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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.
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