Ordinary differential equations

 

In Reduce

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

inputs outputs

• load the module odesolve for the analytical solution of ordinary differential equations

      load_package odesolve;
  
      depend y,x;
  
      odesolve(df(y,x) + y * sin x/cos x - 1/cos x,y,x);
  

     {y=arbconst(1)*cos(x) + sin(x)}

• Bernoulli equation

      odesolve(x*(1-x**2)*df(y,x) + (2*x**2 -1)*y - x**3*y**3,y,x);
  

                                5
        1    5*arbconst(2) + 2*x
      {----=----------------------}
         2          4      2
        y        5*x  - 5*x

      solve(ws,y);
  

                  2
            sqrt(x  - 1)*sqrt(5)*x
      {y=----------------------------,
                                  5
          sqrt(5*arbconst(2) + 2*x )
  
                   2
           - sqrt(x  - 1)*sqrt(5)*x
       y=----------------------------}
                                  5
          sqrt(5*arbconst(2) + 2*x )

      odesolve(df(y,x,2)+4*df(y,x)+4*y-x*exp(x),y,x);
  

             3*x        3*x
          3*e   *x - 2*e    + 27*arbconst(3)*x + 27*arbconst(3)
      {y=-------------------------------------------------------}
                                     2*x
                                 27*e