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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

4.5. Third-Order Equations

Found 21 equations, 3 pages (10 eqs. per page): << 1 2 3 >>
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1 \noindent
$\displaystyle \frac{\partial w}{\partial t}+aw^k\frac{\partial w}{\partial x}-
b\frac{\partial^3 w}{\partial t^3}=0$. Andrei Polyanin
Submitted: 08 Dec 06 12:42
Edited (author): 08 Dec 06 13:12
Edited (admin): 11 Dec 06 11:04
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2 \noindent
$\displaystyle \frac{\partial w}{\partial t}=
a\frac{\partial^3 w}{\partial x^3}+(b\ln w+c)\frac{\partial w}{\partial x}$. Andrei Polyanin
Submitted: 11 Dec 06 14:52
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3 $\displaystyle \frac{\partial^3 w}{\partial x^2\partial y}\frac{\partial^3 w}{\partial x\partial y^2}-
\frac{\partial^3 w}{\partial x^3}\frac{\partial^3 w}{\partial y^3}+
\left[g(y)\frac{\partial^3 w}{\partial x\partial y^2}-f(x)\frac{\partial^3 w}{\partial y^3}\right]
\frac{\partial^2 w}{\partial x^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:37
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4 $\displaystyle \left[\frac{\partial^2 w}{\partial x\partial y}+
g(y)\frac{\partial w}{\partial x}\right]\frac{\partial^3 w}{\partial x\partial y^2}-
\left[\frac{\partial^2 w}{\partial x^2}+
f(x)\frac{\partial w}{\partial x}\right]\frac{\partial^3 w}{\partial y^3}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:38
Edited (admin): 10 Jan 08 11:20
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5 $\displaystyle \frac{\partial^2 w}{\partial x\partial y}\frac{\partial^3 w}{\partial x^2\partial y}-
\frac{\partial^2 w}{\partial y^2}\frac{\partial^3 w}{\partial x^3}+
\left[g(y)\frac{\partial^2 w}{\partial x\partial y}-f(x)\frac{\partial^2 w}{\partial y^2}\right]
\frac{\partial^2 w}{\partial x^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:37
Edited (admin): 10 Jan 08 12:56
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6 $\displaystyle \frac{\partial w}{\partial x}\frac{\partial^3 w}{\partial x^2\partial y}-
\frac{\partial w}{\partial y}\frac{\partial^3 w}{\partial x^3}+
\left[g(y)\frac{\partial w}{\partial x}-f(x)\frac{\partial w}{\partial y}\right]
\frac{\partial^2 w}{\partial x^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:36
Edited (admin): 10 Jan 08 12:58
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7 $\displaystyle \left(\frac{\partial^3 w}{\partial x\partial y^2}\right)^2-
\left[\frac{\partial^3 w}{\partial y^3}+
h(w)\frac{\partial w}{\partial y}+g(y)\right]\frac{\partial^3 w}{\partial x^2\partial y}+
\left[
h(w)\frac{\partial w}{\partial x}+f(x)\right]\frac{\partial^3 w}{\partial x\partial y^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:35
Edited (admin): 10 Jan 08 12:59
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8 $\displaystyle \left[\frac{\partial^3 w}{\partial y^3}+
h(w)\frac{\partial w}{\partial y}+g(y)\right]\frac{\partial^3 w}{\partial x^3}-
\left[\frac{\partial^3 w}{\partial x\partial y^2}+
h(w)\frac{\partial w}{\partial x}+f(x)\right]\frac{\partial^3 w}{\partial x^2\partial y}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:34
Edited (admin): 10 Jan 08 13:00
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9 $\displaystyle \left(\frac{\partial^3 w}{\partial x^2\partial y}\right)^2-
\frac{\partial^3 w}{\partial x^3}\frac{\partial^3 w}{\partial x\partial y^2}+
f\left(\frac{\partial w}{\partial y}\right)\frac{\partial^2 w}{\partial x\partial y}
\left(\frac{\partial^2 w}{\partial x\partial y}\frac{\partial^3 w}{\partial x^2\partial y}-
\frac{\partial^2 w}{\partial y^2}\frac{\partial^3 w}{\partial x^3}\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:33
Edited (admin): 10 Jan 08 13:01
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10 $\displaystyle \frac{\partial^3 w}{\partial x^3}\frac{\partial^3 w}{\partial y^3}-
\frac{\partial^3 w}{\partial x^2\partial y}\frac{\partial^3 w}{\partial x\partial y^2}+
f(w)\frac{\partial^2 w}{\partial y^2}\left(\frac{\partial w}{\partial y}\frac{\partial^3 w}{\partial x^3}-
\frac{\partial w}{\partial x}\frac{\partial^3 w}{\partial x^2\partial y}\right)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 16:33
Edited (admin): 10 Jan 08 13:02
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Found 21 equations, 3 pages (10 eqs. per page): << 1 2 3 >>

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