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List of Equations

The database contains 327 equations (7 equations are awaiting activation).

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Found 327 equations, 33 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 >>
 CategoryEquation(s)Author/
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1 1. Ordinary Differential Equations
1.2. Second-Order Linear Equations
$\displaystyle y''_{xx} + f(x)y'_x + g(x)y = 0$. Andrei Polyanin
Submitted: 09 Jul 07 14:59
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2 1. Ordinary Differential Equations
1.2. Second-Order Linear Equations
$\displaystyle (c_4x^4+c_3x^3+c_2x^2)y''_{xx}+(b_3x^3+b_2x^2+b_1x+b_0)y'_{x}+(a_2x^2+a_1x+a_0)y=0$\hfill\break Valeriy Stepuchev
Submitted: 27 Sep 10 19:39
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3 1. Ordinary Differential Equations
1.2. Second-Order Linear Equations
$\displaystyle fy''-f''y+\frac{4y}{f^3}=0$,\hfill\break
where $y(x)$ is unknown function, $f(x)>0$ is  given arbitrary function Yakov Dymarskii
Submitted: 07 Jan 11 12:19
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4 1. Ordinary Differential Equations
1.3. Second-Order Nonlinear Equations
\noindent
$\displaystyle [x+(2y-xy'_x)^3(y'_x)^2]y''_{xx}=y'_x$. Valentin Zaitsev
Submitted: 11 Dec 06 08:53
Edited (admin): 11 Dec 06 09:47
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5 1. Ordinary Differential Equations
1.3. Second-Order Nonlinear Equations
\noindent
$\displaystyle [(2x-9y)y'_x+3y]y''_{xx}=2(1-3y'_x)(y'_x)^2$. Valentin Zaitsev
Submitted: 11 Dec 06 09:01
Edited (admin): 12 Dec 06 19:55
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6 1. Ordinary Differential Equations
1.3. Second-Order Nonlinear Equations
$\displaystyle x^{2}y_{xx}^{\prime \prime }=axy_{x}^{\prime }+by+c\left( y_{x}^{\prime
}\right) ^{k}$,\hfill\break
where $a,b,c,k\neq 0$ and $k\neq 1$. Christos Koulovatianos
Submitted: 25 May 12 11:13
Edited (admin): 26 Aug 13 13:17
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7 1. Ordinary Differential Equations
1.4. Higher-Order Linear Equations
$\displaystyle \sum^n_{k=1}f_k(x)y^{[k]}_x+f_0(x)(a+x)y'_x-f_0(x)y=0 $,\hfill\break
where $f_k(x)$ are arbitrary functions, $a$ is an arbitrary constant. Valeriy Stepuchev
Submitted: 15 Apr 13 19:34
Edited (admin): 26 Aug 13 13:38
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8 1. Ordinary Differential Equations
1.5. Higher-Order Nonlinear Equations
\noindent
$\displaystyle y^{(n)}_x=f(x,y,y'_x,\dots,y^{(n-1)}_x)$. Yurii Kosovtsov
Submitted: 08 Dec 06 10:07
Edited (author): 15 Dec 06 09:43
Edited (admin): 25 Jun 08 15:41
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9 1. Ordinary Differential Equations
1.6. Systems of Two Nonlinear Equations
\noindent
$\displaystyle x''_{tt}=xf(x^2+y^2,y/x)-yg(y/x)$,\hfill\break
$\displaystyle y''_{tt}=yf(x^2+y^2,y/x)+xg(y/x)$. Andrei Polyanin
Submitted: 07 Dec 06 11:28
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10 1. Ordinary Differential Equations
1.6. Systems of Two Nonlinear Equations
$\displaystyle x'_t={\lambda_1}x+{\lambda}x^2+{\gamma}xy+{\delta}x^2y+\frac{\lambda_1\gamma\delta}{{\lambda_2}{\lambda}}xy^2$,\hfill\break
$\displaystyle y'_t={\lambda_2}y+{\lambda}xy+{\gamma}y^2-\frac{\lambda_2\lambda\delta}{\lambda_1\gamma}}x^2y-{\delta}xy^2$,\hfill\break
where $\lambda_1\ne\lambda_2$,$\lambda$,$\gamma$,$\delta$ real-valued parameters with obvious limitations on their values. Elbert Naziev
Submitted: 03 Dec 11 23:46
Edited (admin): 01 Sep 13 13:39
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Found 327 equations, 33 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 >>

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