index of differential equations

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

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

单词	IndexOfDifferentialEquations
释义	index of differential equations Differential equations for functions on $\\mathbbmss{R}$ 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
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index of differential equations

Differential equations for functions on ℝ

Ordinary differential equations

Partial differential equations

Complex

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