This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# DSolve

 DSolve[eqn, y, x]solves a differential equation for the function y, with independent variable x. DSolve[{eqn1, eqn2, ...}, {y1, y2, ...}, x]solves a list of differential equations. DSolve[eqn, y, {x1, x2, ...}]solves a partial differential equation.
• DSolve[eqn, y[x], x] gives solutions for y[x] rather than for the function y itself.
• Differential equations must be stated in terms of derivatives such as , obtained with D, not total derivatives obtained with Dt.
• The list of equations given to DSolve can include algebraic ones that do not involve derivatives.
• DSolve generates constants of integration indexed by successive integers. The option GeneratedParameters specifies the function to apply to each index. The default is , which yields constants of integration C[1], C[2], ... .  »
• For partial differential equations, DSolve typically generates arbitrary functions C[n][...].  »
• Boundary conditions can be specified by giving equations such as y'[0]b.
• Solutions given by DSolve sometimes include integrals that cannot be carried out explicitly by Integrate. Dummy variables with local names are used in such integrals.
• DSolve can solve linear ordinary differential equations of any order with constant coefficients. It can solve also many linear equations up to second order with non-constant coefficients.
• DSolve includes general procedures that handle almost all the nonlinear ordinary differential equations whose solutions are given in standard reference books such as Kamke.
• DSolve can find general solutions for linear and weakly nonlinear partial differential equations. Truly nonlinear partial differential equations usually admit no general solutions.
• DSolve can handle not only pure differential equations but also differential-algebraic equations.  »
 Scope   (24)
 Options   (1)
 Applications   (7)