Suppose that y(x) denotes a solution of the initial-value problem y x2 y2 , y(1) 1 and
Chapter 1, Problem 20(choose chapter or problem)
Suppose that y(x) denotes a solution of the initial-value problem \(y^{\prime}=x^{2}+y^{2}\), y(1) = -1 and that y(x) possesses at least a second derivative at x = 1. In some neighborhood of x 1, use the DE to determine whether y(x) is increasing or decreasing, and whether the graph y(x) is concave up or concave down.
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