List of solution strategies for differential equations

Exact methods

• Method of undetermined coefficients
• Integrating factor

For $y'+a(x)y = b(x)$ let $M(x)=\exp{\int a(x)\,dx}$ then

$y(x) = \frac{\int b(x) M(x)\, dx + C}{M(x)}.\,$

• Method of variation of parameters
• Separable differential equation

Approximate (but convergent) methods

• Successive Approximations
• Perturbation Theory
• Multiple scale Analysis
• Series solution
  • Power series solution of differential equations
    • Relation of power series solutions to Taylor series of solution function
  • Generalized Fourier series (see orthogonal functions)

Numerical methods

Main article:

• ODE's: List of numerical methods for ordinary differential equations
• PDE's: List of numerical methods for partial differential equations

See also

• Examples of differential equations
• Table of integrals