In 43 and 44 we saw that every autonomous firstorder differential equation dy/dx f (y)

Chapter 2, Problem 49

(choose chapter or problem)

In Problems 43 and 44 we saw that every autonomous first-order differential equation dy/dx = f (y) is separable. Does this fact help in the solution of the initial-value problem \(\frac{d y}{d x}=\sqrt{1+y^{2}} \sin ^{2} y\), \(y(0)=\frac{1}{2}\)? Discuss. Sketch, by hand, a plausible solution curve of the problem.

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