Calc II Quiz Review

Question 0

If the roots of the auxiliary equation are real and unequal, what is the general solution of ay’‘+by+cy=0?

Answer 0

y=(c1)(e^(r1)x)+(c2)(e^(r2)x)

Question 1

What is the auxiliary equation of the differential equation

ay’‘+by’+cy=0?

Answer 1

ar^2+br+c=0

Question 2

If the auxiliary equation has only one real root r, what is the general solution of ay’‘+by+cy=0?

Answer 2

y = (c1)e^rx + (c2)xe^rx

Question 3

If the roots of the auxiliary equation are the complex numbers r1=α+iβ, r2=α-iβ, what is the general solution of ay’‘+by+cy=0?

Answer 3

y = (e^(αx))(c1cos(βx)+c2*sin(βx))

Question 4

If ay’‘+by+cy=G(x) and G(x) is a polynomial, what should yp(x) be?

Answer 4

A polynomial of the same degree as G

Question 5

If ay’‘+by+cy=G(x) and G(x) = e^(Bx), what should yp(x) be?

Answer 5

Ae^Bx (where B is found in the other equation)

Question 6

If ay’‘+by+cy=G(x) and G(x) = sin(Cx) or cos(Cx), what should yp(x) be?

Answer 6

Acos(Cx)+Bcos(Cx) where C is found in the other equation