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anonymous

  • 5 years ago

How would I use an exact differential equation to solve dy/dt=((-e)^y)/(t(e^y)+2y)?

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  1. anonymous
    • 5 years ago
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    hey

  2. anonymous
    • 5 years ago
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    get it into M(x,y)dx + N(x,y)dy = 0

  3. anonymous
    • 5 years ago
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    How? I've only ever seen this type of equation as a very simple example already in the form M(x,y)dx + N(x,y)dy = 0. How would I separate this one?

  4. anonymous
    • 5 years ago
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    or M(t,y) dt + N(t,y)dy = 0

  5. anonymous
    • 5 years ago
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    i have dy(t e^y + 2y ) = (-e^y dt

  6. anonymous
    • 5 years ago
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    so you start it like the solution to a separable function?

  7. anonymous
    • 5 years ago
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    so e^y dt + (te^y + 2y ) dy = 0

  8. anonymous
    • 5 years ago
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    THANK YOU SO MUCH!

  9. anonymous
    • 5 years ago
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    I don't know why I couldn't separate that on my own.

  10. anonymous
    • 5 years ago
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    i have the formula, its a bit long

  11. anonymous
    • 5 years ago
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    first we have to check that My = Nt ,

  12. anonymous
    • 5 years ago
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    the partial of M(t,y) with respect to y

  13. anonymous
    • 5 years ago
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    deriv wrt to y M(t,y) = e^y and deriv wrt to y N(t,y) = e^y , so its an exact equation

  14. anonymous
    • 5 years ago
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    here http://www.twiddla.com/493184

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