2.3.237 Problems 23601 to 23700

Table 2.1005: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23601

4322

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

11.365

23602

12140

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

11.365

23603

19960

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

11.377

23604

12245

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

11.388

23605

20274

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

11.390

23606

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*}

11.415

23607

8253

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

11.424

23608

11606

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

11.435

23609

8701

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

11.445

23610

12143

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

11.448

23611

5502

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

11.454

23612

23863

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

11.457

23613

14475

\begin{align*} \left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\ y \left (1\right ) &= 4 \\ \end{align*}

11.483

23614

6041

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

11.485

23615

24334

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

11.485

23616

12129

\begin{align*} y^{\prime }&=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \\ \end{align*}

11.488

23617

9153

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

11.508

23618

24291

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

11.513

23619

12167

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

11.518

23620

21354

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

11.528

23621

12116

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

11.532

23622

11352

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

11.550

23623

17914

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

11.551

23624

24344

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

11.557

23625

24279

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

11.558

23626

3022

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

11.560

23627

13442

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

11.562

23628

13236

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

11.565

23629

12177

\begin{align*} y^{\prime }&=\frac {\left (-108 x^{{3}/{2}} y+18 x^{{9}/{2}}-108 x^{{3}/{2}}-216 y^{3}+108 x^{3} y^{2}-18 x^{6} y+x^{9}\right ) \sqrt {x}}{-216 y+36 x^{3}-216} \\ \end{align*}

11.569

23630

6364

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

11.571

23631

8721

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

11.578

23632

25277

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

11.580

23633

6815

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

11.585

23634

24335

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

11.599

23635

3481

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

11.617

23636

24388

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

11.624

23637

12092

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

11.627

23638

14022

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

11.640

23639

13715

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

11.657

23640

8364

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

11.662

23641

11461

\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*}

11.668

23642

23868

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

11.670

23643

19320

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

11.681

23644

8706

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

11.697

23645

12040

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

11.711

23646

21353

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

11.713

23647

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*}

11.716

23648

15632

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

11.718

23649

12438

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

11.730

23650

25708

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

11.732

23651

12137

\begin{align*} y^{\prime }&=-\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \\ \end{align*}

11.738

23652

2946

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

11.744

23653

3471

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

11.746

23654

21336

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

11.799

23655

5307

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

11.815

23656

13322

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

11.816

23657

19407

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

11.818

23658

13443

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

11.826

23659

9481

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

11.829

23660

14869

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

11.835

23661

10451

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

11.845

23662

21340

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

11.856

23663

21797

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

11.879

23664

11840

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

11.902

23665

19069

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

11.903

23666

14867

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

11.904

23667

2915

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

11.915

23668

12872

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

11.915

23669

5085

\begin{align*} \left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \\ \end{align*}

11.921

23670

6295

\begin{align*} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}\right ) y+a^{2} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1-a^{2} \cos \left (x \right )^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}

11.930

23671

4923

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

11.938

23672

20825

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

11.938

23673

4850

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

11.957

23674

14537

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

12.012

23675

11345

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

12.014

23676

21465

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

12.020

23677

2993

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

12.023

23678

12029

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

12.026

23679

25528

\begin{align*} m y^{\prime \prime }+k y&=1 \\ \end{align*}

12.042

23680

3479

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

12.043

23681

12481

\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2 n}+\operatorname {b1} \,x^{n}+\operatorname {c1} \right ) y&=0 \\ \end{align*}

12.044

23682

24154

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

12.056

23683

7743

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

12.060

23684

12087

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

12.068

23685

12210

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

12.074

23686

21092

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

12.078

23687

19797

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

12.092

23688

9204

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

12.103

23689

12559

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

12.106

23690

19235

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

12.109

23691

4276

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

12.133

23692

21376

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

12.133

23693

4989

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

12.137

23694

24339

\begin{align*} 12 x +4 y-8-\left (3 x +y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}

12.137

23695

15142

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

12.144

23696

2886

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

12.150

23697

8673

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

12.152

23698

12166

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

12.159

23699

12209

\begin{align*} y^{\prime }&=-\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 y x -6 y^{2} x^{2}+x^{3} y^{3}}{32 y x} \\ \end{align*}

12.174

23700

606

\begin{align*} x^{\prime }&=2 x-3 y \\ y^{\prime }&=x+y+2 z \\ z^{\prime }&=5 y-7 z \\ \end{align*}

12.187