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Ordinary Differential Equations LISD Flashcards | StudBud
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Ordinary Differential Equations LISD
Ordinary Differential Equations LISD
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1
Find the general solution t for the differential equation given dx/dt = (4
ex
+x)/(4
ex
ln4+1/e).
t=e-1(ln(4ex+x)
None of the "above"
t=((4exln4+1/e)(e4exln4+1)-(4ex+x)(ln4)2e4ex))/(4exln4+1/e)2
A general solution does not exist
2
The rate at which "Nidofish told me wrong" is given by df/dt = t
3
- sint. He's "told me wrong"
t4/4+cost+C times
3t2 - cost times
3t2 - cost + C times
Nidofish is never wrong
3
If dL/dt=e
2t
and dC/dt=-t and if L(0) and C(0)=0, then L(3)-C(3)=
.5e3-9
.5e6-4
.5e3+9
.5e6+4
4
If dy/dx = 1/(1+x
2
) and y(0)=1, the particular solution can be given by:
y=tan-1x+1
y=tan-1x
y=sin-1x
y=sec-1x-1
5
If a differential equation is positive, the value of the original function must be increasing
False
True
6
The second derivative of a function is a diff. equation of what form in Leibniz's notation?
dy/dx
d2y/dx2
d2y/d2x
dy2/dx2
7
Given the differential equation dy/dx = 2ln x, what is the slope of a solution curve at x = 1?
0
e
1
2
8
If a differential equation can be solved by
separating
variables, then it is referred to as a
separable differential equation
Leon-ic differential equation
inseparable differential equation
Look at the bolded words
9
It is possible to integrate the same diff. equation and end up with different function outputs.
True
False
10
Which of the following differential equations is represented by the slope field shown below?
dy/dx = y
dy/dx = x
dy/dx = 2x
dy/dx = y/2
11
Steven's phone goes off during our tests at a rate modeled by the DEQ 3t-lnt. Find the gen. s
3-(1/t)+C
The limit does not exist
Shut up, Steven
1.5t2-(tlnt-t)+C
12
A differential equation provides a
lot of frustration
bound over which it can be evaluated
method through which to evaluate limits of indt. form
A relationship between a function and its derivatives
13
Jack can do the whip while turning his wrist at a constant 5 radians/s. Which DEQ models this?
dθ/dt = 5sinθ
dθ/dt = 5
dθ/dt = 5θ
dθ/dt = θ/5
14
dy/dx=2x+y. What is the m and b value for a solution curve of form y=mx+b?
m = 3, b = -2
m = -2, b = -2
m = 1, b = 2
m = -2, b = 3
15
A slope field (in calculus) is
an open grassy area with some gradient
connect the dots
a solid revolved around the x or y axis about some slope
a graph of a differential equation at various points
16
Havish tells lies at a rate given by dL/dt = k
e
t+t. How many lies has he told at t=3 if L(0)=0?
That differential equation is wrong, he's told many more.
9/2(ke+1)+C
9ke/2+9+C
3ke+3
17
Which of the following differential equations can be represented by the slope field shown?
dy/dx = x2+y2
dy/dx = πx2
dy/dx = x/y
dy/dx = -x/y
18
Force is given by F=dW/dx. If a unit moves in the same direction as F, the integral setup is
F=∫Wdx
W=∫Fdx
x=∭f2dW
W=∑fdx
19
dT/dt = -k(T-T
0
) is
Leibniz's Discovery of The Calculus
Einstein's Theory of Special Relativity
Newton's Law of Gravity
Newton's Law of Cooling
20
Leon solves calculus problems at a rate of dy/dt=sec(t). What is the general solution to y?
y = .5ln∣(sin(t)+1)/(sin(t)-1)∣+C
y = sec(t)+C
y = ln∣sec(t)+tan(t)∣+C
y=sec(t)tan(t)+c
