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Find the order of the given DE. Also, decide if the DE is linear or nonlinear. (a) + yx = x (b) 1- y3 = 3x (c) y'- Iny = 0 (d) + 2 + = 2sin(x) %3D

Find the order of the given DE. Also, decide if the DE is linear or nonlinear. (a) + yx = x (b) 1- y3 = 3x (c) y'- Iny = 0 (d) + 2 + = 2sin(x) %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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## Question 4 Find the order of the given differential equations (DE). Also, decide if the DE is linear or nonlinear. (a) \(\frac{dy}{dx} + y^2x = x\) (b) \(\frac{1}{x} \frac{d^2y}{dx^2} - y^3 = 3x\) (c) \(y' - \ln y = 0\) (d) \(\frac{d^3y}{dx^3} + 2\frac{d^2y}{dx^2} + \frac{dy}{dx} = 2\sin(x)\) ### Explanation of Concepts - **Order of a Differential Equation**: The highest derivative present in the equation. - **Linear vs Nonlinear**: A differential equation is linear if it can be written in the form where all the derivatives of the function are of the first degree, and the function itself is not multiplied or divided by another function of itself. Otherwise, it is nonlinear.
Transcribed Image Text:## Question 4 Find the order of the given differential equations (DE). Also, decide if the DE is linear or nonlinear. (a) \(\frac{dy}{dx} + y^2x = x\) (b) \(\frac{1}{x} \frac{d^2y}{dx^2} - y^3 = 3x\) (c) \(y' - \ln y = 0\) (d) \(\frac{d^3y}{dx^3} + 2\frac{d^2y}{dx^2} + \frac{dy}{dx} = 2\sin(x)\) ### Explanation of Concepts - **Order of a Differential Equation**: The highest derivative present in the equation. - **Linear vs Nonlinear**: A differential equation is linear if it can be written in the form where all the derivatives of the function are of the first degree, and the function itself is not multiplied or divided by another function of itself. Otherwise, it is nonlinear.
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