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## 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?