2.3.240 Problems 23901 to 24000

Table 2.1053: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23901

18597

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

11.375

23902

13436

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

11.381

23903

4278

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

11.391

23904

16686

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

11.391

23905

27517

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

11.392

23906

24273

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

11.404

23907

3470

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

11.405

23908

9162

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

11.405

23909

22437

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

11.408

23910

11811

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

11.411

23911

759

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

11.412

23912

21073

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

11.418

23913

8376

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

11.430

23914

19733

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

11.440

23915

5763

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

11.444

23916

11869

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

11.444

23917

12079

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

11.449

23918

16683

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=\frac {10}{x} \\ \end{align*}

11.454

23919

24249

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

11.454

23920

5321

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

11.455

23921

11713

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

11.455

23922

11997

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

11.467

23923

12086

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

11.468

23924

18042

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

11.474

23925

13271

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

11.477

23926

18062

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

11.481

23927

5812

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

11.483

23928

11916

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

11.484

23929

7555

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

11.488

23930

12174

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

11.488

23931

5459

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

11.494

23932

11510

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

11.499

23933

3460

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

11.503

23934

27248

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

11.506

23935

5839

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

11.514

23936

21346

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

11.514

23937

17635

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

11.515

23938

22455

\begin{align*} r^{\prime }&=t -\frac {r}{3 t} \\ r \left (1\right ) &= 1 \\ \end{align*}

11.527

23939

1706

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

11.531

23940

21807

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

11.531

23941

12193

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

11.541

23942

22045

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

11.543

23943

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*}

11.549

23944

11489

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

11.553

23945

5268

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

11.555

23946

19527

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

11.555

23947

16285

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

11.556

23948

5755

\begin{align*} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a2} \csc \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}

11.559

23949

11900

\begin{align*} y^{\prime }&=\frac {F \left (\frac {\left (y+3\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{3 y}\right ) x y^{2} {\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9} \\ \end{align*}

11.569

23950

13735

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

11.570

23951

27484

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

11.570

23952

17093

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

11.573

23953

23187

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

11.578

23954

13692

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

11.586

23955

5842

\begin{align*} b \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

11.587

23956

1624

\begin{align*} y^{\prime }&=3 x \left (-1+y\right )^{{1}/{3}} \\ y \left (3\right ) &= -7 \\ \end{align*}

11.588

23957

18473

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

11.591

23958

23214

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

11.595

23959

4800

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

11.597

23960

5697

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

11.599

23961

14041

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

11.599

23962

12250

\begin{align*} y^{\prime }&=-\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{216 x^{3}-1296 y+594 y^{7}+2808 y^{4}+1728 y^{3}-648 x y^{3}-432 x y^{4}-1944 x y^{2}-315 y^{9}-1296 y x -1296 y^{2}-648 x^{2} y^{2}-126 y^{10}-8 y^{12}-36 y^{11}+2484 y^{6}-648 x^{2} y-216 x^{2} y^{4}+1080 y^{5} x +594 x y^{6}+72 y^{8} x +216 y^{7} x -18 y^{8}-324 x^{2} y^{3}+4428 y^{5}} \\ \end{align*}

11.605

23963

11973

\begin{align*} y^{\prime }&=\frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4} \\ \end{align*}

11.620

23964

3543

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

11.626

23965

5599

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

11.628

23966

5621

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

11.629

23967

7879

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

11.639

23968

13727

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

11.640

23969

5188

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

11.641

23970

13419

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

11.642

23971

5186

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

11.648

23972

17671

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

11.649

23973

14461

\begin{align*} \tan \left (\theta \right )+2 r \theta ^{\prime }&=0 \\ \end{align*}

11.650

23974

25900

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

11.650

23975

26309

\begin{align*} 2 \sqrt {x}\, y^{\prime }-y&=-\sin \left (\sqrt {x}\right )-\cos \left (\sqrt {x}\right ) \\ y \left (\infty \right ) &= y_{0} \\ \end{align*}

11.652

23976

13266

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

11.657

23977

15639

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

11.658

23978

12270

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

11.664

23979

4992

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

11.669

23980

13221

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

11.671

23981

12874

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

11.680

23982

26310

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

11.688

23983

27316

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

11.689

23984

2940

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

11.695

23985

12143

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

11.702

23986

3636

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

11.703

23987

5035

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

11.704

23988

12158

\begin{align*} y^{\prime }&=\frac {1+y^{4}-8 a x y^{2}+16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y} \\ \end{align*}

11.704

23989

2520

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

11.706

23990

18003

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

11.707

23991

5123

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

11.709

23992

6031

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

11.711

23993

21359

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

11.711

23994

22595

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

11.714

23995

19935

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

11.718

23996

22417

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

11.719

23997

2988

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

11.720

23998

4973

\begin{align*} x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right )&=0 \\ \end{align*}

11.721

23999

1656

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

11.729

24000

8822

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

11.730