2.3.267 Problems 26601 to 26700

Table 2.1107: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

26601

5560

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

47.555

26602

10946

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}

47.648

26603

25445

\begin{align*} z^{\prime }+4 z&={\mathrm e}^{8 i t} \\ \end{align*}

47.652

26604

5116

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

47.658

26605

22401

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

47.717

26606

11810

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

47.748

26607

22413

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

47.763

26608

7411

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

47.765

26609

20696

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

47.792

26610

22755

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

47.819

26611

5298

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

47.866

26612

27427

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

47.875

26613

21360

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

47.916

26614

5119

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

48.021

26615

18601

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

48.076

26616

11992

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

48.090

26617

11551

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

48.121

26618

25447

\begin{align*} z^{\prime }+4 i z&={\mathrm e}^{8 t} \\ \end{align*}

48.147

26619

21322

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

48.170

26620

13263

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

48.215

26621

27464

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

48.231

26622

13746

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

48.274

26623

15624

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

48.282

26624

5369

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

48.301

26625

23278

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

48.357

26626

10073

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

48.467

26627

10288

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

48.596

26628

8360

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

48.796

26629

13532

\begin{align*} y y^{\prime }-y&=A \,x^{2}-\frac {9}{625 A} \\ \end{align*}

48.828

26630

6819

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

48.891

26631

13745

\begin{align*} x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y&=0 \\ \end{align*}

48.937

26632

17037

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

48.957

26633

12590

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

48.961

26634

3247

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

48.987

26635

6092

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

48.995

26636

13382

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

49.003

26637

18735

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

49.062

26638

22347

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

49.074

26639

5357

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

49.248

26640

19048

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

49.264

26641

18573

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

49.365

26642

15621

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

49.432

26643

13763

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

49.447

26644

27500

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

49.469

26645

19924

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

49.539

26646

27201

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

49.588

26647

5205

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

49.641

26648

13563

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

49.659

26649

21598

\begin{align*} x -2 y+1+\left (4 x -3 y-6\right ) y^{\prime }&=0 \\ \end{align*}

49.704

26650

5192

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

49.720

26651

5294

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

49.789

26652

20684

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

49.796

26653

6901

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

49.798

26654

13907

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

49.899

26655

15976

\begin{align*} p^{\prime }&=3 p-2 q-7 r \\ q^{\prime }&=-2 p+6 r \\ r^{\prime }&=\frac {73 q}{100}+2 r \\ \end{align*}

49.921

26656

24305

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

49.968

26657

4274

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

49.985

26658

22965

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

49.997

26659

8836

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

50.087

26660

22532

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

50.194

26661

11528

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

50.236

26662

21929

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

50.286

26663

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*}

50.324

26664

14555

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

50.408

26665

2874

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

50.432

26666

11557

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

50.437

26667

7871

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

50.445

26668

5279

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

50.504

26669

13417

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

50.523

26670

4331

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

50.537

26671

17250

\begin{align*} 2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \\ \end{align*}

50.546

26672

13211

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

50.579

26673

20958

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

50.586

26674

5236

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

50.755

26675

13429

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

50.768

26676

599

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

50.792

26677

5624

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

50.796

26678

6899

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

50.805

26679

18731

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

50.931

26680

15024

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

50.999

26681

14446

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

51.015

26682

7533

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

51.046

26683

11420

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

51.100

26684

4810

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

51.185

26685

2360

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

51.204

26686

4811

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

51.256

26687

13800

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

51.316

26688

13799

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

51.357

26689

14480

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

51.360

26690

19371

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

51.392

26691

11558

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

51.421

26692

11694

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

51.444

26693

25010

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

51.465

26694

13264

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

51.469

26695

6362

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

51.510

26696

10023

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

51.581

26697

21928

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

51.662

26698

2820

\begin{align*} z^{\prime \prime }+z+z^{5}&=0 \\ \end{align*}

51.756

26699

13797

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

51.779

26700

4876

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

51.834