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The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:5. Integral Equations
Subcategory:5.5. Nonlinear Equations with Variable Limit of Integration
Equation(s):$\displaystyle \int^x_0f(t/x)y(t)y(x-t)\,dt=Ax^\mu e^{\lambda x}$.
Solution(s),
Transformation(s),
Integral(s)
:
Solutions:
$$
y(x)=\pm \sqrt{\frac AI}\,x^{\frac{\mu-1}{2}}e^{\lambda x},\qquad
I=\int^1_0f(z)z^{\frac{\mu-1}2}(1-z)^{\frac{\mu-1}2}\,dz.
$$
Novelty:Material has been fully published elsewhere
References:A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, CRC Press, Boca Raton, 1998.
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Wed 01 Aug 2007 10:27
Edits by author:0

Edit (Only for author/contributor)


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