Struct ODEExamples 

pub struct ODEExamples;

Collection of educational ODE examples

Implementations

impl ODEExamples

pub fn separable_simple() -> ODEExplanation

Example: Simplest separable ODE dy/dx = x

Solution

y = x²/2 + C

Common Pitfalls

• Forgetting the constant of integration
• Incorrect integration of x (getting x²/2 instead of x²/2)

pub fn exponential_growth() -> ODEExplanation

Example: Exponential growth dy/dx = y

Solution

y = C·e^x

Common Pitfalls

• Forgetting absolute value in ln|y| = x + C
• Incorrect handling of integration constant when exponentiating
• Not recognizing this as both separable and linear

pub fn linear_first_order() -> ODEExplanation

Example: Linear first-order dy/dx + y = x

Solution

y = x - 1 + C·e^(-x)

Common Pitfalls

• Incorrectly computing integrating factor μ(x) = e^(∫P(x)dx)
• Forgetting to multiply Q(x) by μ(x) before integrating
• Sign errors in the exponent

pub fn product_separable() -> ODEExplanation

Example: Product form dy/dx = xy

Solution

y = C·e^(x²/2)

Common Pitfalls

• Incorrectly integrating x to get x²/2 vs x²
• Forgetting to include constant in exponential
• Not simplifying e^(x²/2 + C) to C’·e^(x²/2)

pub fn initial_value_problem() -> ODEExplanation

Example: Initial value problem dy/dx = x, y(0) = 1

Solution

y = x²/2 + 1

Common Pitfalls

• Forgetting to apply initial condition
• Incorrectly solving for constant C
• Not verifying that y(0) = 1 in final solution

pub fn all_examples() -> Vec<ODEExplanation>

Get all example explanations

pub fn get_example(name: &str) -> Option<ODEExplanation>

Get example by name

pub fn example_names() -> Vec<&'static str>

Get list of available example names