Question

(1 point) Given the following initial value problem

(x2+2y2)dxdy=xy,y(−3)=3

find the following:

(a) The coefficient functions are M(x,y)= and N(x,y)= . (Please
input values for both boxes.)

(b) The separable equation using a substitution of y=ux, is

dx+ du=0 (Separate the variables with x with dx only and u with du
only.) (Please input values for both boxes.)

(c) The implicit solution is

x=

I just need part C.

Answer #1

(1 point) Given the following differential equation
(x2+2y2)dxdy=1xy,
(a) The coefficient functions are M(x,y)= and N(x,y)= (Please input
values for both boxes.)
(b) The separable equation, using a substitution of y=ux, is
dx+ du=0 (Separate the variables with x with dx only and u with du
only.) (Please input values for both boxes.)
(c) The solution, given that y(1)=3, is
x=
Note: You can earn partial credit on this
problem.
I just need part C. thank you

A Bernoulli differential equation is one of the form
dxdy+P(x)y=Q(x)yn
Observe that, if n=0 or 1, the Bernoulli equation is linear. For
other values of n, the substitution u=y^(1−n) transforms the
Bernoulli equation into the linear equation
du/dx+(1−n)P(x)u=(1−n)Q(x)
Use an appropriate substitution to solve the equation
y'−(3/x)y=y^4/x^2 and find the solution that satisfies y(1)=1

Find the derivative of each of the following functions:
(a) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(b) y =63 (d) w=3u^(-1) (f) w=4u^(1/4)
2. Find the following:
(a) d/dx(-x^(-4)) (c) d/dw 5w^4 (e) d/du au^b
(b) d/dx 9x^(1/3) (d) d/dx cx^2 (f) d/du-au^(-b)
3. Find f? (1) and f? (2) from the following functions: Find the
derivative of each of the following functions:
(c) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(d) y =63 (d)w=3u^(-1) (f) w=4u^(1/4)
4.
(a) y=f(x)=18x (c) f(x)=-5x^(-2)...

Let U=X1/2Y2,
dU/dX=(1/2)X-1/2Y2,
dU/dY=2X1/2Y
Px=$15, Py=$3 and I=$300
1.(2 pts)_______________________ What is the level of happiness
at X=16, Y=6?
2. (2 pts)_______________________What is the marginal utility of
X at this point?
3.(2 pts)________________________ What is the slope of the
indifference curve at this point?
4.(2 pts)_______________________ At this point, which is larger:
the marginal utility of the last dollar spent on X or the marginal
utility of the last dollar spent on Y? (You must show both marginal
utilities per...

1)Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1. Let af/ax = (x + y)2 =
x2 + 2xy + y2. Integrate each term of this
partial derivative with respect to x, letting
h(y) be an unknown function in y.
f(x, y) = + h(y)
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt + (8y + 6t
− 1) dy...

1) Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1
Let af/ax = (x + y)2 = x2 + 2xy +
y2.
Integrate each term of this partial derivative with respect to
x, letting h(y)
be an unknown function in y.
f(x, y) = + h(y)
Find the derivative of h(y).
h′(y) =
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt...

Consider the following five utility functions.
G(x,y) = x2 + 3 y2
H(x,y) =ln(x) + ln(2y)
L(x,y) = x1/2 + y1/2
U(x,y) =x y
W(x,y) = (4x+2y)2
Z(x,y) = min(3x ,y)
In the case of which function or functions can the Method of
Lagrange be used to find the complete solution to the consumer's
utility maximization problem?
a.
H
b.
U
c.
G
d.
Z
e.
L
f.
W
g.
None.

Suppose the joint probability distribution of X and Y is given
by the following table.
Y=>3 6 9 X
1 0.2 0.2 0
2 0.2 0 0.2
3 0 0.1 0.1
The table entries represent the probabilities. Hence the
outcome [X=1,Y=6] has probability
0.2.
a) Compute E(X), E(X2), E(Y), and E(XY). (For all answers show
your work.) b) Compute E[Y | X = 1], E[Y | X = 2], and E[Y | X =
3].
c) In this case, E[Y...

Solve the initial-value problem. y"-6y'+9y=0; y(0)=2,
y'(0)=3
Given that y1=x2 is a solution to y"+(1/x)
y'-(4/x2) y=0, find a second, linearly independent
solution y2.
Find the Laplace transform. L{t2 *
tet}
Thanks for solving!

4.4-JG1 Given the following joint density function in Example
4.4-1:
fx,y(x,y)=(2/15)d(x-x1)d(y-y1)+(3/15)d(x-x2)d(y-y1)+(1/15)d(x-x2)d(y-y2)+(4/15)d(x-x1)d(y-y3)
a) Determine fx(x|y=y1) Ans: 0.4d(x-x1)+0.6d(x-x2)
b) Determine fx(x|y=y2) Ans: 1d(x-x2)
c) Determine fy(y|x=x1) Ans: (1/3)d(y-y1)+(2/3)d(y-y3)
d) Determine fx(y|x=x2) Ans:
(3/9)d(y-y1)+(1/9)d(y-y2)+(5/9)d(y-y3)
4.4-JG2
Given fx,y(x,y)=2(1-xy) for 0 a) fx(x|y=0.5) (Point Conditioning)
Ans: (4/3)(1-x/2)
b) fx(x|0.5

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