Math Problem Statement
Solve the problem
Solution
The differential equation provided is:
This is a second-order linear ordinary differential equation with constant coefficients. The hint indicates that the auxiliary polynomial has two real roots, suggesting a particular solution structure.
Step 1: Homogeneous Form
To solve this, we begin by rewriting the equation in standard form:
Now, the equation is:
Step 2: Solving the Homogeneous Equation
First, let's solve the homogeneous part of the equation, i.e., when :
The auxiliary equation for this differential equation is:
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Second-Order Linear ODEs
Formulas
m(d^2x/dt^2) + r(dx/dt) - mg = 0
Auxiliary equation: mλ^2 + rλ = 0
Theorems
Solution of second-order differential equations with constant coefficients
Suitable Grade Level
Undergraduate level (Calculus/Differential Equations)
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