Consider the differential equations d2y dx2 - dy dx - 30y

Question

Differential Equations: The D-operator Method

Note: A useful DE to know: dy/ dx = ky gives y = Ae^kx

Exercise 1

Consider the DE

(d²y / dx²) - (dy / dx) - 30y = 0

(a) Write the DE using D-operator notation

(b) Solve the DE for y by solving two first-order DEs

Exercise 2

Consider the DE

(d²y / dx²) - 10 (dy / dx) + 25y = 0

(a) Write the DE using D-operator notation

(b) Solve the DE for y by solving two first-order DEs

Exercise 3

Consider the DE

(d²y / dx²) - 3 (dy / dx) = 0

(a) Write the DE using D-operator notation

(b) Solve the DE for y by solving two first-order DEs.