In Problems, first verify that y (x) satisfies the given differential equation. Then determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator (if desired) to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition.
y′ = 3x2(y2 + 1); y(x) = tan(x3 + C), y(0) = 1
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