Ordinary differential equations

 

In Axiom

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inputs outputs

    y:= operator('y);

                                                          Type: BasicOperator

    solve(D(y(x), x) + y(x) * sin x/cos x - 1/cos x = 0, y, x)

    [particular= sin(x),basis= [cos(x)]]
Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)

• Bernoulli equation

      solve(x*(1-x**2)*D(y(x), x) + (2*x**2 -1)*y(x) - x**3*y(x)**3 = 0, y, x)
  

          5    2     4     2
      - 2x y(x)  + 5x  - 5x
      ----------------------
                   2
              5y(x)
                                            Type: Union(Expression Integer,...)

      solve(D(y(x), x, 2)+4*D(y(x), x)+4*y(x)-x*exp(x) = 0, y, x)
  

                             - 2x   x 3
                   (3x - 2)%e    (%e )            - 2x     - 2x
      [particular= --------------------,basis= [%e    ,x %e    ]]
                            27
  Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...)