Differential Equations

Ist order equations

\[ \frac{dy}{dx} = f(x, y) \]

Types

• Variable Separable
• Homogeneous Equations
• Reducible to Homogeneous
• Exact Differential Equations
• Reducible to Exact
  • Using Integration Factor
• Linear Equation
• Reducible to Linear
  • Bernoulli's equation

Application

• Netwon's law of cooling
• Law of natural growth

Higher order Linear Differential Equations

General case, $$ y^{(n)} + p_1y^{(n-1)} + \cdots + p_ny = f(x) $$

With constant coefficients,

\[ y^{(n)} + k_1y^{(n-1)} + \cdots + k_ny = f(x) \]