2.3.228 Problems 22701 to 22800

Table 2.999: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22701

7339

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

11.590

22702

5268

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

11.592

22703

21390

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

11.592

22704

7562

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

11.600

22705

11875

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

11.600

22706

6447

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

11.601

22707

13658

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

11.602

22708

12358

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

11.605

22709

14499

\begin{align*} y^{\prime } x -2 y&=2 x^{4} \\ y \left (2\right ) &= 8 \\ \end{align*}

11.605

22710

17099

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

11.609

22711

19072

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

11.612

22712

25824

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

11.614

22713

3553

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

11.625

22714

11938

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

11.628

22715

17634

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

11.631

22716

3681

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

11.632

22717

4703

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

11.633

22718

13464

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

11.636

22719

17297

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

11.638

22720

20248

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

11.639

22721

8722

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

11.643

22722

23899

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

11.644

22723

12064

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

11.645

22724

4230

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

11.663

22725

22573

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

11.676

22726

4921

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

11.681

22727

4800

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

11.684

22728

6919

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

11.689

22729

17527

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

11.690

22730

12478

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

11.692

22731

20264

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

11.701

22732

23740

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

11.706

22733

25767

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

11.706

22734

24301

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

11.713

22735

23739

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

11.723

22736

4308

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

11.725

22737

14162

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

11.725

22738

17925

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

11.726

22739

8370

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

11.729

22740

16333

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

11.729

22741

9057

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

11.732

22742

12270

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

11.733

22743

5704

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

11.736

22744

14064

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

11.736

22745

22535

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

11.753

22746

25830

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

11.753

22747

14004

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

11.762

22748

3000

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

11.765

22749

12007

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

11.770

22750

17947

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

11.770

22751

5285

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

11.771

22752

4097

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

11.772

22753

12858

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

11.780

22754

16435

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

11.780

22755

2875

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

11.785

22756

20984

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

11.799

22757

7745

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

11.808

22758

24942

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

11.815

22759

739

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

11.816

22760

14234

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

11.817

22761

18583

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

11.817

22762

21841

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

11.817

22763

26202

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

11.818

22764

15348

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

11.826

22765

2863

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

11.829

22766

5229

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

11.847

22767

3772

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

11.849

22768

13553

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

11.850

22769

20831

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

11.851

22770

20964

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

11.853

22771

18551

\begin{align*} y^{\prime }&=\frac {t -y}{2 t +5 y} \\ \end{align*}

11.856

22772

23269

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

11.864

22773

14980

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

11.865

22774

5254

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

11.871

22775

804

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

11.872

22776

24169

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

11.873

22777

4824

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

11.875

22778

5608

\begin{align*} {y^{\prime }}^{3}&=a \,x^{n} \\ \end{align*}

11.875

22779

24226

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

11.882

22780

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*}

11.892

22781

5912

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

11.898

22782

17633

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

11.908

22783

7144

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

11.918

22784

4313

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

11.920

22785

7561

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

11.925

22786

5462

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

11.931

22787

24166

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

11.931

22788

4085

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

11.933

22789

5701

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

11.937

22790

5134

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

11.948

22791

3646

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

11.951

22792

12476

\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*}

11.955

22793

7857

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

11.960

22794

11386

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

11.960

22795

5020

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

11.963

22796

5130

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

11.967

22797

24391

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

11.969

22798

13792

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

11.979

22799

17871

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

11.999

22800

9279

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

12.009