What is the order of ?

0 1 2 3

0% 0%0%0%

0332

2

ydx

yd

dx

dy

1. 0

2. 1

3. 2

4. 3

In general the solution to the equation is:

1 2 3 4

0% 0%0%0%

)()( ygxfdx

dy

dxxfdyyg )()(1.

dyxfdxyg )()(2.

dxxfdyyg

)()(

13.

dyxfdxyg

)()(

14.

Consider the equation

When we separate the variables, this equation becomes:

0% 0% 0%0%0%

yexdx

dy6

xdxdye y

6

11.

dxexdy y62.

xdxdye y

6

3.

xdxydye y 64.

Equation is not separable

5.

Which of the following are separable differential equations?

1 2 3 4 5

0% 0% 0%0%0%

22 yxy1.

xyxy 22.

yxey 23.

yxy cos)1( 4.

yxy 3ln 5.

Use separation of variables to solve

1 2 3 4

0% 0%0%0%

y

x

dx

dy

cos

2

cxy 21sin1.

cxy 21sin2.

cxy 21 2sin3.

cxy 21 2sin4.

Find the solution to which satisfies the initial condition y(0)=2

1 2 3 4

0% 0%0%0%

2xydx

dy

1

12

x

y

1.

1

22

x

y

2.

1

22

x

y

3.

2

22

x

y

4.

Solve the differential equation

given that y(0)=π

0% 0%0%0%

y

x

dx

dy

sin

3

1

2

3cos 21 xy

1.

1

2

3cos 21 xy

2.

1

2

3cos 21 xy

3.

1

2

3cos 21 xy

4.

We want to test the function to see if it is a solution. What equation is the result?

0% 0%0%0%

tetxtx 2)()(2

tt BeAetx 2)(

ttttt eBeAeBeAe 22242 1.

ttttt eBeAeBeAe 22222 2.

ttt eBeAe 2242 3.

None of the above4.

Which of the following would be the best trial solution to use, given

1 2 3 4

0% 0%0%0%

32

2

46 xydx

dy

dx

yd

3ax1.

bax 32.

dcxbxax 233.

123 xxxa4.

The equation is exact.It can be rewritten as which of the

following?

1 2 3 4

0% 0%0%0%

)()()( xgxfydx

dyxf

)()( xgxfdx

dy

1.

)()( xgxfdx

dy

2.

)())(( xgxyfdx

d

3.

)()( xfyxgdx

d

4.

Which of the following equations are exact?

1 2 3 4

0% 0%0%0%

xydx

dyx 2

1.

34 2 xxydx

dyx

2.

63

x

y

dx

dy3.

xxydx

dye x 23

4.

Solve the exact equation

1 2 3 4

0% 0%0%0%

22 2 xxydx

dyx

23 x

Cxy

1.

2

3

x

C

xy

2.

23

x

Cxy

3.

22

3

x

C

xy

4.

Solve the exact equation

y =

cotx

+ C

si...

y =

cotx

+ C

co...

y =

tanx

+ C

si...

y =

tanx

+ C

co...

0% 0%0%0%

xxydx

dsinsin

1. y = cotx + Csinx

2. y = cotx + Ccosecx

3. y = tanx + Csinx

4. y = tanx + Ccosec x

What factor can this equation be multiplied by to make it exact?

x x²

x³

None

0% 0%0%0%

34 ydx

dyx

1. x

2. x²

3. x³

4. None of the above

If then the integrating

factor is given by which of the following?

1 2 3 4

0% 0%0%0%

)()( xgyxfdx

dy

dxxgexp1.

dxxfexp2.

dxxgxf )(exp3.

)()(exp xgxf4.

Solve the equation by

finding its integrating factor

1 2 3 4

0% 0%0%0%

xeydx

dy 33

xeCxy 31.

xeCxy 32.

xe

xy

3

3.

Cxey x 34.

Which of the following is an example of a second order linear

ODE?

1 2 3 4

0% 0%0%0%

)(xfdx

dyc

dx

dyb

dx

dya

1.

)(xfcydx

dyb

dx

dya

2.

)(2

2

xfadx

dya

dx

yda

3.

)(2

2

xfcydx

dyb

dx

yda

4.

Find the auxiliary equation for

1 2 3 4

0% 0%0%0%

03232

2

ydx

dy

dx

yd

1. 3k² - 2k - 3y = 0

2. 3k² - 2k - 3 = 0

3. 3y’’ – 2y’ - 3y = 0

4. None of the above

Find the general solution to

1 2 3 4

0% 0%0%0%

062

2

ydx

dy

dx

yd

1. y = Ae-2x + Be3x

2. y = Ae2x + Be-3x

3. y = Ae-2x + Be-3x

4. y = Ae2x + Be3x

Find the general solution to

1 2 3 4

0% 0%0%0%

092

2

ydx

yd

1. y = (A + B)e3x

2. y = Ae-3x + Be3x

3. y = Ae-9x + Be9x

4. y = (A + B)e-9x

Given a second order linear inhomogeneous equation

the general solution is given by:

0% 0%0%0%

cfp yyy 1.

pcf yyy 2.

cfp yyy 3.

All of the above4.

)(2

2

xfcydx

dyb

dx

yda

What is the complimentary function of

1 2 3 4

0% 0%0%0%

xdx

dy

dx

ydln5103

2

2

xxcf BeAey 52

1.

xxcf BeAey 52

2.

xxcf BeAey 103

3.

xxcf BeAey 103

4.

If the auxiliary equation has complex roots, α + βi and α - βi,

then the complimentary function is:

1 2 3 4

0% 0%0%0%

xBxAey xcf sincos

1.

xBxAey xcf sincos

2.

xBxAey xcf sincos

3.

xBxAey xcf sincos

4.

Is a particular integral of

Yes N

o

Don’t

know

0% 0%0%

xp ey 3

12

1

1. Yes

2. No

3. Don’t know

xeydx

dy

dx

yd 32

2

32

Find a particular integral of the equation in the form

y = Acos2x + Bsin2x

1 2 3 4

0% 0%0%0%

xydx

dy

dx

yd2sin23

2

2

xxy 2sin12

12cos

12

1

1.

xxy 2sin12

12cos

12

1

2.

xxy 2sin12

12cos

12

1

3.

xxy 2sin12

12cos

12

1

4.

Find the general solution of

1 2 3 4

0% 0%0%0%

22

2

632 xydx

dy

dx

yd

xx BeAexxy 2

32 1242

1.

xx BeAexxy 2

32 1242

2.

xx BeAexxy 2

32

9

28

3

42

3.

xx BeAexxy 2

32

9

28

3

42

4.