# index of differential equations

## Differential equations for functions on $\mathbbmss{R}$

1. 1.

General solution, particular solutions, singular solution

2. 2.

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

3. 3.
4. 4.

ODE types reductible to the variables separable case

5. 5.
6. 6.
7. 7.
8. 8.
9. 9.
10. 10.

Bessel’s equation

11. 11.
12. 12.
13. 13.
14. 14.
15. 15.

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

16. 16.
17. 17.
18. 18.

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

19. 19.

Clairaut’s equation

20. 20.

## Ordinary differential equations

1. 1.
2. 2.

Differential equation of the isogonal trajectories, the tilt curves

3. 3.
4. 4.

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

5. 5.
6. 6.
7. 7.

## Partial differential equations

1. 1.

2. 2.

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

3. 3.

Hamilton equations

4. 4.
5. 5.
6. 6.

Poisson’s equation

7. 7.
8. 8.

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

9. 9.
10. 10.

Maxwell’s equations

11. 11.

Korteweg - de Vries equation

12. 12.

Schrödinger’s wave equation

13. 13.
14. 14.
15. 15.

Hamilton-Jacobi equation

16. 16.
17. 17.

Black-Scholes equation

18. 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

Title index of differential equations IndexOfDifferentialEquations 2013-03-22 15:14:44 2013-03-22 15:14:44 matte (1858) matte (1858) 39 matte (1858) Topic msc 35-00 msc 34-00 ClairautsEquation