Differential Equations | Part IA, 2003

Consider the equation

dydx=1y2.\frac{d y}{d x}=1-y^{2} .

Using small line segments, sketch the flow directions in x0,2y2x \geqslant 0,-2 \leqslant y \leqslant 2 implied by the right-hand side of ()(*). Find the general solution (i) in y<1|y|<1, (ii) in y>1|y|>1.

Sketch a solution curve in each of the three regions y>1,y<1y>1,|y|<1, and y<1y<-1.

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