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baldymcgee6

  • 2 years ago

Solve dx/dt = = (1+sqrt(t))/(1+sqrt(x))

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  1. baldymcgee6
    • 2 years ago
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    \[\frac{ dx }{ dt } = \frac{ 1+\sqrt{t} }{ 1+\sqrt{x} }\]

  2. baldymcgee6
    • 2 years ago
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    i ended up with something, but I cant explicitly solve for t

  3. baldymcgee6
    • 2 years ago
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    The way we were tough is to separate the variables and then integrate each side.

  4. baldymcgee6
    • 2 years ago
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    taught*

  5. baldymcgee6
    • 2 years ago
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    that's not how we were taught to do it.. http://en.wikipedia.org/wiki/Separation_of_variables

  6. ksaimouli
    • 2 years ago
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    hmm sorry i have not yet learned those so sorry what chapter is this

  7. baldymcgee6
    • 2 years ago
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    What chapter? It would depend what textbook. And what class.

  8. ksaimouli
    • 2 years ago
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    i mean name of the chapter

  9. baldymcgee6
    • 2 years ago
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    its on ODE's

  10. ksaimouli
    • 2 years ago
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    is this college calculus

  11. baldymcgee6
    • 2 years ago
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    yeah calc 2

  12. ksaimouli
    • 2 years ago
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    okay

  13. wio
    • 2 years ago
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    It's separable, no?

  14. abb0t
    • 2 years ago
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    :O I think it is separable!

  15. wio
    • 2 years ago
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    Multiply both sides by \(1+\sqrt{x}\). Integrate with respect to \(t\).

  16. oldrin.bataku
    • 2 years ago
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    This is very clearly a separable first-order ordinary differential equation. We can easily separate as follows: $$\frac{dx}{dt}=\frac{1+\sqrt{t}}{1+\sqrt{x}}\\(1+\sqrt{x})\ dx=(1+\sqrt{t})\ dt$$Now, it should be clear that we integrate both sides.$$\int(1+\sqrt{x})\ dx=\int(1+\sqrt{t})\ dt\\x+\frac23x^\frac32=t+\frac23t^\frac32+C$$ This yields an implicit solution; for an explicit one, you'll need to isolate \(x\)... it won't be pretty.

  17. baldymcgee6
    • 2 years ago
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    @oldrin.bataku thanks for the reply, that is the same thing I did, but I couldn't figure out how to get an explicit solution. I suppose I will leave it at this. Thank you

  18. oldrin.bataku
    • 2 years ago
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    I *highly* doubt your teacher wants an explicit solution ;-) http://www.wolframalpha.com/input/?i=solve+x+%2B+2%2F3+x%5E%283%2F2%29+%3D+t+%2B+2%2F3+t%5E%283%2F2%29%2Bc

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