why is this nonlinear....x(d³y/dx³) - (dy/dx)^5 + y = 0
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Because the derivative of y is raised to the 5th power (dy/dx)^5
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That is a differential equation. Its solution will not be of the form y = mx + c, a linear relationship between x and y. It will not be linear because (dy/dx) is raised to the fifth power and there is also the 3rd. derivative of y with respect to x.