Ordinary differential equations

 

In Mathematica

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

inputs outputs

    DSolve[ y'[x] + y[x] Sin[x]/Cos[x] - 1/Cos[x]==0, y[x],x ]

    {{y[x] -> C[1] Cos[x] + Sin[x]}}

• Bernoulli equation

      Simplify[
       DSolve[ x (1-x^2) y'[x] + (2x^2-1) y[x]- x^3 y^3 == 0,
               y[x], x] ]
  

                    3             2
      {{y[x] -> x (y  + Sqrt[1 - x ] C[1])}}

      Simplify[
       DSolve[ y''[x] + 4y'[x] + 4y[x] - x Exp[x] == 0,
               y[x], x ] ]
  

                    x    x
                -2 E    E  x   C[1]   x C[2]
      {{y[x] -> ----- + ---- + ---- + ------}}
                 27      9      2 x     2 x
                               E       E