2.2.111 Problems 11001 to 11100

Table 2.223: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

11001

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

[[_2nd_order, _linear, _nonhomogeneous]]

13.765

11002

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

[[_2nd_order, _missing_x]]

2.043

11003

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.297

11004

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.993

11005

\[ {}y^{\prime \prime }+l y = 0 \]

[[_2nd_order, _missing_x]]

3.281

11006

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

[[_2nd_order, _with_linear_symmetries]]

0.523

11007

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

[[_2nd_order, _with_linear_symmetries]]

0.706

11008

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

[[_2nd_order, _with_linear_symmetries]]

0.415

11009

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

[[_2nd_order, _with_linear_symmetries]]

0.816

11010

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

[[_Emden, _Fowler]]

0.750

11011

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

[_Titchmarsh]

0.343

11012

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

[[_2nd_order, _with_linear_symmetries]]

0.332

11013

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

[[_2nd_order, _with_linear_symmetries]]

0.516

11014

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

[[_2nd_order, _with_linear_symmetries]]

0.501

11015

\[ {}y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.383

11016

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

[[_2nd_order, _with_linear_symmetries]]

0.385

11017

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

[[_2nd_order, _with_linear_symmetries]]

0.899

11018

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

[_ellipsoidal]

0.765

11019

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

[_ellipsoidal]

0.934

11020

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

[[_2nd_order, _with_linear_symmetries]]

0.854

11021

\[ {}y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (n -1\right )}{\sin \left (x \right )^{2}}+a \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

6.010

11022

\[ {}y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.356

11023

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

[[_2nd_order, _with_linear_symmetries]]

0.416

11024

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

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

1.378

11025

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

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

0.871

11026

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

[[_2nd_order, _missing_x]]

3.342

11027

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.631

11028

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

[[_2nd_order, _with_linear_symmetries]]

0.686

11029

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

[[_2nd_order, _with_linear_symmetries]]

0.462

11030

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.142

11031

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

[[_2nd_order, _with_linear_symmetries]]

1.405

11032

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

[[_2nd_order, _with_linear_symmetries]]

0.593

11033

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

[[_2nd_order, _with_linear_symmetries]]

0.608

11034

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

[_Hermite]

0.993

11035

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

[_Hermite]

0.612

11036

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

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

1.159

11037

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

[[_2nd_order, _with_linear_symmetries]]

0.517

11038

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

[[_2nd_order, _with_linear_symmetries]]

0.536

11039

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

[[_2nd_order, _with_linear_symmetries]]

0.643

11040

\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

3.854

11041

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

[[_2nd_order, _with_linear_symmetries]]

0.573

11042

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.009

11043

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

[[_2nd_order, _with_linear_symmetries]]

0.687

11044

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

[[_2nd_order, _with_linear_symmetries]]

34.889

11045

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

[[_2nd_order, _with_linear_symmetries]]

0.905

11046

\[ {}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2.629

11047

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

[[_2nd_order, _with_linear_symmetries]]

1.459

11048

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

[[_2nd_order, _with_linear_symmetries]]

1.043

11049

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

[[_2nd_order, _with_linear_symmetries]]

1.027

11050

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

[[_2nd_order, _with_linear_symmetries]]

1.623

11051

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

[[_2nd_order, _with_linear_symmetries]]

0.682

11052

\[ {}y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} = 0 \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.391

11053

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

[[_2nd_order, _with_linear_symmetries]]

1.101

11054

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.558

11055

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

[[_2nd_order, _linear, _nonhomogeneous]]

26.267

11056

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

[[_2nd_order, _with_linear_symmetries]]

1.769

11057

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

[[_2nd_order, _with_linear_symmetries]]

3.436

11058

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

[[_2nd_order, _with_linear_symmetries]]

2.872

11059

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

[[_2nd_order, _with_linear_symmetries]]

1.419

11060

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

[[_2nd_order, _with_linear_symmetries]]

2.496

11061

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

[[_2nd_order, _with_linear_symmetries]]

1.595

11062

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

[[_2nd_order, _with_linear_symmetries]]

1.687

11063

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

[[_2nd_order, _with_linear_symmetries]]

3.370

11064

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

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

1.449

11065

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

[[_2nd_order, _with_linear_symmetries]]

0.813

11066

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

[[_2nd_order, _with_linear_symmetries]]

1.579

11067

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

[[_2nd_order, _with_linear_symmetries]]

1.711

11068

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

[[_Emden, _Fowler]]

0.804

11069

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

[[_2nd_order, _with_linear_symmetries]]

0.432

11070

\[ {}4 y^{\prime \prime }+4 y^{\prime } \tan \left (x \right )-\left (5 \tan \left (x \right )^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2.142

11071

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

[[_2nd_order, _with_linear_symmetries]]

1.054

11072

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

[[_2nd_order, _with_linear_symmetries]]

1.371

11073

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.973

11074

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

[[_2nd_order, _with_linear_symmetries]]

0.464

11075

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

[[_2nd_order, _missing_y]]

0.748

11076

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

[[_Emden, _Fowler]]

0.556

11077

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

[[_2nd_order, _with_linear_symmetries]]

0.807

11078

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

[[_2nd_order, _with_linear_symmetries]]

0.695

11079

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

[[_Emden, _Fowler]]

0.704

11080

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

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

1.568

11081

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

[[_2nd_order, _with_linear_symmetries]]

0.451

11082

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.744

11083

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

[[_2nd_order, _with_linear_symmetries]]

3.362

11084

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

[[_Emden, _Fowler]]

0.708

11085

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

[[_Emden, _Fowler]]

0.699

11086

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

[[_Emden, _Fowler]]

0.826

11087

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

[[_2nd_order, _with_linear_symmetries]]

0.966

11088

\[ {}x y^{\prime \prime }+a y^{\prime }+b \,x^{\operatorname {a1}} y = 0 \]

[[_Emden, _Fowler]]

0.965

11089

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

[[_2nd_order, _with_linear_symmetries]]

0.925

11090

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

[[_2nd_order, _with_linear_symmetries]]

1.127

11091

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.106

11092

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

[_Laguerre]

0.483

11093

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

[_Laguerre]

0.880

11094

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

[[_2nd_order, _with_linear_symmetries]]

0.908

11095

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

[_Laguerre]

0.908

11096

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

[[_2nd_order, _with_linear_symmetries]]

0.536

11097

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

[[_2nd_order, _with_linear_symmetries]]

0.671

11098

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

[[_2nd_order, _with_linear_symmetries]]

1.209

11099

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

[[_2nd_order, _with_linear_symmetries]]

1.310

11100

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

[[_2nd_order, _with_linear_symmetries]]

1.667