A spring attached to the ceiling is stretched 245 meters by

A spring attached to the ceiling is stretched 2.45 meters by a four-kg mass.

c.) If the mass from part b. is pulled down two centimeters and released, the solution for the position is ?

Solution

Rewrite the equation so that the leading coefficient is 1. y 00 1 + t t y 0 + 1 t y = te2t . The Wronskian is W(y1, y2)(t) = ¯ ¯ ¯ ¯ 1 + t 1 e t e t ¯ ¯ ¯ ¯ = tet and Y (t) = (1 + t) Z e t (te2t ) tet dt + e t Z (1 + t)te2t tet dt = (1 + t) Z e 2t dt + e t Z (1 + t)e t dt = 1 + t 2 e 2t + e t ((1 + t)e t e t ) = 1 2 e 2t + 1 2 te2t = 1 2 e 2t (t 1).