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Abel's Differential Equation


The Abel equation of the first kind is given by

 y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3+...

(Murphy 1960, p. 23; Zwillinger 1997, p. 120), and the Abel equation of the second kind by

 [g_0(x)+g_1(x)y]y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3

(Murphy 1960, p. 25; Zwillinger 1997, p. 120).


See also

Abel's Differential Equation Identity

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References

Murphy, G. M. Ordinary Differential Equations and Their Solution. Princeton, NJ: Van Nostrand, 1960.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 120, 1997.

Referenced on Wolfram|Alpha

Abel's Differential Equation

Cite this as:

Weisstein, Eric W. "Abel's Differential Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbelsDifferentialEquation.html

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