Explore BrainMass

Wronskian property

Suppose that y1, y2 are linearly independent solutions to the differential equation:
a2 (x) y'' + a1 (x) y' + a0 (x) y = 0.

a) Show that a2 (y1 y2'' - y2 y1'') + a1(y1 y2' - y1' y2) = 0
b) show that (a) implies a2 W' + a1 W = 0 {here W means the Wronskian)
c) show that the equation in (b) implies W = C e(-(a1/ a2)x)


Solution Summary

This shows how to prove a given Wronskian property for a differential equation.