Question

Solve this:(2x+y)+(x+5y) dx/dy=0, u=x–y, v=x+2y.

a)x=2, y=−1
b)x=−2, y=1
c) x=1,y=−2
d)-x=1,y=−2

Answer 1

The question is missing vital information needed to solve the given differential equation, but the new variables u and v can still be evaluated for each option to see if they satisfy the relationships u = x - y and v = x + 2y.

Step-by-step explanation:

The provided question appears to be a differential equation that involves substitution using variables u and v. Solving it requires us to express dx/dy through these new variables. However, with the given options and the nature of the problem, it seems that there is a need for a concrete equation or additional context to solve it fully, as the information provided is not sufficient to determine the values of x and y directly. Nevertheless, given the options, we can certainly check which of the provided (x, y) pairs satisfies both the new variables u = x - y and v = x + 2y.

• For option (a), u = 2 - (-1) = 3 and v = 2 + 2(-1) = 0
• For option (b), u = -2 - 1 = -3 and v = -2 + 2(1) = 0
• For option (c), u = 1 - (-2) = 3 and v = 1 + 2(-2) = -3
• For option (d), u = -1 - (-2) = 1 and v = -1 + 2(-2) = -5

Without the actual differential equation to solve, we cannot definitively choose the correct (x, y) pair from the options provided.