2.3.240 Problems 23901 to 24000

Table 2.1011: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23901

5429

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

13.945

23902

2919

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

13.948

23903

13648

\begin{align*} 9 y^{\prime }&=-x^{m} \left (a \,x^{1-m}+b \right )^{2 \lambda +1} y^{3}-x^{-2 m} \left (9 a +2+9 b m \,x^{m -1}\right ) \left (a \,x^{1-m}+b \right )^{-\lambda -2} \\ \end{align*}

13.955

23904

15557

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

13.977

23905

7930

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

14.019

23906

12155

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

14.030

23907

11777

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

14.034

23908

1601

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

14.037

23909

23885

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

14.068

23910

19931

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

14.086

23911

11966

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

14.088

23912

21389

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

14.102

23913

24165

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

14.118

23914

21424

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

14.124

23915

13740

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

14.127

23916

17977

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

14.158

23917

10416

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

14.166

23918

10258

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

14.168

23919

12275

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

14.172

23920

12276

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

14.185

23921

21380

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

14.187

23922

2334

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

14.211

23923

12099

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

14.217

23924

24232

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

14.217

23925

19395

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

14.228

23926

20975

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

14.245

23927

16518

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

14.247

23928

13377

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

14.253

23929

6357

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

14.285

23930

11630

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

14.289

23931

5263

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

14.290

23932

15183

\begin{align*} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right )&=0 \\ \end{align*}

14.296

23933

24177

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

14.306

23934

12102

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

14.309

23935

24157

\begin{align*} x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

14.348

23936

5420

\begin{align*} {y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right )&=0 \\ \end{align*}

14.354

23937

13610

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

14.368

23938

3049

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

14.392

23939

22383

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

14.403

23940

12055

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

14.404

23941

21346

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

14.425

23942

6414

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

14.433

23943

24357

\begin{align*} 9 x -4 y+4-\left (1+2 x -y\right ) y^{\prime }&=0 \\ \end{align*}

14.437

23944

5192

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

14.454

23945

2339

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

14.463

23946

11945

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

14.470

23947

19920

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

14.476

23948

11967

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

14.518

23949

14444

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

14.525

23950

3546

\begin{align*} y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \\ \end{align*}

14.535

23951

13026

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

14.558

23952

11375

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

14.566

23953

17244

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

14.579

23954

10038

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

14.596

23955

5279

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

14.599

23956

12208

\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 \right ) {\mathrm e}^{\frac {y}{x}}}{x \left (x +1\right )} \\ \end{align*}

14.612

23957

5938

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

14.630

23958

20963

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

14.630

23959

2927

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

14.631

23960

2511

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

14.634

23961

12039

\begin{align*} y^{\prime }&=\frac {-4 y x +x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \\ \end{align*}

14.636

23962

19951

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

14.674

23963

12131

\begin{align*} y^{\prime }&=\frac {1}{\sin \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (\cos \left (x \right )+1\right )\right ) \\ \end{align*}

14.690

23964

7862

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

14.703

23965

20976

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

14.710

23966

19942

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

14.711

23967

19968

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

14.718

23968

12061

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

14.750

23969

12009

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

14.767

23970

19799

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

14.784

23971

12159

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

14.795

23972

12043

\begin{align*} y^{\prime }&=\frac {-4 y x -x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8} \\ \end{align*}

14.811

23973

5294

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

14.815

23974

8696

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

14.832

23975

12049

\begin{align*} y^{\prime }&=\frac {-8 y x -x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \\ \end{align*}

14.852

23976

2898

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

14.857

23977

16856

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

14.872

23978

15029

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

14.874

23979

20477

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

14.890

23980

16241

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

14.904

23981

18601

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

14.924

23982

23958

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

14.931

23983

11938

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

14.932

23984

5152

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

14.937

23985

2893

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

14.944

23986

11932

\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y} \\ \end{align*}

14.977

23987

11940

\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y} \\ \end{align*}

14.981

23988

12479

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

14.987

23989

13966

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

14.991

23990

21077

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

14.997

23991

13641

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

15.069

23992

24386

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

15.091

23993

14470

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

15.096

23994

21622

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

15.107

23995

2896

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

15.109

23996

4665

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

15.109

23997

11933

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

15.113

23998

4275

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

15.125

23999

12240

\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 ) x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \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*}

15.133

24000

9990

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

15.136