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Determine the values of the constants $r$ and $s$ such that $I(x, y)=x^{r} y^{s}$ is an integrating factor for the given differential equation.$$2 y\left(y+2 x^{2}\right) d x+x\left(4 y+3 x^{2}\right) d y=0$$

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Calculus 2 / BC

Chapter 1

First-Order Differential Equations

Section 9

Exact Differential Equations

Differential Equations

Missouri State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

13:37

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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