Symbolic Implementation of Preliminary Group Classiffication for Ordinary Differential Equations

Algorithm 3

?  A#;

@: {DIF (F# (3, U1, X1), U1, 2),

  DIF (F# (1, U1, X1), U1, 2) - 2*DIF (F# (3, U1, X1), U1, X1),

  −3*U1^∧2*U2*DIF (F# (3, U1, X1), U1) +  2*DIF (F# (1, U1, X1), U1, X1) −  DIF

(F# (3, U1, X1), X1, 2),

  −2*U1*U2*F# (1, U1, X1) + U1^∧2*U2*DIF (F# (1, U1, X1), U1)  −  2*U1^∧2*U2*DIF

(F# (3, U1, X1), X1) −  U1^∧2*F# (2, U1, U2, X1) + DIF (F# (1, U1, X1), X1, 2),

  UUU#1 == F# (1, U1, X1),

  UUU#2 == F# (2, U1, U2, X1),

  XXX#1 == F# (3, U1, X1)}