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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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211 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{f'(x)}{f(x)}\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}-
\frac{1}{f^2(x)}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:16
Edited (admin): 10 Jan 08 15:37
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212 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
2\frac{\partial^2 w}{\partial x^2}+(a+1)\frac{\partial^2 w}{\partial x\partial y}+a=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:14
Edited (admin): 10 Jan 08 15:38
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213 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
b\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}-
\left(a+b\frac{\partial w}{\partial x}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:13
Edited (admin): 10 Jan 08 15:39
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214 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\left(\frac{\partial w}{\partial y}\right)^2\frac{\partial^2 w}{\partial x^2}+
\left[\left(a+\frac{\partial w}{\partial x}\right)^2-
f(x)\left(\frac{\partial w}{\partial y}\right)^{-1}\right]\frac{\partial^2 w}{\partial y^2}-
f(x)\frac{\partial w}{\partial y}=0$.\hfill\break Valentin Zaitsev
Submitted: 09 Jan 08 13:12
Edited (admin): 10 Jan 08 15:40
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215 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
b\left(\frac{\partial w}{\partial y}\right)^2\frac{\partial^2 w}{\partial x^2}+
b\left(a+\frac{\partial w}{\partial x}\right)^2\frac{\partial^2 w}{\partial y^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:10
Edited (admin): 10 Jan 08 15:41
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216 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
\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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217 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{a^2}{(y+b)^4}=0$,\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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218 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\left[f\left(x,\frac{\partial w}{\partial y}\right)\right]^2=0$,\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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219 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\frac{\partial w}{\partial y}\left(a\frac{\partial^2 w}{\partial x\partial y}-
b\frac{\partial^2 w}{\partial x^2}\right)=0$.\hfill\break Valentin Zaitsev
Submitted: 05 Sep 07 13:36
Edited (admin): 11 Jan 08 09:31
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220 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\frac1w\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}
\left(a\frac{\partial^2 w}{\partial x^2}-\frac{\partial^2 w}{\partial x\partial y}\right)=0$.\hfill\break Valentin Zaitsev
Submitted: 05 Sep 07 13:39
Edited (admin): 11 Jan 08 09:31
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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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