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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 >>
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1 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^{\!2}-\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}
=f(w)\left(\frac{\partial w}{\partial x}\right)^{\!4}$. Andrei Polyanin
Submitted: 06 Dec 06 11:32
Edited (admin): 11 Dec 06 11:09
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2 \noindent
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^{\!2}-\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}
=-f(w)\left(\frac{\partial w}{\partial x}\right)^{\!3}\frac{\partial w}{\partial y}$. Andrei Polyanin
Submitted: 08 Dec 06 15:58
Edited (admin): 11 Dec 06 11:12
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3 \noindent
$\displaystyle \left(\frac{\partial w}{\partial t}+a\right)\frac{\partial^2 w}{\partial t\partial x}
-\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial t^2} 
+\frac{\partial w}{\partial x}\left[2\left(\frac{\partial w}{\partial t}\right)^2+3a \frac{\partial w}{\partial t}+a^2 \right]=0$.

%\noindent
%$\displaystyle \left(\frac{\partial w}{\partial t}+a\right)\frac{\partial^2 w}{\partial t\partial x} +\frac{\partial w}{\partial x}\left[2\left(\frac{\partial w}{\partial t}\right)^2+3a \frac{\partial w}{\partial t}-\frac{\partial^2 w}{\partial t^2}+a^2 \right]=0$,\hfill\break
%where $a$ is a constant. Yurii Kosovtsov
Submitted: 12 Dec 06 12:13
Edited (admin): 13 Dec 06 09:40
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4 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{1}{(w+ax+b)^2}\left(\frac{\partial w}{\partial x}+
a\right)^2\left(\frac{\partial w}{\partial y}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:30
Edited (admin): 10 Jan 08 13:03
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5 $\displaystyle \left[f(x)\frac{\partial w}{\partial y}+
\frac{\partial^2 w}{\partial x\partial y}\right]\frac{\partial^2 w}{\partial z^2}+
\left[g(z)\frac{\partial w}{\partial y}-
\frac{\partial^2 w}{\partial y\partial z}\right]\frac{\partial^2 w}{\partial x\partial z}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:31
Edited (admin): 10 Jan 08 13:04
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6 $\displaystyle \frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y\partial z}-
\frac{\partial^2 w}{\partial x\partial y}\left(\frac{\partial^2 w}{\partial x\partial z}-
f(z)\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:30
Edited (admin): 10 Jan 08 13:05
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7 $\displaystyle \frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y\partial z}-
\left(\frac{\partial w}{\partial z}-f(z)\right)\frac{\partial^2 w}{\partial x\partial y}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:29
Edited (admin): 10 Jan 08 13:05
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8 $\displaystyle \left(\frac{\partial^2 w}{\partial y\partial z}+
\frac{\partial w}{\partial z}\right)\frac{\partial^2 w}{\partial x^2}+
\left[f(z)-\frac{\partial^2 w}{\partial x\partial z}\right]
\left(\frac{\partial^2 w}{\partial x\partial y}+\frac{\partial w}{\partial x}\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:29
Edited (admin): 10 Jan 08 13:06
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9 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2+
\frac{\partial^2 w}{\partial x\partial y}\frac{\partial^2 w}{\partial x\partial z}+
\left[f(x)-\frac{\partial^2 w}{\partial x^2}\right]
\left(\frac{\partial^2 w}{\partial y^2}+\frac{\partial^2 w}{\partial y\partial z}\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:28
Edited (admin): 10 Jan 08 13:06
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10 \begin{multline*} f(x)\left[\left(\frac{\partial^2 w}{\partial y\partial z}\right)^2-
\frac{\partial^2 w}{\partial y^2}\frac{\partial^2 w}{\partial z^2}\right]+
g(y)\left(\frac{\partial^2 w}{\partial x\partial y}\frac{\partial^2 w}{\partial z^2}-
\frac{\partial^2 w}{\partial y\partial z}\frac{\partial^2 w}{\partial x\partial z}\right)+\\
+h(z)\left(\frac{\partial^2 w}{\partial x\partial z}\frac{\partial^2 w}{\partial y^2}-
\frac{\partial^2 w}{\partial y\partial z}\frac{\partial^2 w}{\partial x\partial y}\right)=0.
\end{multline*} Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:27
Edited (admin): 10 Jan 08 13:07
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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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