Linearity in Differential Equations

  • #1

Homework Statement



Is the following differential equation linear:

[itex]yy' + 2 = 0[/itex]

The Attempt at a Solution



I have the definition of linear as being [itex]a_0 (t) y^{(n)} + a_1(t) y^{n-1} + a_2 (t) y^{n-2} ... = 0[/itex]. Now, presumably y is a function of t. Thus, I could define [itex]y = a_0 (t) [/itex] and let n=1. Thus I would satisfy my definition of linearity in differential equations. Thus, the differential equation is linear.

Is it not so?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
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No, [itex]a_0(t)[/itex] has to be a known function of t, not y or anything involving y. This equation is non-linear because you have a product of things "involving" the dependent variable y.
 

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