Differential Equations

Question 1

Aux. Eq.: b^2 - 4ac > 0
2 Real Roots (x - α)(x - beta)

Answer 1

Ae^(α)x + Be^(β)x

Question 2

Aux. Eq.: b^2 - 4ac = 0
1 Repeated Root (x - α)^2

Answer 2

(A +Bx)e^(α)x

Question 3

Aux. Eq.: b^2 - 4ac < 0
2 Complex Roots (p +/- qi)

Answer 3

e^px(Acos(qx) +Bcos(qx))

Question 4

P.I.: p

Answer 4

λ

Question 5

P.I.: p + qx

Answer 5

λ + μx

Question 6

P.I.: e.g. p + qx + rx^2

Answer 6

λ + μx + γx^2

Question 7

P.I.: Any form of pcosωx or qsinωx

Answer 7

λcosωx + μcosωx

Question 8

P.I.: pe^kx

Answer 8

λe^kx