1st and 2nd Order Diffs

Question 2

For a 2nd order homogeneous if the roots of the auxilliary eqn are real and distinct what is the general soln?

Answer 2

Y = Ae^(m1) + Be^(m2)

Question 3

For a 2nd order homogeneous if the roots of the auxilliary eqn are real and equal (repeated) what is the general soln ?

Answer 3

Y = Ae^(m) + Bxe^(m)

Question 4

For a 2nd order homogeneous if the roots of the auxilliary eqn are complex what is the general soln?

Answer 4

Y = e^(px) [Acosqx + Bsinqx]

Question 5

For a non-homogeneous if the f(x) is an exponential and its indice is not the same as one of the roots of the complementary function what is the form of the Particular Intergral?

Answer 5

yp = k e^(nx)

Question 6

For a 2nd order non-homogeneous if the f(x) is an exponential and its indice is the same as one of the roots of the complementary function what is the form of the Particular Intergral?

Answer 6

yp = kx e^(nx)

Question 7

For a 2nd order non-homogeneous if the f(x) is an exponential and its indice is the same as the repeated root of the complementary function what is the form of the Particular Intergral?

Answer 7

yp = kx^(2) e^(nx)

Question 8

What 2 parts do you need for the General soln of a 2nd order non-homogeneous eqn?

Answer 8

The Complementary fn and the particular integral:Y = yc + yp

Question 9

For a 2nd order non-homogeneous if the f(x) is an polynomial of degree1 what is the form of the Particular Intergral?

Answer 9

yp = ax + b(Note: Multiply thro by x if part of the CF is of the same degree)

Question 10

For a 2nd order non-homogeneous if the f(x) is an polynomial of degree 2 what is the form of the Particular Intergral?

Answer 10

yp = ax^(2) + bx + c(Note: Multiply thro by x if part of the CF is of the same degree)

Question 11

For a 2nd order non-homogeneous if the f(x) is an constant what is the form of the Particular Intergral?

Answer 11

yp = a(Note: Multiply thro by x if part of the CF is of the same degree)

Question 12

For a 2nd order non-homogeneous if the f(x) is a trig fn what is the form of the Particular Intergral?

Answer 12

yp = psin nx + qsin nx

Question 13

What information do you need to get the particulal solution of 2nd order eqn?

Answer 13

The initial conditions

Question 14

For a 1st order linear eqn what are the 2 methods you can use to solve it depending on its form?

Answer 14

1. Seperable variables2. Integrating Factor

Question 15

For a 1st order linear eqn what form must the eqn be to use the integrating factor method?

Answer 15

dy/dx + P(x) y = f(x)

Question 16

How do you find the Integrating factor I(x), of the 1st order linear eqn: dy/dx + P(x) y = f(x)

Answer 16

I(x) = e ^ (integral of P(x) )

Question 17

For a 1st order linear eqn what form must the eqn be to use the seperable variables method?

Answer 17

f(y) dy = f(x) dx

Question 18

Write a differential for:The rate of growth of the germ is dependant on the growth of the germ.

Answer 18

dg/dx = kG

Question 19

Write a differential for:The rate of decrease of the germ is dependant on the decrease of the germ.

Answer 19

dg/dx = - kG