anonymous
  • anonymous
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
Mathematics
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anonymous
  • anonymous
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
Mathematics
jamiebookeater
  • jamiebookeater
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watchmath
  • watchmath
non linear since we have a y^2 there and it is separable since we can rewrite as dy/(-4y^2)=dt
anonymous
  • anonymous
ok I understand the linear equation part, but not so much the separable part.
watchmath
  • watchmath
what is your definition for separable differential eq.?

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anonymous
  • anonymous
an equations that has y'=f(x)g(y)
watchmath
  • watchmath
ok, then y'=(-4)y^2 and you can take f(x)=-4 and g(y)=y^2
anonymous
  • anonymous
ok thanks, and for first order linear just look for highest power of y?
anonymous
  • anonymous
some of the equations have x's
watchmath
  • watchmath
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
anonymous
  • anonymous
ok thanks
anonymous
  • anonymous
would y''+x^2y+z=0 be separable?

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