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anonymous

  • 5 years ago

given y>0 and dy/dx=3x^2+4x/y. if the point (1,sqrt{10}) is on the graph relating x and y, then what is y when x=0?

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  1. myininaya
    • 5 years ago
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    do you know to find y given y'?

  2. anonymous
    • 5 years ago
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    dy/dx

  3. anonymous
    • 5 years ago
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    ?

  4. myininaya
    • 5 years ago
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    you have to integrate y' to get y

  5. myininaya
    • 5 years ago
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    oh wait

  6. myininaya
    • 5 years ago
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    i didn't see that other y

  7. myininaya
    • 5 years ago
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    is it \[y'=\frac{3x^2+4x}{y} ?\]

  8. anonymous
    • 5 years ago
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    yes

  9. myininaya
    • 5 years ago
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    ok do you know separation of variables?

  10. anonymous
    • 5 years ago
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    quotient rule product rule ?

  11. myininaya
    • 5 years ago
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    \[\frac{dy}{dx}=\frac{3x^2+4x}{y}\] you want y so we need to integrate but before we do that we need to separate our y's from our x's

  12. myininaya
    • 5 years ago
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    \[y dy=(3x^2+4x) dx\]

  13. anonymous
    • 5 years ago
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    oh yes i know how to do that

  14. myininaya
    • 5 years ago
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    i multiplied y on both sides and I multiplied dx on both sides now we need to integrate both sides

  15. myininaya
    • 5 years ago
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    \[\int\limits_{}^{}y dy=\int\limits_{}^{}(3x^2+4x) dx\]

  16. anonymous
    • 5 years ago
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    whats that long thing u just put

  17. myininaya
    • 5 years ago
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    \[\frac{y^2}{2}=\frac{3x^3}{3}+\frac{4x^2}{2}+C\] whenever you integrate you need to do +C

  18. anonymous
    • 5 years ago
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    i havent learned that thing yet

  19. myininaya
    • 5 years ago
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    its the only way

  20. myininaya
    • 5 years ago
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    what about finding the antiderivative?

  21. myininaya
    • 5 years ago
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    do you know what that means?

  22. anonymous
    • 5 years ago
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    i learned that friday

  23. anonymous
    • 5 years ago
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    yes

  24. myininaya
    • 5 years ago
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    thats with weird symbol means

  25. myininaya
    • 5 years ago
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    what*

  26. anonymous
    • 5 years ago
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    but i dont think i can use that symbol yet

  27. myininaya
    • 5 years ago
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    hmmm... that's weird to me

  28. anonymous
    • 5 years ago
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    oh :/

  29. anonymous
    • 5 years ago
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    its fine i guess i should skip that problem and just ask the teacher 2morrow. ill put up a new one.

  30. myininaya
    • 5 years ago
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    ok but that is all i did was found the antiderivative of both sides with respect to whatever varaible was in d( )

  31. anonymous
    • 5 years ago
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    oh okay thanks either way :)

  32. myininaya
    • 5 years ago
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    np

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