1. State in your own words what a Linear Relation is. (5 pts)2. Give an example of a real life Linear Relation scenario (you cannot use any from the lessons). Give ALL the details of your example: (5 pts )a. Give a table of 3 ordered pairs and interpret each ordered pair. (12 pts)b. What is the SLOPE? (4 pts)c. What information is the SLOPE giving? (10 pts)d. What is the Y-INTERCEPT? (4 pts)e. What information is the Y-INTERCEPT giving? (10 pts)
Obtain the general solution of the following DEs: i. y′′′ + y′′ − 4y′ + 2y = 0 ii. y(4) + 4y(2) = 0 iii. x(x − 2)y′′ + 2(x − 1)y′ − 2y = 0; use y1 = (1 − x) iv. y′′ − 4y = sin2(x) v. y′′ − 4y′ + 3y = x ; use y1 = e3x vi. y′′ + 5y′ + 6y = e2xcos(x) vii. y′′ + y = sec(x) tan(x)
Obtain the general solution of the following DEs: i. y′′′ + y′′ − 4y′ + 2y = 0 ii. y(4) + 4y(2) = 0 iii. x(x − 2)y′′ + 2(x − 1)y′ − 2y = 0; use y1 = (1 − x) iv. y′′ − 4y = sin2(x) v. y′′