Determine whether the following ordinary differential equation cosh (3/y) - In(7y)y" = 11cos(4yx) - y³y¹ + 9x is linear or nonlinear by matching it with the differential equation an(x) dny dx" +an-1(x) an-ly + dxn-1 + a₁(x) dy + ao(x)y= g(x) dx Linear Nonlinear
Determine whether the following ordinary differential equation cosh (3/y) - In(7y)y" = 11cos(4yx) - y³y¹ + 9x is linear or nonlinear by matching it with the differential equation an(x) dny dx" +an-1(x) an-ly + dxn-1 + a₁(x) dy + ao(x)y= g(x) dx Linear Nonlinear
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Determining the Linearity of a Given Ordinary Differential Equation
**Question: Determine whether the following ordinary differential equation is linear or nonlinear by matching it with the standard form shown below:**
\[ \cosh\left(\frac{3}{y}\right) - \ln(7y) y'' = 11 \cos(4yx) - y^3 y' + 9x \]
**Standard Form of a Linear Ordinary Differential Equation:**
\[ a_n(x) \frac{d^n y}{dx^n} + a_{n-1}(x) \frac{d^{n-1} y}{dx^{n-1}} + \cdots + a_1(x) \frac{dy}{dx} + a_0(x) y = g(x) \]
**Answer Options:**
- Linear
- Nonlinear](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e521a1e-f4ee-4c02-af71-8dfc2cc184d3%2Fe735d674-fa07-4a24-ad84-144554de658a%2Fn1ifm6_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining the Linearity of a Given Ordinary Differential Equation
**Question: Determine whether the following ordinary differential equation is linear or nonlinear by matching it with the standard form shown below:**
\[ \cosh\left(\frac{3}{y}\right) - \ln(7y) y'' = 11 \cos(4yx) - y^3 y' + 9x \]
**Standard Form of a Linear Ordinary Differential Equation:**
\[ a_n(x) \frac{d^n y}{dx^n} + a_{n-1}(x) \frac{d^{n-1} y}{dx^{n-1}} + \cdots + a_1(x) \frac{dy}{dx} + a_0(x) y = g(x) \]
**Answer Options:**
- Linear
- Nonlinear
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