2.2.61 Problems 6001 to 6100

Table 2.123: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

6001

r=kr2

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

67.089

6002

y=3ky22

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

4.298

6003

y=2ky3

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

5.529

6004

yy+y2y=0

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

1.254

6005

r=h2r3kr2

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

6.184

6006

yy+y3y2=0

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.750

6007

yy3y2=0

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.694

6008

(x2+1)y+1+y2=0

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

1.060

6009

(x2+1)y+2x(y+1)=0

[[_2nd_order, _missing_y]]

1.188

6010

(1+y)y=3y2
i.c.

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.645

6011

y=eyy
i.c.

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]

3.135

6012

y=2yy
i.c.

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

14.013

6013

2y=ey
i.c.

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.446

6014

x2y+yx=1
i.c.

[[_2nd_order, _missing_y]]

0.959

6015

xyy=x2
i.c.

[[_2nd_order, _missing_y]]

1.286

6016

xyy2xy2+yy=0

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.308

6017

xyy+xy2yy=0

[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

1.260

6018

xyy2xy2+(1+y)y=0

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.258

6019

ay3bx3/2+y=0

[[_homogeneous, ‘class G‘], _rational, _Abel]

3.983

6020

axy3+by2+y=0

[[_homogeneous, ‘class G‘], _Abel]

2.476

6021

yxay3+3y2xayx2a+axa1=0

[_Abel]

3.348

6022

y(yf(x))(yg(x))(yaf(x)+bg(x)a+b)h(x)f(x)(yg(x))f(x)g(x)g(x)(yf(x))g(x)f(x)=0

[_Abel]

41.888

6023

x2y+xy3+ay2=0

[_rational, _Abel]

1.212

6024

(ax+b)2y+(ax+b)y3+cy2=0

[_rational, _Abel]

2.636

6025

y+ytan(x)=0

[_separable]

1.367

6026

x2y2yx+2y=0

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.015

6027

yy2+2yxy=0

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

1.857

6028

(x2+1)y2+1=0

[_quadrature]

0.455

6029

y=eax+ay

[[_linear, ‘class A‘]]

0.831

6030

(1+y2)3=a2y2

[[_2nd_order, _missing_x]]

211.332

6031

x(1y)y+(x+1)y=0

[_separable]

1.636

6032

y=axy2

[_separable]

1.615

6033

y2+xy2+(x2x2y)y=0

[_separable]

1.858

6034

xy(x2+1)y=1+y2

[_separable]

3.799

6035

x1+y=yyx+1

[_separable]

1.649

6036

y+b2y2=a2

[_quadrature]

3.639

6037

y=1+y2x2+1

[_separable]

1.863

6038

sin(x)cos(y)=cos(x)sin(y)y

[_separable]

2.792

6039

axy+2y=xyy

[_separable]

2.167

6040

xy+(x+n)y+(n+1)y=0

[[_2nd_order, _with_linear_symmetries]]

0.846

6041

y+xy=0

[[_Emden, _Fowler]]

0.302

6042

2x2yyx+(x2+1)y=x2

[[_2nd_order, _linear, _nonhomogeneous]]

0.700

6043

xy+2y+a3x2y=2

[[_2nd_order, _linear, _nonhomogeneous]]

0.693

6044

y+ax2y=x+1

[[_2nd_order, _linear, _nonhomogeneous]]

0.442

6045

x4y+yx+y=0

[[_2nd_order, _with_linear_symmetries]]

0.228

6046

x2y+(2x2+x)y4y=0

[[_2nd_order, _with_linear_symmetries]]

0.777

6047

(x2+x)y+3y+2y=0

[[_2nd_order, _exact, _linear, _homogeneous]]

0.739

6048

(4x314x22x)y(6x27x+1)y+(6x1)y=0

[[_2nd_order, _with_linear_symmetries]]

0.898

6049

x2y+x2y+(x2)y=0

[[_2nd_order, _with_linear_symmetries]]

0.860

6050

x2yx2y+(x2)y=0

[[_2nd_order, _with_linear_symmetries]]

0.817

6051

x2(14x)y+((1n)x(64n)x2)y+n(1n)xy=0

[[_2nd_order, _with_linear_symmetries]]

0.989

6052

x2y+(x2+x)y+(x9)y=0

[[_2nd_order, _with_linear_symmetries]]

0.937

6053

(a2+x2)y+yxn2y=0

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.593

6054

(x2+1)yyx+a2y=0

[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.585

6055

xy+y+y=0

[[_Emden, _Fowler]]

0.628

6056

xy+y+pxy=0

[[_2nd_order, _with_linear_symmetries]]

0.561

6057

xy+y=0

[[_Emden, _Fowler]]

1.224

6058

x3y(2x1)y=0

[[_2nd_order, _with_linear_symmetries]]

0.163

6059

x2y+x(x+1)y+(3x1)y=0

[[_2nd_order, _with_linear_symmetries]]

1.371

6060

(x2+x)yy=0

[[_2nd_order, _with_linear_symmetries]]

1.421

6061

x(x2+1)y+(3x2+1)yxy=0

[[_elliptic, _class_I]]

0.604

6062

y+ayx3/2=0

[[_Emden, _Fowler]]

0.213

6063

x2y(x2+4x)y+4y=0

[[_2nd_order, _with_linear_symmetries]]

1.385

6064

x(x2+1)y+(x2+1)y+xy=0

[[_elliptic, _class_II]]

0.622

6065

4x(1x)y4yy=0

[_Jacobi]

1.544

6066

x3y+y=x3/2

[[_2nd_order, _linear, _nonhomogeneous]]

0.170

6067

2x2y(3x+2)y+(2x1)yx=x

[[_2nd_order, _linear, _nonhomogeneous]]

0.213

6068

(x2+x)y+3y+2y=3x2

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.944

6069

x(1x)y+(322x)yy4=0

[_Jacobi]

0.772

6070

2x(1x)y+yxy=0

[[_2nd_order, _with_linear_symmetries]]

1.427

6071

2x(1x)y+(111x)y10y=0

[_Jacobi]

0.766

6072

x(1x)y+(2x+1)y3+20y9=0

[_Jacobi]

0.817

6073

2x(1x)y+y+4y=0

[[_2nd_order, _exact, _linear, _homogeneous]]

0.780

6074

4y+3(x2+2)y(x2+1)2=0

[[_2nd_order, _with_linear_symmetries]]

0.520

6075

y+y2=a2x4

[_rational, _Riccati]

1.968

6076

ua2ux2/3=0

[[_Emden, _Fowler]]

0.295

6077

u2uxa2u=0

[[_2nd_order, _with_linear_symmetries]]

0.734

6078

u+2uxa2u=0

[[_2nd_order, _with_linear_symmetries]]

0.692

6079

u+2ux+a2u=0

[[_2nd_order, _with_linear_symmetries]]

0.671

6080

u+4uxa2u=0

[[_2nd_order, _with_linear_symmetries]]

0.676

6081

u+4ux+a2u=0

[[_2nd_order, _with_linear_symmetries]]

0.787

6082

ya2y=6yx2

[[_2nd_order, _with_linear_symmetries]]

0.712

6083

y+n2y=6yx2

[[_2nd_order, _with_linear_symmetries]]

0.792

6084

x2y+yx(x2+14)y=0

[[_2nd_order, _with_linear_symmetries]]

0.694

6085

x2y+yx+(9a2+4x2)y4a2=0

[[_2nd_order, _with_linear_symmetries]]

0.858

6086

x2y+yx+(x2254)y=0

[[_2nd_order, _with_linear_symmetries]]

0.723

6087

y+qy=2yx2

[[_2nd_order, _with_linear_symmetries]]

0.636

6088

y+e2xy=n2y

[[_2nd_order, _with_linear_symmetries]]

0.321

6089

y+y4x=0

[[_Emden, _Fowler]]

0.298

6090

xy+y+y=0

[[_Emden, _Fowler]]

0.317

6091

xy+3y+4x3y=0

[[_Emden, _Fowler]]

0.706

6092

y=y

[_quadrature]

0.697

6093

yx=y
i.c.

[_separable]

1.588

6094

x1y2+yx2+1y=0
i.c.

[_separable]

2.793

6095

ysin(x)=yln(y)
i.c.

[_separable]

3.228

6096

xyy+1+y2=0
i.c.

[_separable]

2.390

6097

xyyxy=y
i.c.

[_quadrature]

0.777

6098

y=2xy2+xx2yy
i.c.

[_separable]

2.729

6099

yy+xy28x=0
i.c.

[_separable]

2.648

6100

y+2xy2=0
i.c.

[_separable]

2.086