2.3.268 Problems 26701 to 26800

Table 2.1109: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

26701

13802

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

51.864

26702

13967

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

51.938

26703

13555

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

51.981

26704

13847

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

52.019

26705

20742

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

52.036

26706

13388

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

52.185

26707

22961

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

52.197

26708

4111

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

52.214

26709

26313

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

52.217

26710

5573

\begin{align*} y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y&=0 \\ \end{align*}

52.244

26711

6106

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

52.325

26712

6834

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}

52.338

26713

21824

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

52.347

26714

13917

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

52.357

26715

19912

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

52.365

26716

22473

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

52.439

26717

7154

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

52.460

26718

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*}

52.504

26719

2895

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

52.507

26720

20319

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

52.549

26721

6888

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

52.552

26722

6880

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

52.586

26723

27401

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

52.640

26724

6858

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}

52.658

26725

4277

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

52.680

26726

21837

\begin{align*} 2 x -y-1+\left (3 x +2 y-5\right ) y^{\prime }&=0 \\ \end{align*}

52.687

26727

11525

\begin{align*} \left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62&=0 \\ \end{align*}

52.737

26728

7550

\begin{align*} 3 x -y-5+\left (x -y+1\right ) y^{\prime }&=0 \\ \end{align*}

52.777

26729

11732

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

52.779

26730

23257

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

52.802

26731

13505

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

52.898

26732

13769

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

52.931

26733

5977

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

52.994

26734

8232

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

53.152

26735

11560

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

53.202

26736

192

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

53.204

26737

5301

\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*}

53.213

26738

13862

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

53.249

26739

14865

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

53.254

26740

5682

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

53.262

26741

20129

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

53.303

26742

4774

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

53.305

26743

5015

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

53.338

26744

9686

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\ x_{2}^{\prime }&=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\ x_{3}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\ x_{4}^{\prime }&=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\ x_{5}^{\prime }&=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \\ \end{align*}

53.359

26745

14023

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

53.450

26746

2536

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

53.563

26747

10459

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

53.574

26748

14841

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

53.603

26749

19092

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

53.610

26750

4820

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

53.626

26751

27405

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

53.631

26752

21385

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

53.719

26753

13497

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

53.872

26754

22391

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

53.872

26755

5014

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

53.987

26756

20457

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\ \end{align*}

53.995

26757

19071

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

54.034

26758

26684

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

54.038

26759

14531

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

54.047

26760

15016

\begin{align*} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \\ \end{align*}

54.057

26761

24321

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

54.107

26762

12017

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

54.206

26763

6577

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

54.369

26764

12512

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

54.415

26765

11450

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

54.425

26766

19074

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

54.477

26767

22462

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

54.575

26768

8399

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

54.648

26769

27300

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

54.755

26770

15154

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

54.867

26771

25653

\begin{align*} R^{\prime \prime }&=-\frac {k}{R^{2}} \\ \end{align*}

54.960

26772

18035

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

55.093

26773

25009

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

55.099

26774

5323

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

55.118

26775

10008

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

55.136

26776

23207

\begin{align*} 2 x -3 y+\left (7 y^{2}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

55.146

26777

24272

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

55.164

26778

6890

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

55.328

26779

19275

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

55.444

26780

13304

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

55.463

26781

5184

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

55.773

26782

15593

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

55.773

26783

6084

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

55.819

26784

11740

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

55.872

26785

22602

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

56.033

26786

13402

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

56.072

26787

12067

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

56.125

26788

18611

\begin{align*} 3 t y^{\prime }+9 y&=2 t y^{{5}/{3}} \\ \end{align*}

56.161

26789

24326

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

56.243

26790

5336

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

56.276

26791

19819

\begin{align*} \left (x -3 y+4\right ) y^{\prime }&=5 x -7 y \\ \end{align*}

56.342

26792

14551

\begin{align*} 10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \\ \end{align*}

56.347

26793

784

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

56.396

26794

6590

\begin{align*} 6 y y^{\prime \prime }-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+\left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}&=36 {y^{\prime }}^{2} x \\ \end{align*}

56.477

26795

6572

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

56.520

26796

20035

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

56.595

26797

5379

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

56.625

26798

10410

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

56.648

26799

4988

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

56.664

26800

13215

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

56.734