The solutions to the differential equation dy/dx = x^2 + y^2 + 1 are increasing

Question

The solutions to the differential equation dy/dx = x^2 + y^2 + 1 are increasing at every point. True False Suppose that y = f(x) is a solution of the differential equation dy/dx = 2x - y, Determine if the following are true or false. If f(a) = b, the slope of the graph of f at (a, b) is 2a - b. True False The graph of f is decreasing whenever it lies above the line y = 2x and is increasing whenever it lies below the line y = 2x. True False If g(x) is another solution to the differential equation dy/dx = 2x-y, then g(x) = f(x) + C. True False

Explanation / Answer

8)True

9) (a) True since slope = dy/dx

(b) 2x-y >0 --> 2x>y   it is satisfied only below the line, so increasing below the line

so True

(c) True

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