2.2.117 Problems 11601 to 11700

Table 2.235: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

11601

\[ {}y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0 \]

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

2.979

11602

\[ {}y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0 \]

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

5.492

11603

\[ {}y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.328

11604

\[ {}y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0 \]

[[_2nd_order, _missing_x]]

5.862

11605

\[ {}8 y^{\prime \prime }+9 {y^{\prime }}^{4} = 0 \]

[[_2nd_order, _missing_x]]

1.014

11606

\[ {}x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.132

11607

\[ {}x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.152

11608

\[ {}x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.145

11609

\[ {}x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.144

11610

\[ {}x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.182

11611

\[ {}x y^{\prime \prime }+\left (y-1\right ) y^{\prime } = 0 \]

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

0.454

11612

\[ {}x y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2} = 0 \]

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

0.130

11613

\[ {}x y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.134

11614

\[ {}2 x y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0 \]

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

1.086

11615

\[ {}x^{2} y^{\prime \prime } = a \left (y^{n}-y\right ) \]

[[_2nd_order, _with_linear_symmetries]]

0.147

11616

\[ {}x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.157

11617

\[ {}x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.671

11618

\[ {}x^{2} y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b \,x^{2} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.135

11619

\[ {}x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.119

11620

\[ {}x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.239

11621

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]

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

0.850

11622

\[ {}4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.128

11623

\[ {}9 x^{2} y^{\prime \prime }+a y^{3}+2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.148

11624

\[ {}x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.154

11625

\[ {}x^{3} y^{\prime \prime }-a \left (-y+x y^{\prime }\right )^{2} = 0 \]

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

0.144

11626

\[ {}2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 y^{2} x^{2}\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.164

11627

\[ {}2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+y a x +b = 0 \]

[NONE]

0.352

11628

\[ {}x^{4} y^{\prime \prime }+a^{2} y^{n} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.131

11629

\[ {}x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2} = 0 \]

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

0.128

11630

\[ {}x^{4} y^{\prime \prime }-x^{2} \left (x +y^{\prime }\right ) y^{\prime }+4 y^{2} = 0 \]

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

0.132

11631

\[ {}x^{4} y^{\prime \prime }+\left (-y+x y^{\prime }\right )^{3} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.125

11632

\[ {}y^{\prime \prime } \sqrt {x}-y^{{3}/{2}} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.154

11633

\[ {}\left (a \,x^{2}+b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {a \,x^{2}+b x +c}}\right ) = 0 \]

[NONE]

8.835

11634

\[ {}y^{\prime \prime } y-a = 0 \]

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

0.820

11635

\[ {}y^{\prime \prime } y-a x = 0 \]

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.112

11636

\[ {}y^{\prime \prime } y-a \,x^{2} = 0 \]

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.115

11637

\[ {}y^{\prime \prime } y+{y^{\prime }}^{2}-a = 0 \]

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

3.016

11638

\[ {}y^{\prime \prime } y+y^{2}-a x -b = 0 \]

[NONE]

0.125

11639

\[ {}y^{\prime \prime } y+{y^{\prime }}^{2}-y^{\prime } = 0 \]

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

0.875

11640

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}+1 = 0 \]

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

1.173

11641

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}-1 = 0 \]

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

1.309

11642

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0 \]

[NONE]

0.289

11643

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}-y^{2} \ln \left (y\right ) = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

2.118

11644

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-f^{\prime }\left (x \right ) y-y^{3} = 0 \]

[NONE]

0.217

11645

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-f^{\prime \prime }\left (x \right ) y+f \left (x \right ) y^{3}-y^{4} = 0 \]

[NONE]

0.313

11646

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

1.621

11647

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}+a y y^{\prime }-2 a y^{2}+b y^{3} = 0 \]

[[_2nd_order, _missing_x]]

3.319

11648

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}-\left (-1+a y\right ) y^{\prime }+2 a^{2} y^{2}-2 b^{2} y^{3}+a y = 0 \]

[[_2nd_order, _missing_x]]

6.093

11649

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (y+1\right ) \left (b^{2} y^{2}-a^{2}\right ) = 0 \]

[[_2nd_order, _missing_x]]

10.332

11650

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right ) = 0 \]

[[_2nd_order, _reducible, _mu_xy]]

4.381

11651

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2} = 0 \]

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

0.222

11652

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (g \left (x \right )+y^{2} f \left (x \right )\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right ) = 0 \]

[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

0.372

11653

\[ {}y^{\prime \prime } y-3 {y^{\prime }}^{2}+3 y y^{\prime }-y^{2} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

3.953

11654

\[ {}y^{\prime \prime } y-a {y^{\prime }}^{2} = 0 \]

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

0.344

11655

\[ {}y^{\prime \prime } y+a \left (1+{y^{\prime }}^{2}\right ) = 0 \]

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

1.703

11656

\[ {}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y^{3} = 0 \]

[[_2nd_order, _missing_x]]

3.175

11657

\[ {}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y y^{\prime }+c y^{2}+d y^{1-a} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

10.645

11658

\[ {}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4} = 0 \]

[[_2nd_order, _missing_x]]

3.474

11659

\[ {}y^{\prime \prime } y-\frac {\left (a -1\right ) {y^{\prime }}^{2}}{a}-f \left (x \right ) y^{2} y^{\prime }+\frac {a f \left (x \right )^{2} y^{4}}{\left (a +2\right )^{2}}-\frac {a f^{\prime }\left (x \right ) y^{3}}{a +2} = 0 \]

[NONE]

0.382

11660

\[ {}y^{\prime \prime } y-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0 \]

[[_2nd_order, _missing_x]]

48.854

11661

\[ {}y^{\prime \prime } \left (x +y\right )+{y^{\prime }}^{2}-y^{\prime } = 0 \]

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

3.250

11662

\[ {}y^{\prime \prime } \left (x -y\right )+2 y^{\prime } \left (y^{\prime }+1\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.123

11663

\[ {}y^{\prime \prime } \left (x -y\right )-\left (y^{\prime }+1\right ) \left (1+{y^{\prime }}^{2}\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.126

11664

\[ {}y^{\prime \prime } \left (x -y\right )-h \left (y^{\prime }\right ) = 0 \]

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.406

11665

\[ {}2 y^{\prime \prime } y+{y^{\prime }}^{2}+1 = 0 \]

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

1.905

11666

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}+a = 0 \]

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

1.062

11667

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}+y^{2} f \left (x \right )+a = 0 \]

[NONE]

0.204

11668

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}-8 y^{3} = 0 \]

[[_2nd_order, _missing_x]]

74.992

11669

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}-8 y^{3}-4 y^{2} = 0 \]

[[_2nd_order, _missing_x]]

66.453

11670

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}-4 \left (x +2 y\right ) y^{2} = 0 \]

[NONE]

0.140

11671

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}+\left (a y+b \right ) y^{2} = 0 \]

[[_2nd_order, _missing_x]]

16.109

11672

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0 \]

[NONE]

0.144

11673

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}+\left (b x +a y\right ) y^{2} = 0 \]

[NONE]

0.139

11674

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}-3 y^{4} = 0 \]

[[_2nd_order, _missing_x]]

1.333

11675

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0 \]

[[_Painleve, ‘4th‘]]

0.163

11676

\[ {}2 y^{\prime \prime } y-3 {y^{\prime }}^{2} = 0 \]

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

0.349

11677

\[ {}2 y^{\prime \prime } y-3 {y^{\prime }}^{2}-4 y^{2} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

2.629

11678

\[ {}2 y^{\prime \prime } y-3 {y^{\prime }}^{2}+y^{2} f \left (x \right ) = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.193

11679

\[ {}2 y^{\prime \prime } y-6 {y^{\prime }}^{2}+\left (1+a y^{3}\right ) y^{2} = 0 \]

[[_2nd_order, _missing_x]]

2.154

11680

\[ {}2 y^{\prime \prime } y-{y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right ) = 0 \]

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

2.516

11681

\[ {}2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]

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

1.519

11682

\[ {}3 y^{\prime \prime } y-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0 \]

[NONE]

0.132

11683

\[ {}3 y^{\prime \prime } y-5 {y^{\prime }}^{2} = 0 \]

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

0.430

11684

\[ {}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+4 y = 0 \]

[[_2nd_order, _missing_x]]

2.087

11685

\[ {}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}-12 y^{3} = 0 \]

[[_2nd_order, _missing_x]]

24.495

11686

\[ {}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y = 0 \]

[[_2nd_order, _missing_x]]

4.702

11687

\[ {}4 y^{\prime \prime } y-5 {y^{\prime }}^{2}+a y^{2} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

2.518

11688

\[ {}12 y^{\prime \prime } y-15 {y^{\prime }}^{2}+8 y^{3} = 0 \]

[[_2nd_order, _missing_x]]

1.218

11689

\[ {}n y y^{\prime \prime }-\left (n -1\right ) {y^{\prime }}^{2} = 0 \]

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

0.397

11690

\[ {}a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0 \]

[[_2nd_order, _missing_x]]

4.088

11691

\[ {}a y y^{\prime \prime }+b {y^{\prime }}^{2}-\frac {y y^{\prime }}{\sqrt {c^{2}+x^{2}}} = 0 \]

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

0.417

11692

\[ {}\left (a y+b \right ) y^{\prime \prime }+c {y^{\prime }}^{2} = 0 \]

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

0.373

11693

\[ {}x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0 \]

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

1.118

11694

\[ {}x y y^{\prime \prime }+x {y^{\prime }}^{2}+a y y^{\prime }+f \left (x \right ) = 0 \]

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

0.192

11695

\[ {}x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right ) = 0 \]

[[_Painleve, ‘3rd‘]]

0.168

11696

\[ {}x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+b x y^{3} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.145

11697

\[ {}x y y^{\prime \prime }+2 x {y^{\prime }}^{2}+a y y^{\prime } = 0 \]

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

0.759

11698

\[ {}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (y+1\right ) y^{\prime } = 0 \]

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

0.121

11699

\[ {}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+a y y^{\prime } = 0 \]

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

0.214

11700

\[ {}x y y^{\prime \prime }-4 x {y^{\prime }}^{2}+4 y y^{\prime } = 0 \]

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

0.546