There are some close connections between finding a "local minimum" and solving a set of nonlinear equations. Given a set of n equations in n unknowns, seeking a solution r(x) ...

The ODEs that arise in practical applications often have non-rational coefficients. In such cases, DSolve attempts to convert the equation into one with rational coefficients ...

In general, a system of ordinary differential equations (ODEs) can be expressed in the normal form, The derivatives of the dependent variables x are expressed explicitly in ...

 

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.

If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

The systems of equations that govern certain phenomena (in electrical circuits, chemical kinetics, etc.) contain a combination of differential equations and algebraic ...

A partial differential equation (PDE) is a relationship between an unknown function u(x_1,x_2,…,x_n) and its derivatives with respect to the variables x_1,x_2,…,x_n. Here is ...

The numerical method of lines is a technique for solving partial differential equations by discretizing in all but one dimension, and then integrating the semi-discrete ...

DiscreteLQRegulatorGains[ss, {q, r}, \[Tau]] gives the optimal discrete-time state feedback gain matrix with sampling period \[Tau] for the continuous-time StateSpaceModel ...