differential equations

Question 1

dy/dx + p(x)y = Q(x)

what is the integrating factor

Answer 1

P(x)

Question 2

f(x) dy/dx + p(x)y = Q(x)

what is the integrating factor

Answer 2

p(x)/f(x)

Question 3

solution to auxilary equation are two distinct real roots

Answer 3

y = Ae^αx + Be^βx

Question 4

solution to auxilary equation are one repeated root

Answer 4

y = (A + Bx) e^αx

Question 5

solution to auxilary equation are complex roots

Answer 5

p +_ qi y = e^px ( Acos(qx) + Bsin(qx))

Question 6

Particular Integral, equation is form of a + bx

Answer 6

λ + μx

Question 7

Particular Integral, equation is form of acos(nx) + bsin(nx)

Answer 7

λcos(nx) + μsin(nx)

Question 8

Particular Integral, equation is form of pe^kx

Answer 8

λe^kx

Question 9

general solution = ….

Answer 9

Complimentary function + particular integral

Question 10

form of heavy damping

Answer 10

two real roots

Question 11

form of critical damping

Answer 11

repeated roots

Question 12

form of light damping

Answer 12

complex roots

Question 13

how to know when to use IF vs separating variables

Answer 13

if they cannot be separated, use IF. is there is both an x term and y term in the equation