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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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61 $\displaystyle \left[1+f\left(\frac{\partial w}{\partial x}\right)
\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}\right]\left[\frac{\partial^2 w}{\partial x^2}
\frac{\partial^2 w}{\partial y^2}-\left(\frac{\partial^2 w}{\partial x\partial y}\right)^2\right]+
f\left(\frac{\partial w}{\partial x}\right)\left(\frac{\partial w}{\partial y}\right)^3
\frac{\partial^2 w}{\partial x\partial y}+\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial y^2}
=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:34
Edited (admin): 10 Jan 08 15:17
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62 $\displaystyle (ax-ay-b)^2\left[\frac{\partial^2 w}{\partial x^2}
\frac{\partial^2 w}{\partial y^2}-\left(\frac{\partial^2 w}{\partial x\partial y}\right)^2\right]+
c\left(\frac{\partial^2 w}{\partial x^2}+
2\frac{\partial^2 w}{\partial x\partial y}+
\frac{\partial^2 w}{\partial y^2}\right)+\left(a\frac{\partial w}{\partial x}+
a\frac{\partial w}{\partial y}+d\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:33
Edited (admin): 10 Jan 08 15:18
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63 $\displaystyle \left(\frac{\partial w}{\partial x}+f(x)\right)
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial x\partial y}-
\left(\frac{\partial w}{\partial y}+g(y)\right)\left(\frac{\partial^2 w}{\partial x^2}\right)^2-
\left(\frac{\partial w}{\partial x}+f(x)\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:32
Edited (admin): 10 Jan 08 15:19
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64 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{1}{(bx+ay+d)^2}\left(a\frac{\partial w}{\partial x}-b\frac{\partial w}{\partial y}+c\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:31
Edited (admin): 10 Jan 08 15:20
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65 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\left[f(x)\frac{\partial w}{\partial x}+f'_x(x)w\right]\frac{\partial^2 w}{\partial y^2}-
f^2(x)\left(\frac{\partial w}{\partial y}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:29
Edited (admin): 10 Jan 08 15:21
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66 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
g(y)\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial x\partial y}-
f(y)\frac{\partial^2 w}{\partial x^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:28
Edited (admin): 10 Jan 08 15:22
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67 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{2a}{ax+b}\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x\partial y}+
\frac{2a^2}{(ax+b)^2}\left(\frac{\partial w}{\partial y}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:27
Edited (admin): 10 Jan 08 15:22
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68 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\frac{a}{ax+by}\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}-
\frac{b^2}{(ax+by)^2}\left(\frac{\partial w}{\partial x}\right)^2=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:26
Edited (admin): 10 Jan 08 15:23
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69 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\frac{\partial w}{\partial y}\left[\frac{\partial w}{\partial y}-
f(y)\right]\frac{\partial^2 w}{\partial x^2}-
\left(\frac{\partial w}{\partial x}\right)^2\frac{\partial^2 w}{\partial y^2}-
f(y)\left(\frac{\partial w}{\partial x}\right)^2\frac{\partial w}{\partial y}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:25
Edited (admin): 10 Jan 08 15:24
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70 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{a}{y}\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}=0$. Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:24
Edited (admin): 10 Jan 08 15:27
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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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