Divide both the numerator and denominator by 5 and you get 8/17. your answer is 8/17.
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


P would equal negative three.
The system of equations can be used to determine how much of product x and product y the store owner bought is x + y = 4,000
0.10x + 0.04y = 352
<h3>Simultaneous equation</h3>
- product x
- Product y
- Total units of x and y = 4,000 units
- Cost of shipping each product x = $0.10
- Cost of shipping each product y = $0.04
- Total cost of shipping = $352
The equation:
x + y = 4,000
0.10x + 0.04y = 352
Therefore, the system of equations can be used to determine how much of product x and product y the store owner bought is x + y = 4,000
0.10x + 0.04y = 352
Learn more about simultaneous equation:
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