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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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71 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{1}{a^2y^2}\left(x\frac{\partial w}{\partial x}+
a^2y\frac{\partial w}{\partial y}\right)\frac{\partial^2 w}{\partial x^2}-
\frac{1}{a^2y^2}\left(\frac{\partial w}{\partial x}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:23
Edited (admin): 10 Jan 08 15:28
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72 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{1}{2bx}\left(\frac{\partial w}{\partial y}\right)^{-1}
\left(a+b\frac{\partial w}{\partial y}\right)
\left(\frac{\partial^2 w}{\partial x^2}+
2\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x\partial y}\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:22
Edited (admin): 10 Jan 08 15:29
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73 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
a\frac{\partial^2 w}{\partial x^2}-b^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:21
Edited (admin): 10 Jan 08 15:30
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74 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{1}{x^2}\left[y\frac{\partial w}{\partial y}+
x\frac{\partial w}{\partial x}+xf(x)\right]\frac{\partial^2 w}{\partial y^2}-
\frac{1}{x^2}\left(\frac{\partial w}{\partial y}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:21
Edited (admin): 10 Jan 08 15:31
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75 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
ae^{-2x}\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}+
\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}-
\frac{\partial w}{\partial y}\left(ae^{-2x}\frac{\partial w}{\partial x}+
\frac{\partial w}{\partial y}\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:20
Edited (admin): 10 Jan 08 15:32
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76 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
f(x)\frac{\partial^2 w}{\partial y^2}-1=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:19
Edited (admin): 10 Jan 08 15:33
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77 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
f(y)\left(x-\frac{\partial w}{\partial y}\right)\frac{\partial^2 w}{\partial x^2}-1=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:18
Edited (admin): 10 Jan 08 15:34
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78 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\left(\frac{\partial w}{\partial x}\right)^{-1}
\left[f(x)\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}+
2\frac{\partial w}{\partial x}+f(x)w\right]\left(\frac{\partial^2 w}{\partial x\partial y}+1\right)
-1=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:17
Edited (admin): 10 Jan 08 15:37
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79 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{f'(x)}{f(x)}\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}-
\frac{1}{f^2(x)}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:16
Edited (admin): 10 Jan 08 15:37
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80 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
2\frac{\partial^2 w}{\partial x^2}+(a+1)\frac{\partial^2 w}{\partial x\partial y}+a=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:14
Edited (admin): 10 Jan 08 15:38
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Found 106 equations, 11 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 >>

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