2.3.241 Problems 24001 to 24100

Table 2.1013: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24001

14079

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

15.140

24002

12123

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

15.141

24003

12083

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

15.151

24004

3653

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

15.155

24005

10322

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

15.158

24006

5695

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

15.167

24007

15032

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

15.173

24008

14154

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

15.199

24009

19822

\begin{align*} \left (2 x -2 y+5\right ) y^{\prime }&=x -y+3 \\ \end{align*}

15.221

24010

17282

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

15.224

24011

19309

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

15.224

24012

4247

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

15.247

24013

12864

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

15.290

24014

21371

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

15.300

24015

13370

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

15.309

24016

11901

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

15.316

24017

21067

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

15.331

24018

1161

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

15.332

24019

11951

\begin{align*} y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 x}}{{\mathrm e}^{-x} y+1} \\ \end{align*}

15.345

24020

15821

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

15.353

24021

12257

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

15.355

24022

6318

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

15.367

24023

11750

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

15.367

24024

24161

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

15.372

24025

13541

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

15.374

24026

24233

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

15.375

24027

12008

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

15.394

24028

5057

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

15.436

24029

12085

\begin{align*} y^{\prime }&=\frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \\ \end{align*}

15.437

24030

19823

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

15.437

24031

9656

\begin{align*} x^{\prime }&=-3 x+4 y-9 z \\ y^{\prime }&=6 x-y \\ z^{\prime }&=10 x+4 y+3 z \\ \end{align*}

15.443

24032

19821

\begin{align*} \left (5 x -2 y+7\right ) y^{\prime }&=10 x -4 y+6 \\ \end{align*}

15.460

24033

11722

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

15.488

24034

12079

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

15.575

24035

6489

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

15.582

24036

12145

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

15.591

24037

15668

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

15.591

24038

21597

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

15.631

24039

18098

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

15.637

24040

21072

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

15.654

24041

13916

\begin{align*} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) \left (c \,x^{n}+d \right ) y^{\prime }+n \left (-a d +b c \right ) x^{n -1} y&=0 \\ \end{align*}

15.669

24042

18339

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

15.670

24043

11952

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

15.691

24044

4729

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

15.710

24045

24297

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

15.712

24046

23864

\begin{align*} x \left (6 x^{2}+14 y^{2}\right )+y \left (13 x^{2}+30 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

15.720

24047

12156

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

15.730

24048

2918

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

15.737

24049

19746

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

15.741

24050

5116

\begin{align*} \left (3+9 x +21 y\right ) y^{\prime }&=45+7 x -5 y \\ \end{align*}

15.753

24051

7315

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

15.774

24052

5169

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

15.810

24053

13445

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

15.819

24054

12256

\begin{align*} y^{\prime }&=\frac {y \left (y^{2} x^{7}+x^{4} y+x -3\right )}{x} \\ \end{align*}

15.837

24055

11942

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

15.853

24056

5032

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

15.935

24057

12122

\begin{align*} y^{\prime }&=\frac {b \,x^{3}+c^{2} \sqrt {a}-2 c b \,x^{2} \sqrt {a}+2 c y^{2} a^{{3}/{2}}+b^{2} x^{4} \sqrt {a}-2 y^{2} a^{{3}/{2}} b \,x^{2}+a^{{5}/{2}} y^{4}}{a \,x^{2} y} \\ \end{align*}

15.935

24058

5153

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

15.941

24059

11498

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

15.974

24060

2925

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

15.999

24061

17843

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

16.003

24062

15024

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

16.013

24063

11953

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

16.043

24064

12929

\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }-2 a y^{2}+y^{3} b&=0 \\ \end{align*}

16.086

24065

11499

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

16.121

24066

12007

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

16.125

24067

12081

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

16.130

24068

5168

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

16.155

24069

22034

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

16.170

24070

2347

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

16.188

24071

11943

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

16.203

24072

4252

\begin{align*} 2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\ \end{align*}

16.220

24073

5264

\begin{align*} 2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }&=x^{2} y-y^{3} \\ \end{align*}

16.223

24074

11944

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

16.227

24075

11995

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

16.274

24076

12136

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

16.295

24077

11361

\begin{align*} y^{\prime }-\frac {\sqrt {y^{2}-1}}{\sqrt {x^{2}-1}}&=0 \\ \end{align*}

16.304

24078

4966

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

16.308

24079

21307

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{3} \\ x_{3}^{\prime }&=-a x_{3}-b x_{2}-c x_{1} \\ \end{align*}

16.309

24080

24343

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

16.356

24081

21594

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

16.361

24082

15883

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

16.367

24083

21369

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

16.385

24084

22396

\begin{align*} y^{\prime }&=\frac {2 x +3 y+1}{3 x -2 y-5} \\ \end{align*}

16.410

24085

11923

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

16.423

24086

21378

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

16.425

24087

2933

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

16.471

24088

5115

\begin{align*} \left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y&=0 \\ \end{align*}

16.484

24089

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*}

16.487

24090

4381

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

16.532

24091

17304

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

16.548

24092

12867

\begin{align*} y^{\prime \prime }-3 y^{\prime } y-3 a y^{2}-4 a^{2} y-b&=0 \\ \end{align*}

16.553

24093

5298

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

16.611

24094

5376

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

16.619

24095

4944

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

16.660

24096

11489

\begin{align*} \sqrt {x^{2}-1}\, y^{\prime }-\sqrt {y^{2}-1}&=0 \\ \end{align*}

16.737

24097

21386

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

16.738

24098

12086

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

16.752

24099

13768

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

16.760

24100

12560

\begin{align*} \operatorname {a2} \,x^{2} y^{\prime \prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x \right ) y^{\prime }+\left (\operatorname {a0} \,x^{2}+\operatorname {b0} x +\operatorname {c0} \right ) y&=0 \\ \end{align*}

16.794