2.3.241 Problems 24001 to 24100

Table 2.1055: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24001

7146

\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*}

11.735

24002

12165

\begin{align*} y^{\prime }&=-\frac {i \left (32 i x +64+64 y^{4}+32 x^{2} y^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 y^{2} x^{4}+x^{6}\right )}{128 y} \\ \end{align*}

11.740

24003

12195

\begin{align*} y^{\prime }&=-\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \\ \end{align*}

11.746

24004

2947

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

11.753

24005

5830

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

11.763

24006

5831

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

11.769

24007

6581

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

11.769

24008

16348

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

11.770

24009

22553

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

11.770

24010

9336

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

11.772

24011

1651

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

11.773

24012

1652

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

11.773

24013

6790

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

11.774

24014

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*}

11.774

24015

17926

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

11.775

24016

16435

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

11.780

24017

15649

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

11.782

24018

15461

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

11.786

24019

22871

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

Series expansion around \(x=0\).

11.787

24020

5334

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

11.789

24021

20813

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

11.790

24022

13652

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

11.792

24023

5833

\begin{align*} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

11.793

24024

22861

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

Series expansion around \(x=0\).

11.793

24025

5134

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

11.794

24026

14907

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

11.796

24027

13689

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

11.798

24028

9017

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

11.801

24029

9116

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

11.801

24030

26165

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

11.803

24031

3772

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

11.805

24032

8253

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

11.805

24033

22418

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

11.807

24034

9789

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

11.810

24035

22511

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

11.810

24036

11774

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

11.822

24037

13660

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

11.823

24038

25770

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

11.827

24039

1709

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

11.829

24040

20258

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

11.832

24041

11994

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

11.834

24042

13973

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

11.835

24043

5222

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

11.840

24044

22591

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

11.848

24045

11884

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

11.855

24046

4824

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

11.857

24047

19289

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

11.858

24048

8786

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

11.863

24049

17257

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

11.863

24050

5330

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

11.866

24051

24228

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

11.868

24052

25840

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

11.868

24053

5901

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

11.871

24054

13273

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

11.872

24055

22873

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

Series expansion around \(x=0\).

11.882

24056

12199

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

11.883

24057

27516

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

11.883

24058

3555

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

11.890

24059

18486

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

11.894

24060

10258

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

11.898

24061

27233

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

11.902

24062

5819

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

11.905

24063

18086

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

11.909

24064

21358

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

11.910

24065

5678

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

11.914

24066

4097

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

11.917

24067

16678

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=\frac {5}{x^{3}} \\ \end{align*}

11.921

24068

27431

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

11.921

24069

9122

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

11.924

24070

8170

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

11.932

24071

3652

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

11.933

24072

22869

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

Series expansion around \(x=0\).

11.935

24073

22454

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

11.938

24074

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*}

11.941

24075

2327

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

11.942

24076

2875

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

11.949

24077

19397

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

11.951

24078

16356

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

11.954

24079

3777

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

11.958

24080

5861

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

11.963

24081

4697

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

11.964

24082

14913

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

11.964

24083

13731

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

11.976

24084

25275

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

11.980

24085

5367

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

11.982

24086

22959

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

11.985

24087

14269

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

11.992

24088

760

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

11.993

24089

13996

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

12.006

24090

24784

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

12.008

24091

12423

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

12.017

24092

22534

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

12.026

24093

16856

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

Series expansion around \(x=2\).

12.033

24094

22380

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

12.042

24095

3648

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

12.047

24096

19746

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

12.047

24097

20254

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

12.047

24098

22526

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

12.047

24099

13495

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

12.049

24100

2982

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

12.052