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

5325

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

9.668

23902

12116

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

9.671

23903

5641

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

9.672

23904

7156

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

9.675

23905

23869

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

9.675

23906

22064

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

9.677

23907

7415

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

9.682

23908

17050

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}

9.682

23909

20322

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

9.683

23910

2685

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

Using Laplace transform method.

9.687

23911

4779

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

9.687

23912

5504

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

9.690

23913

6842

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

9.694

23914

20177

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

9.697

23915

5287

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

9.703

23916

11588

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

9.704

23917

2520

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

9.705

23918

5237

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

9.708

23919

17959

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

9.711

23920

20418

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

9.711

23921

2347

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

9.712

23922

13674

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

9.715

23923

19070

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

9.715

23924

12194

\begin{align*} y^{\prime }&=\frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\ \end{align*}

9.717

23925

17979

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

9.725

23926

6826

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

9.728

23927

6839

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

9.728

23928

15602

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

9.728

23929

18614

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

9.730

23930

5207

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

9.731

23931

15650

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

9.735

23932

16220

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

9.737

23933

25031

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

9.747

23934

9998

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

9.758

23935

2926

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

9.760

23936

20238

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

9.760

23937

17103

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

9.764

23938

20817

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

9.768

23939

15556

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

9.773

23940

14022

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

9.781

23941

26402

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

9.782

23942

19098

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

9.788

23943

27426

\begin{align*} 2 y y^{\prime } x^{3}+3 y^{2} x^{2}+7&=0 \\ \end{align*}

9.790

23944

12875

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

9.800

23945

16335

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

9.802

23946

21839

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

9.812

23947

19284

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

9.816

23948

17235

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

9.822

23949

10434

\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=8 x^{3} \sin \left (x \right )^{2} \\ \end{align*}

9.824

23950

26318

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

9.826

23951

12887

\begin{align*} 9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\ \end{align*}

9.834

23952

11915

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

9.842

23953

11789

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

9.845

23954

25883

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

9.845

23955

12175

\begin{align*} y^{\prime }&=\frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \\ \end{align*}

9.849

23956

26871

\begin{align*} y^{\prime }&=3 x^{2} \left (y+2\right ) \\ y \left (2\right ) &= 8 \\ \end{align*}

9.849

23957

3318

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

9.860

23958

7951

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

9.860

23959

7114

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

9.867

23960

13389

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

9.871

23961

12137

\begin{align*} y^{\prime }&=-\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \\ \end{align*}

9.874

23962

15585

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

9.876

23963

20798

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

9.876

23964

13283

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

9.879

23965

15826

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

9.880

23966

1675

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

9.889

23967

14467

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

9.895

23968

11921

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

9.908

23969

13279

\begin{align*} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=\alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s} \\ \end{align*}

9.908

23970

1503

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

9.909

23971

13680

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

9.914

23972

20575

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

9.915

23973

11840

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

9.917

23974

7341

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

9.921

23975

119

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

9.925

23976

5924

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

9.932

23977

2884

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

9.936

23978

26175

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

9.940

23979

26264

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

9.945

23980

7464

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

9.952

23981

6914

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

9.957

23982

7681

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

9.957

23983

11676

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

9.957

23984

16252

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

9.958

23985

27531

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

9.959

23986

7456

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

9.960

23987

20267

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

9.966

23988

8705

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

9.970

23989

6486

\begin{align*} 3 y y^{\prime \prime }&=36 y^{2}+2 {y^{\prime }}^{2} \\ \end{align*}

9.974

23990

19990

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

9.974

23991

7541

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

9.977

23992

17039

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

9.984

23993

11352

\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*}

9.986

23994

12140

\begin{align*} y^{\prime }&=-\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \\ \end{align*}

9.987

23995

7401

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

9.988

23996

4816

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

9.997

23997

27317

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

10.000

23998

7160

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

10.001

23999

6801

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

10.003

24000

19668

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

10.004