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anonymous

  • 4 years ago

who to identify that the given differential equation is homogeneous and linear

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  1. anonymous
    • 4 years ago
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    I think it was homogenous if it didnt have a constant in the equation. And its linear if it doesnt have any of the \(y^2, y^3\) etc. or \(y'*y\) or \(y'^2\). I'm not sure if \(x^2\) parts ruins the linearity of the equation.

  2. anonymous
    • 4 years ago
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    can you tell me what homogeneous equation actually means

  3. anonymous
    • 4 years ago
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    http://en.wikipedia.org/wiki/Homogeneous_differential_equation

  4. mathmate
    • 4 years ago
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    Linear: the equation contains only y' or y terms, without y^2, y^4, (y')^2 etc in the equation. Homogeneous Examples: \(y′+4x^2y=0\) is a homogeneous differential equation. \(y′+6x^2y=5 \) is inhomogeneous For a linear equation, if you have non-zero terms that do not contain y or y', it is not homogeneous.

  5. anonymous
    • 4 years ago
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    the second equation in the example you gave is linear ?

  6. amistre64
    • 4 years ago
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    there are 2 definitions of homogenous

  7. amistre64
    • 4 years ago
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    the usual definition meaning: this = 0 the other is: f(x,y) such that T(tx,ty) = t f(x,y) or some such

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