Question

1. Use the procedures developed in this chapter to find the general solution of the differential equation.

a.)  (Let x be the independent variable.) y''' − 2y'' = 12

b.) 20x²y'' + 21xy' − y = 0

c.) x²y'' − 6xy' + 10y = −2x⁴ + 3x²

d.) Solve the given differential equation subject to the indicated conditions. y'' − 4y = x + sin x, y(0) = 3, y'(0) = 4

e.)  Solve the given differential equation subject to the indicated conditions. y'y'' = 16x, y(1) = 8, y'(1) = 4

Answer 1