Differential Equation Calculator

Solve differential equations step by step

Equation Input

Input Format:

  • • Use y' for first derivative
  • • Use y'' for second derivative
  • • Use * for multiplication
  • • Use ^ for exponents
  • • Include = sign in equation

Understanding Differential Equations

Types of Equations

  • • First-order: Contains only first derivatives
  • • Second-order: Contains second derivatives
  • • Linear: Variable and derivatives appear linearly
  • • Separable: Variables can be separated

Solution Methods

  • • Separation of variables
  • • Integrating factor method
  • • Characteristic equation
  • • Variation of parameters

Applications

Physics

  • • Motion equations
  • • Wave equations
  • • Heat transfer
  • • Quantum mechanics

Engineering

  • • Circuit analysis
  • • Control systems
  • • Structural analysis
  • • Fluid dynamics

Biology

  • • Population growth
  • • Disease spread
  • • Chemical reactions
  • • Neural networks