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:
1. Product
2. Difference
3. Difference
Step-by-step explanation:
:)
Answer:
Step-by-step explanation:
Answer:
J=12
Step-by-step explanation:
(2/3)*j = 8 // - 8
(2/3)*j-8 = 0
2/3*j-8 = 0 // + 8
2/3*j = 8 // : 2/3
j = 8/2/3
j = 12
Sqaure
rhombus
parallelogram
quadrilateral
hope it helps