The solutions to many second-order ODEs can be expressed in terms of special functions. Solutions to certain higher-order ODEs can also be expressed using AiryAi, BesselJ, ...

A differential system can sometimes be solved by analytic means. The function DSolve implements many of the known algorithmic techniques. However, differential systems that ...

While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as ...

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

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 ...

Following are two examples of nonlinear systems of ODEs that can be solved symbolically using DSolve. The first three equations in this system of four nonlinear ODEs can be ...

"How to" Topics Numbers Algebraic Calculations

The hypergeometric functions play a unifying role in mathematical analysis since many important functions, such as the Bessel functions and Legendre functions, are special ...

The differential equations that arise in modern applications often have discontinuous coefficients. DSolve can handle a wide variety of such ODEs with piecewise coefficients. ...

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 ...