2.3.238 Problems 23701 to 23800

Table 2.1007: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23701

19898

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

12.187

23702

21392

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

12.193

23703

19310

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

12.195

23704

2358

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

12.201

23705

14868

\begin{align*} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3}&=0 \\ \end{align*}

12.202

23706

5201

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

12.228

23707

2894

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

12.234

23708

3676

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

12.253

23709

15172

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

12.254

23710

19279

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

12.257

23711

13808

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

12.262

23712

3460

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

12.274

23713

5708

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

12.283

23714

13110

\begin{align*} x^{\prime }&=6 x-72 y+44 z \\ y^{\prime }&=4 x-4 y+26 z \\ z^{\prime }&=6 x-63 y+38 z \\ \end{align*}

12.287

23715

22386

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

12.288

23716

11986

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

12.299

23717

11533

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

12.319

23718

12016

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

12.326

23719

3037

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

12.329

23720

11368

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

12.329

23721

15784

\begin{align*} y^{\prime }&=t y^{{1}/{3}} \\ \end{align*}

12.329

23722

19918

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

12.340

23723

8695

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

12.352

23724

12158

\begin{align*} y^{\prime }&=\frac {1+y^{4}-8 a x y^{2}+16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y} \\ \end{align*}

12.352

23725

23917

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

12.353

23726

21379

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

12.356

23727

20948

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

12.358

23728

22447

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

12.365

23729

22013

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

12.379

23730

2867

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

12.391

23731

4419

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

12.408

23732

19321

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

12.409

23733

12001

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

12.410

23734

21439

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

12.412

23735

25655

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

12.420

23736

5071

\begin{align*} \left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\ \end{align*}

12.431

23737

12241

\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}} \\ \end{align*}

12.458

23738

11999

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

12.470

23739

24403

\begin{align*} 4 x +3 y-7+\left (4 x +3 y+1\right ) y^{\prime }&=0 \\ \end{align*}

12.474

23740

15820

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

12.477

23741

5261

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

12.478

23742

13326

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

12.508

23743

12023

\begin{align*} y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (a y^{2}+b \,x^{2}+a \right ) y} \\ \end{align*}

12.514

23744

19969

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

12.526

23745

21073

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

12.540

23746

1668

\begin{align*} y^{\prime }&=\frac {-x +3 y-14}{x +y-2} \\ \end{align*}

12.551

23747

25505

\begin{align*} y^{\prime }&=\frac {-3 t^{2}-2 y^{2}}{4 t y+6 y^{2}} \\ \end{align*}

12.593

23748

12246

\begin{align*} y^{\prime }&=-\frac {1296 y}{216-648 x^{2} y+216 x^{2}-432 y x -882 y^{6}-216 x^{2} y^{4}-1296 y+216 x y^{2}-1944 y^{4}+1080 x y^{3}-570 y^{8}-648 y^{2} x^{2}+216 y^{7} x -1728 y^{3}+72 y^{8} x +216 x^{3}-2376 y^{2}-612 y^{5}-324 x^{2} y^{3}+594 x y^{6}+1080 x y^{5}+1152 y^{4} x -846 y^{7}-126 y^{10}-8 y^{12}-36 y^{11}-315 y^{9}} \\ \end{align*}

12.604

23749

18073

\begin{align*} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \\ \end{align*}

12.612

23750

11957

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

12.634

23751

19355

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

12.647

23752

19350

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

12.648

23753

12046

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

12.663

23754

7931

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

12.672

23755

12472

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

12.681

23756

12215

\begin{align*} y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 y x +\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 y^{2} x^{2}}{4}-3 x y^{2}+\frac {3 x^{4} y}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \\ \end{align*}

12.688

23757

14535

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

12.698

23758

20284

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

12.713

23759

19288

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

12.714

23760

21048

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

12.723

23761

21454

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

12.730

23762

25732

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

12.730

23763

10019

\begin{align*} p^{\prime }&=a p-b p^{2} \\ p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\ \end{align*}

12.736

23764

2895

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

12.754

23765

8781

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

12.757

23766

19413

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

12.760

23767

22391

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

12.776

23768

21343

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

12.782

23769

17987

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

12.795

23770

21457

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

12.800

23771

12120

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

12.805

23772

11538

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

12.813

23773

3053

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

12.815

23774

7568

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

12.815

23775

19727

\begin{align*} \left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \\ \end{align*}

12.816

23776

15823

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

12.834

23777

17277

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

12.836

23778

12124

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

12.839

23779

15822

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

12.842

23780

17112

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

12.843

23781

9140

\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*}

12.845

23782

7548

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

12.869

23783

19284

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

12.873

23784

5343

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

12.885

23785

20828

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

12.890

23786

21420

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

12.914

23787

6538

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

12.917

23788

12114

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

12.937

23789

7740

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

12.940

23790

12227

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

12.945

23791

15819

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

12.952

23792

24376

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

12.954

23793

21419

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

12.971

23794

12228

\begin{align*} y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}} \\ \end{align*}

12.977

23795

4082

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

12.980

23796

12486

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

12.990

23797

23219

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

13.011

23798

5260

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

13.029

23799

13767

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

13.033

23800

12248

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

13.039