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

Equation data
Category:5. Integral Equations
Subcategory:5.1. Linear Equations of the First Kind with Variable Limit of Integration
Equation(s):\noindent
$\displaystyle \int^x_0\frac{\sin[\lambda(x-t)]}
{\sqrt{x-t}}\,y(t)\,dt=f(x), \qquad f(0)=f'_x(0)=0$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Solution:\hfill\break
$\displaystyle y(x)=\frac2{\pi\lambda}\int^x_0\frac{\cos[\lambda
(x-t)]}{\sqrt{x-t}}[f''_{tt}(t)+\lambda^2f(t)]\,dt$.
Novelty:Material has been fully published elsewhere
References:A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev. Integrals and Series. Volume 5. Inverse Laplace Transforms. Gordon & Breach Sci. Publ., New York, 1992 (page 445).
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Thu 07 Dec 2006 10:22
Edits by author:0

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