DSolveValue

DSolveValue[eqn,expr,x]
gives the value of expr determined by a symbolic solution to the ordinary differential equation eqn with independent variable x.

DSolveValue[eqn,expr,{x,xmin,xmax}]
uses a symbolic solution for x between and .

DSolveValue[{eqn1,eqn2,},expr,]
uses a symbolic solution for a list of differential equations.

DSolveValue[eqn,expr,{x1,x2,}]
uses a solution for the partial differential equation eqn.

Details and OptionsDetails and Options

  • DSolveValue[eqn,y[x],x] gives a solution 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.
  • Boundary conditions can be specified by giving equations such as .
  • The list of equations given to DSolveValue can include algebraic ones that do not involve derivatives.
  • DSolveValue can also solve delay differential equations.
  • In delay differential equations, initial history functions are given in the form , where is in general a function of x.
  • WhenEvent[event,action] may be included in the equations to specify an action that occurs when event becomes True.
  • DSolveValue[eqn,y,{x,xmin,xmax}] gives a solution valid for x between and .
  • DSolveValue can generate 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 DSolveValue.
  • For partial differential equations, DSolveValue typically generates arbitrary functions C[n][].
  • Expressions given by DSolveValue sometimes include integrals that cannot be carried out explicitly by Integrate. Variables , , , are used in such integrals.
  • DSolveValue 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.
  • DSolveValue includes general procedures that handle almost all the nonlinear ordinary differential equations whose solutions are given in standard reference books such as Kamke.
  • DSolveValue can find general solutions for linear and weakly nonlinear partial differential equations. Truly nonlinear partial differential equations usually admit no general solutions.
  • DSolveValue can handle not only pure differential equations but also differentialalgebraic equations.
Introduced in 2014
(10.0)