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## Homework Statement

Is this differential equation linear or nonlinear? Assume that y' means dy/dx.

## Homework Equations

1. Homework Statement [/b]

Is this differential equation linear or nonlinear? Assume that y' means dy/dx.

## Homework Equations

[itex]\sqrt{xy'+2x

^{2}}[/itex]=5

## The Attempt at a Solution

It seems to me that squaring both sides and subtracting 2x

^{2}from both sides renders a linear equation:

xy' + 2x

^{2}=25.

xy' = 25 - 2x

^{2}

This is of the form

a

_{n}(x)y

^{(n)}+ a

_{n-1}(x)y

^{(n-1)}+ ... a

_{0}(x)y=g(x)

if you take a

_{0}= 0... isn't it?

The problem is that my professor says otherwise; namely, that it is a nonlinear DE.

Where am I making my mistake?

Thanks.