Hello everybody! I have a general question concerning DEs :0 Can one use the symmetry of the equation to somehow get the solution faster? What does such symmetry tell us? e.g.: [tex]\dot x=y[/tex] [tex]\dot y=x[/tex] is the symmetrical system to the second order DE [tex]\ddot x-x=0[/tex] Now we can easily see the solutions (whether e^t or e^(-t)) actually have the same properties as functions. They are even one and the same function, rotated over the y-axis! So, is the symmetry really providing help or this is just a coincidence?