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Duplicate of Ordinary Differential Equations LISD Flashcards | StudBud
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Duplicate of Ordinary Differential Equations LISD
Duplicate of Ordinary Differential Equations LISD
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1
A differential equation provides a
method through which to evaluate limits of indt. form
bound over which it can be evaluated
lot of frustration
A relationship between a function and its derivatives
2
Which of the following differential equations is represented by the slope field shown below?
dy/dx = y
dy/dx = y/2
dy/dx = 2x
dy/dx = x
3
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 = ln∣sec(t)+tan(t)∣+C
y=sec(t)tan(t)+c
4
If a differential equation is positive, the value of the original function must be increasing
True
False
5
Which of the following differential equations can be represented by the slope field shown?
dy/dx = -x/y
dy/dx = πx2
dy/dx = x/y
dy/dx = x2+y2
6
If a differential equation can be solved by
separating
variables, then it is referred to as a
separable differential equation
Leon-ic differential equation
Look at the bolded words
inseparable differential equation
7
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
8
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
.5e6-4
.5e3+9
9
Given the differential equation dy/dx = 2ln x, what is the slope of a solution curve at x = 1?
1
0
2
e
10
Given df/dt = t
3
- sint. Find the general solution.
t4/4+cost+C
3t2 - cost
None of the above
3t2 - cost + C
11
A slope field (in calculus) is
a solid revolved around the x or y axis about some slope
an open grassy area with some gradient
connect the dots
a graph of a differential equation at various points
12
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
3-(1/t)+C
1.5t2-(tlnt-t)+C
Jenn needs to turn her phone off
13
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
14
It is possible to integrate the same diff. equation and end up with different function outputs.
False
True
15
Find the general solution t for the differential equation given dx/dt = (4
ex
+x)/(4
ex
ln4+1/e).
A general solution does not exist
None of the "above"
t=((4exln4+1/e)(e4exln4+1)-(4ex+x)(ln4)2e4ex))/(4exln4+1/e)2
t=e-1(ln(4ex+x)
16
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?
t^3/3 + t^2/2 + C
That differential equation is wrong, he's told many more.
3t^3 +2t^2 + C
2t + 1 + C