index of differential equations

Differential equations for functions on $ℝ$

1. General solution, particular solutions, singular solution

2. Equation  y” = f(x) (http://planetmath.org/EquationYFx)

3. Separation of variables

4. ODE types reductible to the variables separable case

5. Exact differential equation

6. Linear differential equation of first order

7. Second order linear differential equation with constant coefficients

8. General solution of linear differential equation

9. Frobenius method

10. Bessel’s equation

11. Chebyshev equation

12. Hermite equation

13. van der Pol equation

14. Hypergeometric equation

15. Laguerre’s differential equation (http://planetmath.org/LaguerrePolynomial)

16. Second order ordinary differential equation

17. Bernoulli equation

18. d’Alembert’s equation (http://planetmath.org/DAlembertsEquation)

19. Clairaut’s equation

20. Riccati equation

Ordinary differential equations

1. Linear ordinary differential equations

2. Differential equation of the isogonal trajectories, the tilt curves

3. Frenet equations

4. Hamilton equations (http://planetmath.org/HamiltonianEquations)

5. Geodesic equation

6. Gradient system

7. Lorenz equation

Partial differential equations

1. Gradient system

2. Euler-Lagrange equations (http://planetmath.org/EulerLagrangeDifferentialEquation)

3. Hamilton equations

4. Heat equation

5. Laplace equation

6. Poisson’s equation

7. Wave equation

8. d’Alembert and D. Bernoulli solutions of wave equation (http://planetmath.org/DAlembertAndDBernoulliSolutionsOfWaveEquation)

9. Helmholtz equation

10. Maxwell’s equations

11. Korteweg - de Vries equation

12. Schrödinger’s wave equation

13. Dirac equation

14. Klein-Gordon equation

15. Hamilton-Jacobi equation

16. Telegraph equation

17. Black-Scholes equation

18. Solved examples:
    a) example of solving the heat equation
    b) time-dependent example of heat equation
    c) using Laplace transform to solve heat equation
    d) solving the wave equation due to D. Bernoulli (http://planetmath.org/SolvingTheWaveEquationByDBernoulli)

Complex

1. Beltrami differential equation

2. Cauchy-Riemann equations

Title	index of differential equations
Canonical name	IndexOfDifferentialEquations
Date of creation	2013-03-22 15:14:44
Last modified on	2013-03-22 15:14:44
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	39
Author	matte (1858)
Entry type	Topic
Classification	msc 35-00
Classification	msc 34-00
Related topic	ClairautsEquation