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BUILTIN MATHEMATICA SYMBOL
DSolve
DSolve[eqn, y, x]
solves a differential equation for the function y, with independent variable x.
DSolve[{eqn_{1}, eqn_{2}, ...}, {y_{1}, y_{2}, ...}, x]
solves a list of differential equations.
DSolve[eqn, y, {x_{1}, x_{2}, ...}]
solves a partial differential equation.
Details and OptionsDetails and Options
 DSolve[eqn, y[x], x] gives solutions for 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 GeneratedParameters>C, which yields constants of integration C[1], C[2], .... »
 GeneratedParameters>(Module[{C}, C]&) guarantees that the constants of integration are unique, even across different invocations of DSolve.
 For partial differential equations, DSolve typically generates arbitrary functions C[n][...]. »
 Boundary conditions can be specified by giving equations such as .
 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 sometimes gives implicit solutions in terms of Solve. »
 DSolve can solve linear ordinary differential equations of any order with constant coefficients. It can also solve many linear equations up to second order with nonconstant 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 differentialalgebraic equations. »
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