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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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191 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\left[g(y)+h(w)\frac{\partial w}{\partial y}\right]\frac{\partial^2 w}{\partial x\partial y}-
\left[f(x)+h(w)\frac{\partial w}{\partial x}\right]\frac{\partial^2 w}{\partial y^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:36
Edited (admin): 10 Jan 08 15:16
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192 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
\begin{multline*} \frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\left(\frac{\partial^2 w}{\partial x\partial y}\right)^2+
\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}-
\left[g(y)+\frac{\partial w}{\partial x}+h(w)\frac{\partial w}{\partial y}\right]\frac{\partial^2 w}{\partial x\partial y}+\\
+\left[f(x)+h(w)\frac{\partial w}{\partial x}\right]\frac{\partial^2 w}{\partial y^2}-
f(x)\frac{\partial w}{\partial y}+g(y)\frac{\partial w}{\partial x}=0.
\end{multline*} Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:35
Edited (admin): 10 Jan 08 15:17
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193 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left[1+f\left(\frac{\partial w}{\partial x}\right)
\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}\right]\left[\frac{\partial^2 w}{\partial x^2}
\frac{\partial^2 w}{\partial y^2}-\left(\frac{\partial^2 w}{\partial x\partial y}\right)^2\right]+
f\left(\frac{\partial w}{\partial x}\right)\left(\frac{\partial w}{\partial y}\right)^3
\frac{\partial^2 w}{\partial x\partial y}+\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial y^2}
=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:34
Edited (admin): 10 Jan 08 15:17
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194 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle (ax-ay-b)^2\left[\frac{\partial^2 w}{\partial x^2}
\frac{\partial^2 w}{\partial y^2}-\left(\frac{\partial^2 w}{\partial x\partial y}\right)^2\right]+
c\left(\frac{\partial^2 w}{\partial x^2}+
2\frac{\partial^2 w}{\partial x\partial y}+
\frac{\partial^2 w}{\partial y^2}\right)+\left(a\frac{\partial w}{\partial x}+
a\frac{\partial w}{\partial y}+d\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:33
Edited (admin): 10 Jan 08 15:18
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195 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial w}{\partial x}+f(x)\right)
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial x\partial y}-
\left(\frac{\partial w}{\partial y}+g(y)\right)\left(\frac{\partial^2 w}{\partial x^2}\right)^2-
\left(\frac{\partial w}{\partial x}+f(x)\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:32
Edited (admin): 10 Jan 08 15:19
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196 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{1}{(bx+ay+d)^2}\left(a\frac{\partial w}{\partial x}-b\frac{\partial w}{\partial y}+c\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:31
Edited (admin): 10 Jan 08 15:20
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197 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\left[f(x)\frac{\partial w}{\partial x}+f'_x(x)w\right]\frac{\partial^2 w}{\partial y^2}-
f^2(x)\left(\frac{\partial w}{\partial y}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:29
Edited (admin): 10 Jan 08 15:21
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198 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
g(y)\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial x\partial y}-
f(y)\frac{\partial^2 w}{\partial x^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:28
Edited (admin): 10 Jan 08 15:22
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199 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{2a}{ax+b}\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x\partial y}+
\frac{2a^2}{(ax+b)^2}\left(\frac{\partial w}{\partial y}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:27
Edited (admin): 10 Jan 08 15:22
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200 4. Nonlinear Partial Differential Equations
4.4. Other Second-Order Equations
$\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\frac{a}{ax+by}\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}-
\frac{b^2}{(ax+by)^2}\left(\frac{\partial w}{\partial x}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:26
Edited (admin): 10 Jan 08 15:23
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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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