Some Well known differential Equation

### Author Topic: Some Well known differential Equation  (Read 2154 times)

#### Masuma Parvin

• Sr. Member
• Posts: 323
##### Some Well known differential Equation
« on: May 22, 2013, 03:40:28 PM »
Abel's differential equation
y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3+...
(26)
[g_0(x)+g_1(x)y]y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3.
(27)

Airy differential equation
y^('')-xy=0.
(28)

Anger differential equation
y^('')+(y^')/x+(1-(nu^2)/(x^2))y=(x-nu)/(pix^2)sin(nupi).
(29)

Baer differential equations
(x-a_1)(x-a_2)y^('')+1/2[2x-(a_1+a_2)]y^'-(p^2x+q^2)y=0,
(30)
(x-a_1)(x-a_2)y^('')+1/2[2x-(a_1+a_2)]y^'-(k^2x^2-p^2x+q^2)y=0.
(31)

Bernoulli differential equation
y^'+p(x)y=q(x)y^n.
(32)

Bessel differential equation
x^2y^('')+xy^'+(lambda^2x^2-n^2)y=0.
(33)

Binomial differential equation
(y^')^m=f(x,y).
(34)

Bôcher equation
y^('')+1/2[(m_1)/(x-a_1)+...+(m_(n-1))/(x-a_(n-1))]y^' +1/4[(A_0+A_1x+...+A_lx^l)/((x-a_1)^(m_1)(x-a_2)^(m_2)...(x-a_(n-1))^(m_(n-1)))]y=0.
(35)

Briot-Bouquet equation
x^my^'=f(x,y).
(36)

Chebyshev differential equation
(1-x^2)y^('')-xy^'+alpha^2y=0.
(37)

Clairaut's differential equation
y=xy^'+f(y^').
(38)

Confluent hypergeometric differential equation
xy^('')+(c-x)y^'-ay=0.
(39)

d'Alembert's equation
y=xf(y^')+g(y^').
(40)

Duffing differential equation
y^('')+omega_0^2y+betay^3=0.
(41)

Eckart differential equation
y^('')+[(alphaeta)/(1+eta)+(betaeta)/((1+eta)^2)+gamma]y=0,
(42)

where eta=e^(deltax).

Emden-Fowler differential equation
(x^py^')^'+/-x^sigmay^n=0.
(43)

Euler differential equation
x^2y^('')+axy^'+by=S(x).
(44)

Halm's differential equation
(1+x^2)^2+y^('')+lambday=0.
(45)

Hermite differential equation
y^('')-2xy^'+lambday=0.
(46)

Heun's differential equation
w^('')+(gamma/x+delta/(x-1)+epsilon/(x-a))w^'+(alphabetax-q)/(x(x-1)(x-a))w=0,
(47)

where w^'=dw/dx.

Hill's differential equation
y^('')+[theta_0+2sum_(n=1)^inftytheta_ncos(2nz)]y=0.
(48)

Hypergeometric differential equation
x(x-1)y^('')+[(1+alpha+beta)x-gamma]y^'+alphabetay=0.
(49)

Jacobi differential equation
(1-x^2)y^('')+[beta-alpha-(alpha+beta+2)x]y^'+n(n+alpha+beta+1)y=0.
(50)

Laguerre differential equation
xy^('')+(1-x)y^'+lambday=0.
(51)

Lamé's differential equation
(x^2-b^2)(x^2-c^2)z^('')+x(x^2-b^2+x^2-c^2)z^'-[m(m+1)x^2-(b^2+c^2)p]z=0,
(52)

where z^'=dz/dx.

Lane-Emden differential equation
1/(xi^2)d/(dxi)(xi^2(dtheta)/(dxi))+theta^n=0.
(53)

Legendre differential equation
(1-x^2)y^('')-2xy^'+alpha(alpha+1)y=0.
(54)

Linear constant coefficients
a_0y^((n))+...+a_(n-1)y^'+a_ny=p(x).
(55)

Lommel differential equation
x^2y^('')+xy^'-(x^2+nu^2)y=kx^(mu+1).
(56)

Löwner's differential equation
y^'=-y(1+kappa(x)y)/(1-kappa(x)y).
(57)

Malmstén's differential equation
y^('')+r/zy^'=(Az^m+s/(z^2))y.
(58)

Mathieu differential equation
V^('')+[a-2qcos(2v)]V=0,
(59)

where V^'=dV/dv.

Modified Bessel differential equation
x^2y^('')+xy^'-(x^2+n^2)y=0.
(60)

Modified spherical Bessel differential equation
r^2R^('')+2rR^'-[k^2r^2+n(n+1)]R=0,
(61)

where R^'=dR/dr

Rayleigh differential equation
y^('')-mu(1-1/3y^('2))y^'+y=0.
(62)

Riccati differential equation
w^'=q_0(x)+q_1(x)w+q_2(x)w^2.
(63)

Riemann P-Differential Equation
u^('')+[(1-alpha-alpha^')/(z-a)+(1-beta-beta^')/(z-b)+(1-gamma-gamma^')/(z-c)]u^' +[(alphaalpha^'(a-b)(a-c))/(z-a)+(betabeta^'(b-c)(b-a))/(z-b)+(gammagamma^'(c-a)(c-b))/(z-c)]u/((z-a)(z-b)(z-c))=0,
(64)

where u^'=du/dz.

Sharpe's differential equation
zy^('')+y^'+(z+A)y=0.
(65)

Spherical Bessel differential equation
r^2R^('')+2rR^'+[k^2r^2-n(n+1)]R=0,
(66)

where R^'=dR/dr.

Struve differential equation
z^2y^('')+zy^'+(z^2-nu^2)y=(4(1/2z)^(nu+1))/(sqrt(pi)Gamma(nu+1/2)).
(67)

Sturm-Liouville equation
d/(dx)[p(x)y^']+[lambdaw(x)-q(x)]y=0.
(68)

Gegenbauer differential equation
(1-x^2)y^('')-(2alpha+1)xy^'+n(n+2alpha)y=0.
(69)

van der Pol equation
y^('')-mu(1-y^2)y^'+y=0.
(70)

Weber differential equation
y^('')+(n+1/2-1/4z^2)y=0,
(71)

where y^'=dy/dz.

Whittaker differential equation
u^('')+u^'+(k/z+(1/4-m^2)/(z^2))u=0,
(72)

where u^'=du/dz.

• Newbie
• Posts: 42
##### Re: Some Well known differential Equation
« Reply #1 on: May 25, 2013, 06:37:19 PM »
Dear M. Parvin,

Your compilation is good. As you might have noticed that your post is quite difficult to read for computer font problem. It will be better to re-post it.

Thanks.
Senior Lecturer (Mathematics)
Department of Natural Sciences,
Daffodil International University,
Faculty of Science and Information Technology.

#### Nizhum

• Full Member
• Posts: 101
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##### Re: Some Well known differential Equation
« Reply #2 on: March 21, 2018, 02:32:21 AM »
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