2.3.241 Problems 24001 to 24100

Table 2.1025: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24001

12118

\begin{align*} y^{\prime }&=\frac {y \left (x -y\right ) \left (1+y\right )}{x \left (y x +x -y\right )} \\ \end{align*}

23.357

24002

12240

\begin{align*} y^{\prime }&=\frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \\ \end{align*}

23.361

24003

17215

\begin{align*} 3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\ \end{align*}

23.368

24004

11904

\begin{align*} y^{\prime }&=\frac {1}{y+\sqrt {x}} \\ \end{align*}

23.404

24005

6322

\begin{align*} y^{\prime \prime }&=y f^{\prime }\left (x \right )+\left (f \left (x \right )-2 y\right ) y^{\prime } \\ \end{align*}

23.438

24006

12317

\begin{align*} y^{\prime \prime }+y^{\prime } x -n y&=0 \\ \end{align*}

23.453

24007

21820

\begin{align*} -y+y^{\prime } x&=x^{2} y y^{\prime } \\ \end{align*}

23.455

24008

25036

\begin{align*} \left (y^{3}-t \right ) y^{\prime }&=y \\ \end{align*}

23.463

24009

8789

\begin{align*} x +y y^{\prime }&=a {y^{\prime }}^{2} \\ \end{align*}

23.471

24010

17635

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x^{2}} \\ \end{align*}

23.471

24011

20263

\begin{align*} \left (x -y\right ) y^{\prime }&=x +y+1 \\ \end{align*}

23.483

24012

9080

\begin{align*} y^{\prime }&=\frac {2 x y^{2}}{1-x^{2} y} \\ \end{align*}

23.490

24013

11673

\begin{align*} {y^{\prime }}^{2}+a x y^{\prime }-b \,x^{2}-c&=0 \\ \end{align*}

23.513

24014

22438

\begin{align*} y^{\prime }&=\frac {y}{y^{3}-3 x} \\ \end{align*}

23.514

24015

13746

\begin{align*} y^{\prime \prime } x +\left (a \,x^{2}+b x +2\right ) y^{\prime }+\left (c \,x^{2}+d x +b \right ) y&=0 \\ \end{align*}

23.521

24016

12248

\begin{align*} y^{\prime }&=\frac {-y \sin \left (\frac {y}{x}\right ) x -y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x \left (x +1\right )} \\ \end{align*}

23.536

24017

7555

\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ y \left (1\right ) &= -4 \\ \end{align*}

23.551

24018

19813

\begin{align*} \left (x^{2}+2 y x \right ) y^{\prime }-3 x^{2}+2 y x -y^{2}&=0 \\ \end{align*}

23.566

24019

13396

\begin{align*} y^{\prime }&=a \tan \left (\lambda x \right )^{n} y^{2}-a \,b^{2} \tan \left (\lambda x \right )^{n +2}+b \lambda \tan \left (\lambda x \right )^{2}+b \lambda \\ \end{align*}

23.600

24020

18620

\begin{align*} y^{\prime }&=\frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y} \\ \end{align*}

23.613

24021

13838

\begin{align*} \left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+d y&=0 \\ \end{align*}

23.616

24022

17153

\begin{align*} y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \\ \end{align*}

23.621

24023

12321

\begin{align*} y^{\prime \prime }-2 y^{\prime } x +a y&=0 \\ \end{align*}

23.635

24024

12106

\begin{align*} y^{\prime }&=\frac {y \left (x^{3}+x^{2} y+y^{2}\right )}{x^{2} \left (x -1\right ) \left (x +y\right )} \\ \end{align*}

23.655

24025

23165

\begin{align*} y^{\prime }-\frac {y}{x}&=-\frac {1}{2 y} \\ \end{align*}

23.658

24026

8710

\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ y \left (-1\right ) &= 0 \\ \end{align*}

23.668

24027

23139

\begin{align*} p^{\prime }&=a p-b p^{2} \\ \end{align*}

23.677

24028

11633

\begin{align*} \left (\frac {\operatorname {e1} \left (a +x \right )}{\left (\left (a +x \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (a +x \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right )&=0 \\ \end{align*}

23.708

24029

24346

\begin{align*} x -4 y-9+\left (4 x +y-2\right ) y^{\prime }&=0 \\ \end{align*}

23.735

24030

17265

\begin{align*} \frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )}&=0 \\ \end{align*}

23.746

24031

19816

\begin{align*} \left (3 x +2 y-7\right ) y^{\prime }&=2 x -3 y+6 \\ \end{align*}

23.756

24032

13372

\begin{align*} y^{\prime }&=\left (\lambda +a \sin \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \sin \left (\lambda x \right )^{2} \\ \end{align*}

23.763

24033

23866

\begin{align*} y x -\left (y^{4}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

23.775

24034

19067

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

23.789

24035

25507

\begin{align*} y^{\prime }&=\frac {4 t -y}{t -6 y} \\ \end{align*}

23.801

24036

12376

\begin{align*} y^{\prime \prime } x -y^{\prime } x -a y&=0 \\ \end{align*}

23.803

24037

24376

\begin{align*} y \left (8 x -9 y\right )+2 x \left (x -3 y\right ) y^{\prime }&=0 \\ \end{align*}

23.805

24038

23835

\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}

23.880

24039

13383

\begin{align*} y^{\prime }&=\left (\lambda +a \cos \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \cos \left (\lambda x \right )^{2} \\ \end{align*}

23.885

24040

18288

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}

23.891

24041

5854

\begin{align*} c y+a \cot \left (b x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

23.900

24042

14454

\begin{align*} 4 x +3 y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}

23.904

24043

8232

\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (1\right ) &= 4 \\ \end{align*}

23.907

24044

13836

\begin{align*} \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (d x +k \right ) y^{\prime }+\left (d -2 a \right ) y&=0 \\ \end{align*}

23.915

24045

14063

\begin{align*} {\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x}&=0 \\ \end{align*}

23.921

24046

7148

\begin{align*} \left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2}&=0 \\ \end{align*}

23.926

24047

3649

\begin{align*} y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \\ \end{align*}

23.928

24048

17966

\begin{align*} y^{\prime }+x \sin \left (2 y\right )&=2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\ \end{align*}

23.944

24049

14001

\begin{align*} \frac {-y+y^{\prime } x}{\sqrt {x^{2}-y^{2}}}&=y^{\prime } x \\ \end{align*}

23.975

24050

6489

\begin{align*} 4 y y^{\prime \prime }&=12 y^{2}+3 {y^{\prime }}^{2} \\ \end{align*}

24.042

24051

13745

\begin{align*} y^{\prime \prime } x +\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y&=0 \\ \end{align*}

24.050

24052

17152

\begin{align*} y^{\prime }-\frac {4 t y}{4 t^{2}-9}&=t \\ \end{align*}

24.074

24053

18284

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x} \\ y \left (\infty \right ) &= 0 \\ \end{align*}

24.101

24054

1678

\begin{align*} y^{\prime }+\frac {3 y}{x}&=\frac {3 y^{2} x^{4}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )} \\ y \left (1\right ) &= 1 \\ \end{align*}

24.114

24055

14013

\begin{align*} x +y y^{\prime }+y-y^{\prime } x&=0 \\ \end{align*}

24.117

24056

6917

\begin{align*} x +2 y+\left (-1+y\right ) y^{\prime }&=0 \\ \end{align*}

24.132

24057

21927

\begin{align*} 2 x +\frac {1}{y}+\left (\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}

24.149

24058

13395

\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \tan \left (x \right )^{m} y-a \tan \left (x \right )^{m} \\ \end{align*}

24.155

24059

12111

\begin{align*} y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\ \end{align*}

24.187

24060

6983

\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}

24.193

24061

6822

\begin{align*} y&=y^{\prime } x +\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\ \end{align*}

24.216

24062

17924

\begin{align*} x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime }&=0 \\ \end{align*}

24.219

24063

15170

\begin{align*} -\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}

24.226

24064

8159

\begin{align*} \sin \left (x^{\prime }\right )+y^{3} x&=\sin \left (y \right ) \\ \end{align*}

24.251

24065

2345

\begin{align*} 3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}

24.259

24066

11369

\begin{align*} y^{\prime }-\sqrt {\frac {a y^{4}+b y^{2}+1}{a \,x^{4}+b \,x^{2}+1}}&=0 \\ \end{align*}

24.277

24067

17323

\begin{align*} r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\ \end{align*}

24.282

24068

8949

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

24.290

24069

5331

\begin{align*} x \left (a +x y^{n}\right ) y^{\prime }+b y&=0 \\ \end{align*}

24.297

24070

10119

\begin{align*} y^{\prime \prime }-x^{3} y-x^{4}&=0 \\ \end{align*}

24.298

24071

20178

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \\ \end{align*}

24.334

24072

2347

\begin{align*} y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

24.337

24073

23354

\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}

24.357

24074

793

\begin{align*} {\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}

24.397

24075

3055

\begin{align*} y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

24.402

24076

26257

\begin{align*} 4 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\ \end{align*}

24.442

24077

201

\begin{align*} {\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}

24.464

24078

3303

\begin{align*} 8 x +1&=y {y^{\prime }}^{2} \\ \end{align*}

24.467

24079

2506

\begin{align*} y^{\prime }&=\frac {t +y+1}{t -y+3} \\ \end{align*}

24.473

24080

11605

\begin{align*} \left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\ \end{align*}

24.477

24081

1615

\begin{align*} y^{\prime }&=\frac {2 x +3 y}{x -4 y} \\ \end{align*}

24.484

24082

11977

\begin{align*} y^{\prime }&=\frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (x +1\right )} \\ \end{align*}

24.486

24083

17893

\begin{align*} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\ y \left (a \right ) &= 0 \\ \end{align*}

24.511

24084

20281

\begin{align*} y^{\prime }+\frac {y \ln \left (y\right )}{x}&=\frac {y}{x^{2}}-\ln \left (y\right )^{2} \\ \end{align*}

24.520

24085

6829

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

24.523

24086

4853

\begin{align*} 2 y^{\prime } x +y \left (1+y^{2}\right )&=0 \\ \end{align*}

24.544

24087

5029

\begin{align*} \left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime }&=\tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \\ \end{align*}

24.554

24088

23020

\begin{align*} z^{\prime \prime }+g z&=0 \\ z \left (\frac {\pi }{3 \sqrt {g}}\right ) &= 5 \\ z \left (\frac {2 \pi }{3 \sqrt {g}}\right ) &= \frac {\pi }{3} \\ \end{align*}

24.568

24089

5546

\begin{align*} y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y&=0 \\ \end{align*}

24.575

24090

12471

\begin{align*} x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}

24.577

24091

5054

\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}

24.579

24092

4421

\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}

24.607

24093

5053

\begin{align*} \left (x -y\right ) y^{\prime }&=y \\ \end{align*}

24.645

24094

8723

\begin{align*} 2 x -4 y+6+\left (x +y-2\right ) y^{\prime }&=0 \\ \end{align*}

24.667

24095

22348

\begin{align*} y^{\prime }&=\frac {1}{\sqrt {x^{2}+4 y^{2}-4}} \\ y \left (3\right ) &= 2 \\ \end{align*}

24.682

24096

19938

\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}

24.727

24097

11608

\begin{align*} x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right )&=0 \\ \end{align*}

24.742

24098

15869

\begin{align*} y^{\prime }&=\cos \left (y\right ) \\ y \left (-1\right ) &= 1 \\ \end{align*}

24.747

24099

16265

\begin{align*} y^{\prime } x +\cos \left (x^{2}\right )&=827 y \\ \end{align*}

24.755

24100

5083

\begin{align*} \left (x -2 y+1\right ) y^{\prime }&=1+2 x -y \\ \end{align*}

24.785