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based on an earlier version of the Wolfram Language.
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Differential Equations
Automatically selecting between hundreds of powerful and in many cases original algorithms, Mathematica provides both numerical and symbolic solving of differential equations (ODEs, PDEs, DAEs, ...). With equations conveniently specified symbolically, Mathematica uses both its rich set of special functions and its unique symbolic interpolating functions to represent solutions in forms that can immediately be manipulated or visualized.
y'[x] (Derivative) derivative of a function
DSolve symbolic solution to differential equations
NDSolve numerical solution to differential equations
InterpolatingFunction interpolating function used in solutions
Method select and tune many possible solver algorithms
StepMonitor, EvaluationMonitor monitor the progress of a solution