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List of Equations

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

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4. Nonlinear Partial Differential Equations

4.4. Other Second-Order Equations

Found 106 equations, 11 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 >>
 Equation(s)Author/
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81 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
b\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}-
\left(a+b\frac{\partial w}{\partial x}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:13
Edited (admin): 10 Jan 08 15:39
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82 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\left(\frac{\partial w}{\partial y}\right)^2\frac{\partial^2 w}{\partial x^2}+
\left[\left(a+\frac{\partial w}{\partial x}\right)^2-
f(x)\left(\frac{\partial w}{\partial y}\right)^{-1}\right]\frac{\partial^2 w}{\partial y^2}-
f(x)\frac{\partial w}{\partial y}=0$.\hfill\break Valentin Zaitsev
Submitted: 09 Jan 08 13:12
Edited (admin): 10 Jan 08 15:40
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83 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
b\left(\frac{\partial w}{\partial y}\right)^2\frac{\partial^2 w}{\partial x^2}+
b\left(a+\frac{\partial w}{\partial x}\right)^2\frac{\partial^2 w}{\partial y^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:10
Edited (admin): 10 Jan 08 15:41
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84 \begin{multline*} \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
b\left(\frac{\partial w}{\partial y}\right)^2\frac{\partial^2 w}{\partial x^2}+\\
+\left(f(y)\frac{\partial w}{\partial x}+a\frac{\partial w}{\partial y}+
b\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}\right)
\frac{\partial^2 w}{\partial x\partial y}+
f(y)\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}\left(a+
b\frac{\partial w}{\partial x}\right)=0.\end{multline*} Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:09
Edited (admin): 10 Jan 08 15:41
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85 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{a^2}{(y+b)^4}=0$,\hfill\break

\textit{Monge--Amp\`ere equation} Valentin Zaitsev
Submitted: 04 Sep 07 18:01
Edited (admin): 11 Jan 08 09:29
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86 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\left[f\left(x,\frac{\partial w}{\partial y}\right)\right]^2=0$,\hfill\break
where $f(x,z)$ is represented in implicit form
$\displaystyle \Psi\left(xf+\frac{\partial w}{\partial y},f\right)=0$, $\Psi$ is arbitrary
function. Valentin Zaitsev
Submitted: 04 Sep 07 17:58
Edited (admin): 11 Jan 08 09:30
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87 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\frac{\partial w}{\partial y}\left(a\frac{\partial^2 w}{\partial x\partial y}-
b\frac{\partial^2 w}{\partial x^2}\right)=0$.\hfill\break Valentin Zaitsev
Submitted: 05 Sep 07 13:36
Edited (admin): 11 Jan 08 09:31
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88 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\frac1w\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}
\left(a\frac{\partial^2 w}{\partial x^2}-\frac{\partial^2 w}{\partial x\partial y}\right)=0$.\hfill\break Valentin Zaitsev
Submitted: 05 Sep 07 13:39
Edited (admin): 11 Jan 08 09:31
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89 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
a\left(1+\frac{\partial w}{\partial y}\right)\frac{\partial^2 w}{\partial x^2}-
a^2\left(1+\frac{\partial w}{\partial x}\right)^2=0$.\hfill\break Valentin Zaitsev
Submitted: 05 Sep 07 13:34
Edited (admin): 11 Jan 08 09:32
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90 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
a\left(\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}+
aw\frac{\partial w}{\partial x}+
\frac{\partial w}{\partial y}\right)\frac{\partial^2 w}{\partial x^2}-
a^2\left(\frac{\partial w}{\partial x}\right)^2=0$.\hfill\break Valentin Zaitsev
Submitted: 05 Sep 07 13:30
Edited (admin): 11 Jan 08 09:33
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Found 106 equations, 11 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 >>

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