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Determine whether the differential equation is linear or nonlinear.$$y y^{\prime \prime}+x\left(y^{\prime}\right)-y=4 x \ln x$$.

nonlinear

Calculus 2 / BC

Chapter 1

First-Order Differential Equations

Section 2

Basic Ideas and Terminology

Differential Equations

Missouri State University

Campbell University

University of Nottingham

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in this problem. We want to decide if this equation circled in blue is linear differential equation or not. And to do so, we can write the equation in terms of some function a two of X as the coefficient of why double prime plus a one is the coefficient of y prime, um, and a zero as the coefficient of why equal to some function of X. And we want to make sure that the A two a one a zero and f of X are all functions of Onley acts not functions of why Well, that's true. In this case, X is a function of X and in this case, negative one. That's a function of X. It's not a function of why. And over here are ffx um four x times Ellen of X. That is a function of X and not a function of why, however, in the beginning here are coefficient toe. Why double prime is why, which is a function of why. Therefore, this is not a linear differential. Quick

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