Differential Equations

Question 1

auxiliary equation

Answer 1

am^2 + bm + c = 0

Question 2

auxiliary equation has roots α + β

Answer 2

y = Ae^(αx) + Be^(βx)

Question 3

auxiliary equation has repeated root m

Answer 3

y = (A + Bx)e^mx

Question 4

auxiliary equation has pure imaginary roots ±ni

Answer 4

y = A cos nx + B sin nx

Question 5

auxiliary equation has complex roots p ± qi

Answer 5

y = e^px (A cos qx + B sin qx)

Question 6

Function is a constant term

Answer 6

Particular Integral is of the form C

Question 7

Linear function

Answer 7

P.I.: ax +b

Question 8

Quadratic

Answer 8

ax^2 + bx + c

Question 9

Exponential function e^px

Answer 9

k e^px

Question 10

Trig Function cos px or sin px

Answer 10

a cos x px + b sin px

Question 11

integrating factor of

dy/dx + Py = Q

Answer 11

e^∫Pdx