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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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51 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
f(x)\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial y^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:41
Edited (admin): 10 Jan 08 15:09
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52 \begin{multline*} \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(u)\left(\frac{\partial w}{\partial y}-\frac{\partial w}{\partial x}\right)+f(w)\right]
\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial x\partial y}+\\
+\left[g(w)\frac{\partial w}{\partial x}-f(w)\right]
\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}-
g(w)\left(\frac{\partial w}{\partial x}\right)^2\frac{\partial^2 w}{\partial y^2}=0.
\end{multline*} Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:41
Edited (admin): 10 Jan 08 15:11
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53 \begin{multline*} \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(w)-g(w)]\frac{\partial w}{\partial x}+[f(w)+g(w)]\frac{\partial w}{\partial y}\right\}
\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial x\partial y}+\\
+\left\{[g(w)-f(w)]\frac{\partial w}{\partial x}-f(w)\frac{\partial w}{\partial y}\right\}
\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}-
g(w)\left(\frac{\partial w}{\partial x}\right)^2\frac{\partial^2 w}{\partial y^2}=0.
\end{multline*} Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:40
Edited (admin): 10 Jan 08 15:11
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54 \begin{multline*} \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(w)\left(\frac{\partial w}{\partial x}\right)^2+\left[f(w)\frac{\partial w}{\partial y}-g(w)\right]\frac{\partial w}{\partial x}+
g(w)\frac{\partial w}{\partial y}\right\}\frac{\partial^2 w}{\partial x\partial y}-\\
-\left[f(w)\left(\frac{\partial w}{\partial y}\right)^2+f(w)\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}-
g(w)\frac{\partial w}{\partial y}\right]\frac{\partial^2 w}{\partial x^2}-g(w)\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}=0.
\end{multline*} Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:39
Edited (admin): 10 Jan 08 15:12
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55 \begin{multline*} \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)\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}+
\left[h(x)\frac{\partial w}{\partial y}+g(y)\frac{\partial w}{\partial x}\right]\frac{\partial^2 w}{\partial x\partial y}-\\
-p(x)\frac{\partial^2 w}{\partial y^2}+[p(x)f(y)+h(x)g(y)]\frac{\partial w}{\partial x}\frac{\partial w}{\partial y}=0.
\end{multline*} Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:38
Edited (admin): 10 Jan 08 15:13
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56 \begin{multline*} \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)\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}+
\left[h(x)\frac{\partial w}{\partial y}+g(y)\right]\frac{\partial^2 w}{\partial x\partial y}-\\
-p(x)\frac{\partial^2 w}{\partial y^2}+[h(x)g(y)+f(y)p(x)]\frac{\partial w}{\partial y}=0.
\end{multline*} Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:38
Edited (admin): 10 Jan 08 15:13
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57 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
f(y)\frac{\partial^2 w}{\partial x^2}+[h(x)+g(y)]\frac{\partial^2 w}{\partial x\partial y}-
p(x)\frac{\partial^2 w}{\partial y^2}+h(x)g(y)+f(y)p(x)=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:37
Edited (admin): 10 Jan 08 15:15
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58 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
g(y)\frac{\partial^2 w}{\partial x^2}-
f(x)\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}-
f(x)g(y)\frac{\partial w}{\partial x}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:36
Edited (admin): 10 Jan 08 15:16
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59 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
\left[g(y)+h(w)\frac{\partial w}{\partial y}\right]\frac{\partial^2 w}{\partial x\partial y}-
\left[f(x)+h(w)\frac{\partial w}{\partial x}\right]\frac{\partial^2 w}{\partial y^2}=0$.\hfill\break Valentin Feodorovich Zaitsev
Submitted: 09 Jan 08 13:36
Edited (admin): 10 Jan 08 15:16
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60 \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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Found 106 equations, 11 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 >>

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