Check if the equation is exact, which happens for ODEs of the form

if
.
We have


so the ODE is not quite exact, but we can find an integrating factor
so that

<em>is</em> exact, which would require


Notice that

is independent of <em>x</em>, and dividing this by
gives an expression independent of <em>y</em>. If we assume
is a function of <em>x</em> alone, then
, and the partial differential equation above gives

which is separable and we can solve for
easily.




So, multiply the original ODE by <em>x</em> on both sides:

Now


so the modified ODE is exact.
Now we look for a solution of the form
, with differential

The solution <em>F</em> satisfies


Integrating both sides of the first equation with respect to <em>x</em> gives

Differentiating both sides with respect to <em>y</em> gives


So the solution to the ODE is


Answer:
So it gives you a little picture and tells you what would the question be if you had this graph.
Step-by-step explanation:
The correct answer would be B, find the area because the 4x + 3 is your length and 3x is your length, A = length * width. So the answer is B, find the area.
Number of people < (should be smaller than or equal to but I don't have that button on my keyboard) (100-7) / 15.50
103/15.50 = 6.64516...
You can't have .645 of a person, so you must round down. Therefore, she can bring 6 people including herself.
Answer is <span>D.
A and D
A = 2(6+2) = 16
D = 2(4+3) = 16
both have perimeters = 16</span>
Answer:
Part 1) 
Part 2)
a) 
b) 
c) 
Step-by-step explanation:
<u><em>The complete question in the attached figure</em></u>
Part 1) Write an expression for the perimeter of the shape
we know that
The figure is composed by a larger square, a rectangle and a smaller square
1) The area of the larger square is given

so
The length and the width of the larger square is x units
2) The area of the rectangle is given

so
The length of the rectangle is x units and the width is 1 unit
3) The length and the width of the smaller square is x units
see the attached figure N 2 to better understand the problem
Find out the perimeter
The perimeter is the sum of all the sides.
so


Part 2) Find the perimeter for each of the given values of x.
a) For x=7 units
Substitute the value of x in the expression of the perimeter

b) For x=5.5 units
Substitute the value of x in the expression of the perimeter

b) For x=7/3 units
Substitute the value of x in the expression of the perimeter
