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:
x=155
Step-by-step explanation:
I hope the pictures are clear and you get the concept!
Heyyyyyyyyyyy Hii what’s up
Answer:
-
Step-by-step explanation:
Answer:
The average rate is 35 miles per hour
Step-by-step explanation:
To get from town A to town B takes 3 hours. The distance is 100 miles
To get from town B to town c takes 1 hours. The distance is 40 miles
To find the average rate , we need to find the total distance and divide by the total time
Total distance = 100 + 40 = 140 miles
Total time = 3 hrs + 1 hr = 4 hours
distance = rate * time
140 miles = rate * 4 hours
140/4 = rate
35 = rate
The average rate is 35 miles per hour