Choose the appropriate table for the differential equation dy/dx=x-y
a) x -2, 0, 1
y -4, 1, 2
dy/dx 2,-1,-1 <---- my answer. Can you check for me, please
b) x -2, 0, 1
y -4, 1, 2
dy/dx 2,-1, 1
c) x -2, 0, 1
y -4, 1, 2
dy/dx -2,-1,-1
d) Cannot be found without solving the differential equation
I agree
To choose the appropriate table for the differential equation dy/dx = x - y, we need to substitute the given values of x and y into the equation and check if the result matches the given values of dy/dx.
Let's go through each option and substitute the values to find the corresponding values of dy/dx:
a) For x = -2, y = -4
Substituting into the equation: dy/dx = (-2) - (-4) = 2 + 4 = 6
The value of dy/dx does not match the given table value (2), so option a is not correct.
b) For x = 0, y = 1
Substituting into the equation: dy/dx = 0 - 1 = -1
The value of dy/dx matches the given table value (-1), so option b could be correct.
c) For x = 1, y = 2
Substituting into the equation: dy/dx = 1 - 2 = -1
The value of dy/dx matches the given table value (-1), so option c could be correct.
d) The option states that the differential equation cannot be found without solving it. This option suggests that the table values are not enough to determine the correct answer.
Based on the values obtained for dy/dx in options b and c, we can see that both match with the corresponding values in the given table. Therefore, either option b or option c could be correct, and we cannot distinguish between them using the given information.
To determine the correct option definitively, we would need to solve the differential equation dy/dx = x - y and check if the solution matches the given table values of x, y, and dy/dx.
To check if your answer is correct, let's substitute the given values of x and y into the differential equation and see if the calculated values of dy/dx match the given values of dy/dx.
Using the table provided:
For x = -2, y = -4:
dy/dx = x - y
= -2 - (-4)
= 2 + 4
= 6
For x = 0, y = 1:
dy/dx = x - y
= 0 - 1
= -1
For x = 1, y = 2:
dy/dx = x - y
= 1 - 2
= -1
Comparing these calculated values of dy/dx with the given values:
a) dy/dx = 2, -1, -1 (Doesn't match)
b) dy/dx = 2, -1, 1 (Doesn't match)
c) dy/dx = -2, -1, -1 (Matches)
d) Cannot be found without solving the differential equation
Based on this analysis, the correct answer is c) x = (-2, 0, 1), y = (-4, 1, 2), dy/dx = (-2, -1, -1).