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S

  • 3 years ago

Use separation of variables to solve differential equation: dy/dt=t/((y+1)^1/2)), y(1)=3 ???

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  1. dumbcow
    • 3 years ago
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    use algebra to get "t" terms with dt on one side, and "y" terms with dy on other side you might try cross-multiplying here

  2. S
    • 3 years ago
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    thanks, I know that step, right now I am stuck with interval part

  3. Algebraic!
    • 3 years ago
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    interval integral?

  4. S
    • 3 years ago
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    correct, sorry

  5. dumbcow
    • 3 years ago
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    oh ok, you didn't say so i thought i'd start from beginning :) im guessing the sqrt(y+1) part

  6. Algebraic!
    • 3 years ago
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    if you can't do the 'y' part in your head... use u=y+1 du =dy \[{ \int\limits_{}^{}} \sqrt{u} du =?\]

  7. dumbcow
    • 3 years ago
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    sqrt is 1/2 power ... just use power rule

  8. S
    • 3 years ago
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    so I get 1/2(y+1)^-1/2=t^2/2 ?

  9. Algebraic!
    • 3 years ago
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    \[\int\limits_{ }^{ } x ^{n} = \frac{ 1 }{ n+1 } * x ^{n+1}\]

  10. Algebraic!
    • 3 years ago
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    n here = 1/2

  11. S
    • 3 years ago
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    i got 2/3(Y+1)^3/2=t^2/2, right?

  12. dumbcow
    • 3 years ago
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    yes ... but don't forget constant "+C" on right side

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