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anonymous

  • 5 years ago

hey I need to find out whether a few differential equations are separable, first order linear, both, or neither. one of the equations is y'+4y^2=0

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  1. watchmath
    • 5 years ago
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    non linear since we have a y^2 there and it is separable since we can rewrite as dy/(-4y^2)=dt

  2. anonymous
    • 5 years ago
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    ok I understand the linear equation part, but not so much the separable part.

  3. watchmath
    • 5 years ago
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    what is your definition for separable differential eq.?

  4. anonymous
    • 5 years ago
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    an equations that has y'=f(x)g(y)

  5. watchmath
    • 5 years ago
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    ok, then y'=(-4)y^2 and you can take f(x)=-4 and g(y)=y^2

  6. anonymous
    • 5 years ago
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    ok thanks, and for first order linear just look for highest power of y?

  7. anonymous
    • 5 years ago
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    some of the equations have x's

  8. watchmath
    • 5 years ago
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    not the power of y but what is the highest derivative that you have for example y'''+xy'-x^3=e^x is linear of order 3

  9. anonymous
    • 5 years ago
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    ok thanks

  10. anonymous
    • 5 years ago
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    would y''+x^2y+z=0 be separable?

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