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View Equation

The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.2. Second-Order Quasilinear Hyperbolic Equations
Equation(s):\noindent
$\displaystyle f(w)\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial x^2}+\left[g(w)\frac{\partial w}{\partial y}-f(w)\frac{\partial w}{\partial x}\right]\frac{\partial^2 w}{\partial x\partial y}-g(w)\frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial y^2}=0$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
$1^\circ$.\enspace First integral:
$$
f(w)\frac{\partial w}{\partial x}+g(w)\frac{\partial w}{\partial y}=\varphi(w),
$$
where $\varphi(w)$ is an arbitrary function.
\medskip

\noindent
$2^\circ$.\enspace General solution in implicit form:
$$
\Psi\left(x-\int\frac{f(w)}{\varphi(w)}\,dw,\,y-\int\frac{g(w)}{\varphi(w)}\,dw\right)=0,
$$
where $\Psi(z_1,z_2)$ and $\varphi(w)$ are arbitrary functions.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Sat 16 Dec 2006 11:44
Edits by author:0

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