Number 2 practice ### Exercises 1.1In Problems 1–8, state the order of the given ordinary differential equation. Determine whether the equation is linear or nonlinear by matching it with (6).1. \((1 - x)y''' - 4xy' + 5y = \cos x\)2. \(x \frac{d^3 y}{dx^3} \left( \frac{dy}{dx} \right)^4 + y = 0\)3. \(t^5 y^{(4)} - t^3 y''' + 6y = 0\)4. \(\frac{d^2 u}{dr^2} + \frac{du}{dr} + u = \cos(r + u)\)5. \(\frac{d^2 x}{dz^2} = \sqrt{1 + \left( \frac{dy}{dx} \right)^2}\)6. \(\frac{d^2 R}{dt^2} = \frac{k}{R^2}\)Ensure to analyze each equation to identify its order (the highest derivative present) and determine whether it is linear or nonlinear based on its form and the presence of any products, quotients, or powers of the function and its derivatives.- **Graph or Diagram Description:**There are no graphs or diagrams included in this image. The content consists solely of ordinary differential equations.This content would be suitable for an educational setting, focusing on the identification and classification of differential equations.

Name: Number 2 practice ### Exercises 1.1In Problems 1–8, state the order of
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Number 2 practice ### Exercises 1.1In Problems 1–8, state the order of the given ordinary differential equation. Determine whether the equation is linear or nonlinear by matching it with (6).1. \((1 - x)y''' - 4xy' + 5y = \cos x\)2. \(x \frac{d^3 y}{