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The Graphical Treatment of Differential Equations
Published online by Cambridge University Press: 03 November 2016
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5. We shall now apply this method to a few typical cases.
(i) The equation y1=x2+y2
gives y2=2x+2y2(x2+y2).
Hence, y1 is always positive; y2 vanishes along the curve
r2=-cot θ,
in which x=r cos θ, y = r sin θ. Hence, in Fig. 5(a), the curves have the form) above the dashed curve (the locus of inflexion), and ( below this curve.
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