A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of the spring and is initially released from the equilib position with an upward velocity of 6 m/s. Give the initial conditions. x(0)=
x ′
(0)=
​
m
m/s
​
Find the equation of motion. x(t)=m The indicated function y 1
​
(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y 2
​
=y 1
​
(x)∫ y 1
2
​
(x)
e −∫P(x)dx
​
dx as instructed, to find a second solution y 2
​
(x). y ′′
+4y=0;y 1
​
=cos(2x) y 2
​
= The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y=c 1
​
+c 2
​
cos(x)+c 3
​
sin(x),(−[infinity],[infinity])
y ′′′
+y ′
=0,y(π)=0,y ′
(π)=6,y ′′
(π)=−1
​
y=