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Riccati Equations   (Mathematica Tutorial)
A Riccati equation is a first-order equation of the form This equation was used by Count Riccati of Venice (1676–1754) to help in solving second-order ordinary differential ...
Exact Equations   (Mathematica Tutorial)
Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.
Sqrt   (Built-in Mathematica Symbol)
Sqrt[z] or Sqrt[z] gives the square root of z.
RotationMatrix   (Built-in Mathematica Symbol)
RotationMatrix[\[Theta]] gives the 2D rotation matrix that rotates 2D vectors counterclockwise by \[Theta] radians.RotationMatrix[\[Theta], w] gives the 3D rotation matrix ...
PowerExpand   (Built-in Mathematica Symbol)
PowerExpand[expr] expands all powers of products and powers. PowerExpand[expr, {x_1, x_2, ...}] expands only with respect to the variables x_i.
Not   (Built-in Mathematica Symbol)
! expr is the logical NOT function. It gives False if expr is True, and True if it is False.
IntegerQ   (Built-in Mathematica Symbol)
IntegerQ[expr] gives True if expr is an integer, and False otherwise.
Sech   (Built-in Mathematica Symbol)
Sech[z] gives the hyperbolic secant of z.
ByteCount   (Built-in Mathematica Symbol)
ByteCount[expr] gives the number of bytes used internally by Mathematica to store expr.
FromCoefficientRules   (Built-in Mathematica Symbol)
FromCoefficientRules[list, {x_1, x_2, ...}] constructs a polynomial from a list of rules for exponent vectors and coefficients.
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