FP2 Ch7

Question 1

SODE homogeneous:
Auxillary has two real roots (a + b)what is form of general solution

Answer 1

y = Ae^ax +Be^bx

Question 2

SODE homogeneous:
Auxillary has one root (a) what is form of general solution

Answer 2

y= (A+Bx)e^ax

Question 3

SODE homogeneous:
Auxillary has imaginary roots (p +- qi) what is form of general solution

Answer 3

y = e^px(Acosqx + Bsinqx)

Question 4

What is complementary function

Answer 4

SODE non- homogeneous:
general solution of corresponding homogeneous funtion

Question 5

SODE non homogeneous:
Particular integral when other side (f(x)) = p

Answer 5

λ

Question 6

SODE non homogeneous:
Particular integral when other side (f(x)) = p + qx

Answer 6

λ+μx

Question 7

SODE non homogeneous:
Particular integral when other side (f(x)) = p + qx +rx^2

Answer 7

λ+μx+νx^2

Question 8

SODE non homogeneous:
Particular integral when other side (f(x)) = pe^kx

Answer 8

λe^kx

Question 9

SODE non homogeneous:
Particular integral when other side (f(x)) = pcos(ωx) + qsin(ωx)

Answer 9

λcos(ωx) + μsin(ωx)

Question 10

General solution =

Answer 10

C.F + P.I