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Determine whether the differential equation is linear or nonlinear.$$\sin x \cdot y^{\prime \prime}+y^{\prime}-\tan y=\cos x$$.

nonlinear

Calculus 2 / BC

Chapter 1

First-Order Differential Equations

Section 2

Basic Ideas and Terminology

Differential Equations

Missouri State University

Campbell University

Boston College

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in this problem, we want to decide whether this equation in blue is a linear differential equation or not to do so. We can write it in the form of a to some function as a coefficient of why double prime Plus a one, which is some function that's coefficient of y prime and a zero. The coefficient of why and set it equal to F of X, some function of X 24 to be a linear differential equation. We need that a two a one a zero and f of X are all functions of X on Lee and not functions of why? Well, that's the case for Sine X. Um, it's the case for the coefficient of y prime. That's not a function of why it's just one. That's not the case, though, unfortunately for the coefficient of why here? Because why is inside this tangent function so this is a function of why right here? Therefore, we do not have a linear differential

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