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List of Equations

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

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Found 327 equations, 33 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 >>
 CategoryEquation(s)Author/
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291 4. Nonlinear Partial Differential Equations
4.7. Systems of Two Equations
$u_x=u^kf(u^nw^m)$,\\ 
$w_t=w^sg(u^nw^m)$. Elena Vyazmina
Submitted: 25 Jan 08 12:21
Edited (admin): 29 Jan 08 16:29
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292 4. Nonlinear Partial Differential Equations
4.8. Systems of Three and More Equations
$$
\frac{\partial u_m}{\partial
t}=L[u_m]+\sum^n_{k=1}u_kf_{mk}\left(t,\frac
{u_1}{u_n},\ldots,\frac{u_{n-1}}{u_n}\right),\qquad m=1,\dots,n.
$$ Elena Vyazmina
Submitted: 25 Jan 08 12:27
Edited (admin): 29 Jan 08 14:44
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293 5. Integral Equations
5.1. Linear Equations of the First Kind with Variable Limit of Integration
\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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294 5. Integral Equations
5.1. Linear Equations of the First Kind with Variable Limit of Integration
\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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295 5. Integral Equations
5.1. Linear Equations of the First Kind with Variable Limit of Integration
$\displaystyle \int_0^x(x-t)^\nu J_\nu(\lambda(x-t))y(t)\,dt=f(x),\qquad {\rm Re}\,\nu>-\frac12$. Alexander Manzhirov
Submitted: 14 Jul 07 13:57
Edited (admin): 14 Jul 07 14:04
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296 5. Integral Equations
5.1. Linear Equations of the First Kind with Variable Limit of Integration
1. $\displaystyle\int_0^{x^\alpha}y(t)dt=\lambda y(x),\ \alpha\in (0,1), y\in L_2[0,1]$.

\vnskip

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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297 5. Integral Equations
5.2. Linear Equations of the Second Kind with Variable Limit of Integration
$\displaystyle y(x)+A\int^x_a\sin[\lambda(x-t)]y(t)\,dt=f(x)$. Andrei Polyanin
Submitted: 01 Aug 07 10:09
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298 5. Integral Equations
5.3. Linear Equations of the First Kind with Constant Limits of Integration
$\displaystyle \int^\infty_0[\sin(xt)+\varphi(x)\psi(t)]y(t)\,dt=f(x)$. Andrei Polyanin
Submitted: 30 Jun 07 11:37
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299 5. Integral Equations
5.3. Linear Equations of the First Kind with Constant Limits of Integration
$\displaystyle \int^\infty_0[\cos(xt)+\varphi(x)\psi(t)]y(t)\,dt=f(x)$. Andrei Polyanin
Submitted: 30 Jun 07 11:40
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300 5. Integral Equations
5.3. Linear Equations of the First Kind with Constant Limits of Integration
$\displaystyle \int^\infty_0[tJ_\nu(xt)+\varphi(x)\psi(t)]y(t)\,dt=f(x)$. Andrei Polyanin
Submitted: 09 Jul 07 12:08
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Found 327 equations, 33 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 >>

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