya
    • 2 years ago
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    We wanted y=-x/4 That is why I said to keep in mine we want it going through (-4,1) :)

  19. myininaya
    • 2 years ago
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    mind*

  20. myininaya
    • 2 years ago
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    The equation y=x/4 doesn't satisfy the point (-4,1) but y=-x/4 does

  21. myininaya
    • 2 years ago
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    Like 1=-(-4)/4

  22. awfawef
    • 2 years ago
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    ohh i get it now

  23. awfawef
    • 2 years ago
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    thanks a lot!!

  24. awfawef
    • 2 years ago
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    i'm going to do the last part now

  25. awfawef
    • 2 years ago
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    c=128 for the last part right?

  26. awfawef
    • 2 years ago
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    oh i got the last part too!!

  27. awfawef
    • 2 years ago
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    thanks a lot again!!!

  28. myininaya
    • 2 years ago
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    yes C=128 for the last one

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