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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
Which of the following differential equations is represented by the slope field shown below?
dy/dx = y/2
dy/dx = 2x
dy/dx = x
dy/dx = y
2
Andrew Park solves calculus problems at a rate of dy/dt=sec(t). What is the gen solution to y?
y = sec(t)+C
y = .5ln∣(sin(t)+1)/(sin(t)-1)∣+C
y=sec(t)tan(t)+c
y = ln∣sec(t)+tan(t)∣+C
3
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=sec-1x-1
y=sin-1x
4
It is possible to integrate the same diff. equation and end up with different function outputs.
True
False
5
If a differential equation can be solved by
separating
variables, then it is referred to as a
inseparable differential equation
separable differential equation
Look at the bolded words
Leon-ic differential equation
6
Given df/dt = t
3
- sint. Find the general solution.
3t2 - cost + C
t4/4+cost+C
None of the above
3t2 - cost
7
A differential equation provides a
bound over which it can be evaluated
A relationship between a function and its derivatives
method through which to evaluate limits of indt. form
lot of frustration
8
If dL/dt=e
2t
and dC/dt=-t and if L(0) and C(0)=0, then L(3)-C(3)=
.5e6+4
.5e3-9
.5e3+9
.5e6-4
9
dT/dt = -k(T-T
0
) is
Einstein's Theory of Special Relativity
Newton's Law of Gravity
Newton's Law of Cooling
Leibniz's Discovery of The Calculus
10
If a differential equation is positive, the value of the original function must be increasing
True
False
11
Which of the following differential equations can be represented by the slope field shown?
dy/dx = -x/y
dy/dx = x/y
dy/dx = x2+y2
dy/dx = πx2
12
Dean tells lies at a rate given by dL/dt = t^2+t. How many lies has he told at t=3 if L(0)=0?
That differential equation is wrong, he's told many more.
t^3/3 + t^2/2 + C
3t^3 +2t^2 + C
2t + 1 + C
13
Find the general solution t for the differential equation given dx/dt = (4
ex
+x)/(4
ex
ln4+1/e).
None of the "above"
t=((4exln4+1/e)(e4exln4+1)-(4ex+x)(ln4)2e4ex))/(4exln4+1/e)2
t=e-1(ln(4ex+x)
A general solution does not exist
14
A slope field (in calculus) is
connect the dots
a graph of a differential equation at various points
an open grassy area with some gradient
a solid revolved around the x or y axis about some slope
15
Given the differential equation dy/dx = 2ln x, what is the slope of a solution curve at x = 1?
1
0
2
e
16
Jenn's phone goes off during our tests at a rate modeled by the dy/dt= 3t-lnt. Find the gen sol
The limit does not exist
Jenn needs to turn her phone off
1.5t2-(tlnt-t)+C
3-(1/t)+C
