Question: Verify that if k is a constant, then the function y(x) kx satisfies the differential equation xy' = y for all x. Construct a

Verify that if k is a constant, then the function y(x) ≡ kx satisfies the differential equation xy' = y for all x. Construct a slope field and several of these straight line solution curves. Then determine (in terms of a and b) how many different solutions the initial value problem xy' = y, y(a) = b has—one, none, or infinitely many.

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