Euler and Legendre Equations (Mathematica Tutorial)

An Euler equation has the general form Euler equations can be solved by transforming them to equations with constant coefficients. This is an example of an Euler equation.

\[PartialD] (Mathematica Character Name)

Unicode: 2202. Alias: Esc pd Esc. Prefix operator with built-in evaluation rules. ∂_xy is by default interpreted as D[y,x]. ∂ is used in mathematics to indicate boundary. Esc ...

DifferentialRoot (Built-in Mathematica Symbol)

DifferentialRoot[lde] represents a function that solves the linear differential equation specified by lde[y, x].

Linear First-Order Equations (Mathematica Tutorial)

The following is a linear first-order ODE because both y[x] and y^ ′[x] occur in it with power 1 and y^′[x] is the highest derivative. Note that the solution contains the ...

ParabolicCylinderD (Built-in Mathematica Symbol)

ParabolicCylinderD[\[Nu], z] gives the parabolic cylinder function D_\[Nu] (z).

Exact Higher-Order Equations (Mathematica Tutorial)

A linear ordinary differential equation of order n is said to be exact if The condition of exactness can be used to reduce the problem to that of solving an equation of order ...

Equation Trekker Package (Equation Trekker Package Guide)

Manipulating Equations and Inequalities (Mathematica Overview)

Equations Solving Equations The Representation of Equations and Solutions

D (Built-in Mathematica Symbol)

D[f, x] gives the partial derivative \[PartialD]f/\[PartialD]x. D[f, {x, n}] gives the multiple derivative \[PartialD]^n f/\[PartialD]x^n. D[f, x, y, ...] differentiates f ...

Exact Linear Second-Order Equations (Mathematica Tutorial)

A linear second-order ordinary differential equation is said to be exact if An exact linear second-order ODE is solved by reduction to a linear first-order ODE.