Question

Solve each of the following ODEs. If initial conditions are given, give the unique solution.

d) y''' − 5y'' + 2y' + 8y = 0, y(0) = 2, y'(0) = −1, y''(0) = −5

e) y''' + 9y'' + 27y' + 27y = 0, y(0) = 2, y'(0) = 0, y''(0) = 3

a) x^2y'' + xy' + 4y = 0, x > 0

b) x^2y'' − 6y = 0, x > 0, y(1) = y'(1) = 5

c) x^2y'' + 5xy' + 4y = 0, x > 0, y(1) = 5, y'(1) = −9

Answer 1