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:
Step-by-step explanation:
a = -1
b = 2
c = 3
a + (-c) = -1 + (-3) = -4
Both numbers have same sign(-Ve).So add and the result will have the -Ve sign.
c - (-b) = c + b = 3 + 2 = 5
b = 2
Least to greatest: a +(-c) , b , c-(-b)
Answer: Each classmate got 9 pencils
Step-by-step explanation: if you divide 8 from 75, you get 9 pencils for each classmate and 3 for Jessica to keep.
For the functions f(x) = 4x + 7 and g(x) = -9x + 11, find f(g(0)). For the functions f(x) = 3x2 - 7 and g(x) = -3x2 + 4, find f(g(2)). (Do NOT put commas in large numbers.)
I'm guessing you want this written as an equation, so here it is.
3n+7>2(n-4)
These can be really tricky at times, so I suggest looking for "clues" in the wording, such as add, subtract, and other things. Also look for what numbers are "paired" together, like in parentheses. Hope that this helps!