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The Graphical Treatment of Differential Equations

Published online by Cambridge University Press:  03 November 2016

S. Brodetsky
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Extract

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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Other
Information
The Mathematical Gazette , Volume 10 , Issue 144 , January 1920 , pp. 3 - 8
Copyright
Copyright © Mathematical Association 1920

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