Geometric equation:

First-order equation with variable coefficients:

A third-order constant coefficient equation:

Initial value conditions:

Plot the solution:

Second-order inhomogeneous equation:

Second-order variable coefficient equation in terms of elementary functions:

Euler-Cauchy equation:

In general, special functions are required to express solutions:

Solvable logistic equations:

Riccati equations:

Solutions in terms of trigonometric and hyperbolic functions:

Higher-order equations:

Nonlinear convolution equation:

Linear system with constant coefficients:

With boundary conditions:

Plot their solution:

Linear fractional systems:

Diagonal system:

Linear constant coefficient difference-algebraic system:

An index-2 system:

First-order linear partial difference equation with constant coefficients:

Substitute the function

Sin for the free function

C:

Plot the resulting solution:

Constant coefficient linear equation of orders 2, 3, and 4:

Inhomogeneous:

Variable coefficient linear equation:

First-order constant coefficient

-difference equation:

Equivalent way of expressing the same equation:

Initial value:

Second-order equation:

Third-order:

Inhomogeneous:

Using a numeric value for

:

Plot solution:

Linear varying coefficient equations:

Nonlinear equations:

Riccati equation:

A linear constant coefficient system of

-difference equations: