Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. (x2 + y2)y' = y2
1. A unique solution exists in the region y ≥ x.
2. A unique solution exists in the entire xy-plane.
3. A unique solution exists in the region y ≤ x.
4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.
5. A unique solution exists in the region x2 + y2 < 1.

4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.

Step-by-step explanation:

Given:

Solving the differential equation, we have:

Thus, except at (0,0), for all real values of x and y, the function is defined.

The (0,0) values of x&y causes the denominator to be 0, so the function is not defined at this (0,0) condition.

Therefore,

.

Apart from the point of origin (0,0), this is continuous.

This means a unique solution exists in the region consisting of all points in the xy-plane except the origin.

step-by-step explanation:

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98