Ordinary differential equations

 

In Macsyma

For comparison with other CAS choose from: Axiom Derive Maple Mathematica Reduce

inputs outputs

    ode('diff(y, x) + y * sin(x)/cos(x) - 1/cos(x), y, x);

                       y = cos(x) (tan(x) + %c)

• Bernoulli equation

      ode(x*(1-x^2)*'diff(y, x) + (2*x^2 -1)*y - x^3*y^3, y, x);
  

                                  log(x + 1)   log(x - 1)
                                  ---------- + ----------
                                      2            2
                              x %e
                  y = --------------------------------------------
                                    3            5      3
                                   x  + 3 x   3 x  + 5 x  + 15 x
                      sqrt(%c - 2 (-------- - ------------------))
                                      3               15

      radcan(%);
  

                           sqrt(5) sqrt(x - 1) x sqrt(x + 1)
                       y = ---------------------------------
                                           5
                                   sqrt(2 x  + 5 %c)

      ode('diff(y, x, 2)+4*'diff(y, x)+4*y-x*exp(x), y, x);
  

                                     x
                         (3 x - 2) %e                    - 2 x
                     y = ------------- + (%k2 x + %k1) %e
                              27