Consider the following initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy = 0, y(1) = 1 Let ∂f ∂x = (x + y)2 = x2 + 2xy + y2. Integrate each term of this partial derivative with respect to x, letting h(y) be an

Suppose the ODE has a solution of the form , with total differential

This ODE is exact if the mixed partial derivatives are equal, i.e.

We have

so the ODE is indeed exact.

Integrating both sides of

with respect to gives

Differentiating both sides with respect to gives

so the general solution to the ODE is

Given that , we find

so that the solution to the IVP is

$450.00 for 6 weeks

or

$300

step-by-step explanation:

$200.00 for first week $50.00 x5 equals $250 plus $200 equals $450.00 for six weeks.

$200 for first week

$200 x 0.10 = $20

$20 x 5 = $100

$200 + $100 = $300

answer:   b

step-by-step explanation:

x2 = 16

x can not be a negative number because 16 is positive

the only answer would be positive 8