2.3.236 Problems 23501 to 23600

Table 2.1003: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23501

18599

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

10.710

23502

12202

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

10.711

23503

8711

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

10.720

23504

13024

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

10.724

23505

24385

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

10.725

23506

23221

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

10.732

23507

11799

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

10.745

23508

15943

\begin{align*} y^{\prime }&=\left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}

10.750

23509

11628

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

10.755

23510

11579

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

10.760

23511

14006

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

10.760

23512

145

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

10.767

23513

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*}

10.779

23514

19815

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

10.801

23515

3480

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

10.802

23516

2289

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

10.803

23517

21012

\begin{align*} t^{2} x^{\prime }-2 t x&=t^{5} \\ x \left (0\right ) &= 0 \\ \end{align*}

10.804

23518

6880

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

10.806

23519

19336

\begin{align*} y^{\prime } x +y+x^{2} y^{5} y^{\prime }&=0 \\ \end{align*}

10.838

23520

13461

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

10.848

23521

21086

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

10.858

23522

12198

\begin{align*} y^{\prime }&=\frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 y^{4} x +32 y^{6} x^{2}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\ \end{align*}

10.876

23523

21090

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

10.879

23524

19809

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

10.883

23525

3278

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

10.884

23526

17270

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

10.886

23527

21372

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

10.889

23528

20260

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

10.890

23529

8717

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

10.908

23530

13570

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

10.910

23531

5028

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

10.925

23532

11991

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

10.930

23533

7493

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

10.931

23534

14525

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

10.933

23535

17038

\begin{align*} \frac {y^{\prime }}{t}&=\sqrt {y} \\ y \left (0\right ) &= 0 \\ \end{align*}

10.939

23536

19914

\begin{align*} {\mathrm e}^{x} x^{4}-2 m x y^{2}+2 m \,x^{2} y y^{\prime }&=0 \\ \end{align*}

10.944

23537

21075

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

10.944

23538

3886

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

10.951

23539

12096

\begin{align*} y^{\prime }&=\frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )} \\ \end{align*}

10.962

23540

12211

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

10.965

23541

11374

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

10.973

23542

11657

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

10.974

23543

12175

\begin{align*} y^{\prime }&=\frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \\ \end{align*}

10.991

23544

13329

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

10.998

23545

13645

\begin{align*} y^{\prime }&=a \,x^{2 n +1} y^{3}+b \,x^{-n -2} \\ \end{align*}

10.998

23546

14037

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

11.016

23547

2887

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

11.019

23548

12037

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

11.041

23549

13561

\begin{align*} y^{\prime } y&=\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1 \\ \end{align*}

11.042

23550

5113

\begin{align*} \left (1+x +9 y\right ) y^{\prime }+1+x +5 y&=0 \\ \end{align*}

11.045

23551

12689

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

11.050

23552

2536

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

11.058

23553

19941

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

11.072

23554

13571

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

11.086

23555

13346

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

11.097

23556

13248

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

11.099

23557

19801

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

11.105

23558

12110

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

11.109

23559

12121

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

11.109

23560

15642

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

11.110

23561

8225

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

11.113

23562

19961

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

11.116

23563

12205

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

11.119

23564

11623

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

11.121

23565

24314

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

11.127

23566

11964

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

11.129

23567

4949

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

11.143

23568

12052

\begin{align*} y^{\prime }&=\frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \\ \end{align*}

11.144

23569

7867

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

11.149

23570

14453

\begin{align*} \frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}}&=0 \\ y \left (1\right ) &= 8 \\ \end{align*}

11.149

23571

22345

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

11.152

23572

10409

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

11.156

23573

13466

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

11.164

23574

2878

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

11.190

23575

2506

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

11.191

23576

13391

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

11.197

23577

17104

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

11.197

23578

21396

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

11.204

23579

20684

\begin{align*} y^{\prime }&=\frac {6 x -2 y-7}{2 x +3 y-6} \\ \end{align*}

11.210

23580

12150

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

11.213

23581

24294

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

11.215

23582

19928

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

11.225

23583

12280

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

11.231

23584

13311

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

11.249

23585

11386

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

11.251

23586

17902

\begin{align*} x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\ y \left (\infty \right ) &= \frac {16 \pi }{3} \\ \end{align*}

11.265

23587

13332

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

11.270

23588

19934

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

11.274

23589

19233

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

11.282

23590

6902

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

11.283

23591

14329

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

11.285

23592

8704

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

11.288

23593

9657

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

11.303

23594

2889

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

11.307

23595

17287

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

11.320

23596

11445

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

11.325

23597

12172

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

11.334

23598

19939

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

11.337

23599

21414

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

11.349

23600

13438

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

11.353