Ordinary differential equations

 

In Maple

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

inputs outputs

    dsolve( diff(y(x),x) + y(x)*sin(x)/cos(x) - 1/cos(x) = 0, y(x) );

                           y(x) = sin(x) + cos(x) \_C1

• Bernoulli equation

      dsolve( x*(1-x^2)* diff(y(x),x) + (2*x^2-1)* y(x) - x^3* y^3 = 0, y(x));
  

                                             5
                               1          2 x  + 5 \_C1
                             ----- = 1/5 -------------
                                 2        2         2
                             y(x)        x  (- 1 + x )

      solve( ", y(x) );
  

                  1/2         5      7                  2 1/2
                 5    x (- 2 x  + 2 x  - 5 \_C1 + 5 \_C1 x )
                 --------------------------------------------,
                                     5
                                - 2 x  - 5 \_C1
  
                        1/2         5      7                  2 1/2
                       5    x (- 2 x  + 2 x  - 5 \_C1 + 5 \_C1 x )
                     - --------------------------------------------
                                           5
                                      - 2 x  - 5 \_C1

      dsolve( diff(y(x),x,x) + 4* diff(y(x),x) + 4*y(x) - x* exp(x) = 0,y(x));
  

       y(x) = 1/9 x exp(x) - 2/27 exp(x) + \_C1 exp(- 2 x) + \_C2 exp(- 2 x) x