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List of Equations

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

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5. Integral Equations

5.1. Linear Equations of the First Kind with Variable Limit of Integration

Found 4 equations
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1 \noindent
$\displaystyle \int^x_0\frac{\sinh[\lambda(x-t)]}{\sqrt{x-t}}\,y(t)\,dt=f(x),\qquad
f(0)=f'_x(0)=0$. Andrei Polyanin
Submitted: 07 Dec 06 10:16
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2 \noindent
$\displaystyle \int^x_0\frac{\sin[\lambda(x-t)]}
{\sqrt{x-t}}\,y(t)\,dt=f(x), \qquad f(0)=f'_x(0)=0$. Andrei Polyanin
Submitted: 07 Dec 06 10:22
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3 $\displaystyle \int_0^x(x-t)^\nu J_\nu(\lambda(x-t))y(t)\,dt=f(x),\qquad {\rm Re}\,\nu>-\frac12$. Alexander Manzhirov
Submitted: 14 Jul 07 13:57
Edited (admin): 14 Jul 07 14:04
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4 1. $\displaystyle\int_0^{x^\alpha}y(t)dt=\lambda y(x),\ \alpha\in (0,1), y\in L_2[0,1]$.

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2. $\displaystyle\int_{x^{1/\alpha}}^1 y(t)dt=\lambda y(x),\ \alpha\in (0,1), y\in L_2[0,1]$. Ignat Yurii Domanov
Submitted: 21 Jun 08 10:31
Edited (admin): 25 Jun 08 12:55
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Found 4 equations

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