#2 # Lesson on Ordinary Differential Equations (ODEs)## Problem Set### 1. Analysis of Differential EquationsFor each ODE below, provide the order, indicate the dependent and independent variables, and determine whether the DE is linear or nonlinear.#### (a) Shortest Time Problem, Galileo 1630:\[ y \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right] = C \]#### (b) Van der Pol’s Equation, Triode Vacuum Tube:\[ \frac{d^2y}{dx^2} - 0.1(1 - y^2)\frac{dy}{dx} + 9y = 0 \]#### (c) Third Order Differential Equation:\[ t^3\frac{dx}{dt} = t^3 + xt \]#### (d) Second Order Differential Equation:\[ \frac{d^2y}{dx^2} - y \frac{dy}{dx} = \cos x \]#### (e) Mixed Order and Nonlinear Differential Equation:\[ x^2 \frac{dy}{dx} + \sin x - y = 0 \]### 2. Formulate a Differential Equation Based on Physical Descriptions#### (a) The velocity at time \( t \) of a particle moving along a straight line is proportional to the fourth power of its position.#### (b) The rate of change of the mass \( A \) of salt at time \( t \) is proportional to the square of the mass present at time \( t \).Use the above problems to practice identifying the characteristics of differential equations and applying physical descriptions to formulate appropriate mathematical models.

Name: #2 # Lesson on Ordinary Differential Equations (ODEs)## Problem Set###
Uploaded: 2024-03-20T07:06:41.000Z
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Description: #2 # Lesson on Ordinary Differential Equations (ODEs)## Problem Set### 1. Analysis of Differential EquationsFor each ODE below, provide the order, indicate the dependent and independent variables, and determine whether the DE is linear or nonlinear.#