anonymous
  • anonymous
What makes a linear differential equation linear?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
A differential equation is linear if it can be written in the form, \[ a_{n}(t) y^{(n)} + a_{n-1}(t) y^{(n-1)}+\cdots+a_{1}(t) y^{\prime}+a_{0}(t) y=g(t) \] where \( y^{(n)}\) is the nth derivative of y. Or, another way to put is it is that the function y and it's derivatives need to be in terms by themselves (i.e. no products/quotients etc of the y or it's derivatives). The function and it's derivatives need to be in the numerator with exponents of 1 and can't be "inside" other functions (i.e. no \( cos(y^{\prime})\), \(e^{y}\), etc)
anonymous
  • anonymous
thank you

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