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Determine whether the differential equation is linear.$ y' + x \sqrt y = x^2 $

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Calculus 2 / BC

Chapter 9

Differential Equations

Section 5

Linear Equations

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A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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we know there's a very specific form for First Order Lanier Differential Equation. The form is Do I over D axe derivative plus p of x times. Why is Q Becks, this is the formula listed in textbooks. Now, in this case, we have a square root of why term that you could see in the problem. So because of this term, this doesn't follow the formula for our first order when your differential equation. Therefore, we know that it is not a linear differential equation.

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