2.3.140 Problems 13901 to 14000

Table 2.829: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13901

9994

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

1.470

13902

14667

\begin{align*} y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }&=x^{3}+x^{2} {\mathrm e}^{-x}+\sin \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}

1.470

13903

15441

\begin{align*} y^{\prime \prime }+n^{2} y&=h \sin \left (r x \right ) \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= c \\ \end{align*}

1.470

13904

23918

\begin{align*} y^{5} y^{\prime }+5 y^{6}&=1 \\ \end{align*}

1.470

13905

25352

\begin{align*} t y^{\prime \prime }-4 y&=0 \\ \end{align*}
Series expansion around \(t=0\).

1.470

13906

25976

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

1.470

13907

130

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

1.471

13908

1234

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

1.471

13909

6097

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

1.471

13910

6150

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

1.471

13911

23105

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

1.471

13912

25453

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

1.471

13913

5609

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

1.472

13914

6096

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

1.472

13915

16569

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

1.472

13916

3955

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

1.474

13917

14699

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

1.474

13918

15885

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

1.474

13919

18094

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

1.474

13920

21629

\begin{align*} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.474

13921

2592

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

1.475

13922

16572

\begin{align*} x^{2} y^{\prime \prime }-11 y^{\prime } x +36 y&=0 \\ y \left (1\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}

1.475

13923

19506

\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}

1.475

13924

20068

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

1.475

13925

22662

\begin{align*} i^{\prime \prime }+2 i^{\prime }+5 i&=0 \\ i \left (0\right ) &= 2 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.475

13926

26182

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

1.475

13927

12377

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

1.476

13928

17882

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

1.476

13929

18095

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

1.476

13930

21605

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

1.476

13931

6579

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

1.477

13932

10276

\begin{align*} c y^{\prime }&=b y \\ \end{align*}

1.477

13933

19525

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

1.477

13934

20884

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

1.477

13935

2098

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

1.478

13936

6510

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

1.478

13937

10382

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

1.478

13938

20844

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

1.478

13939

2636

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

1.479

13940

9211

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

1.479

13941

16520

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*}

1.479

13942

6320

\begin{align*} y^{\prime \prime }&=\operatorname {f2} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f1} \left (x \right ) y^{2}+y^{3}+\left (3 \operatorname {f1} \left (x \right )-y\right ) y^{\prime } \\ \end{align*}

1.480

13943

9908

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

1.480

13944

12575

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

1.480

13945

13756

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

1.480

13946

17133

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

1.480

13947

20771

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

1.480

13948

20949

\begin{align*} y^{\prime }&=y^{2}-6 y-16 \\ \end{align*}

1.480

13949

4579

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}

1.481

13950

9919

\begin{align*} x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.481

13951

15655

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

1.481

13952

17760

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y&={\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \\ \end{align*}

1.481

13953

2070

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (-9 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.482

13954

2095

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

1.482

13955

10273

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

1.482

13956

1265

\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{4}} \\ \end{align*}

1.483

13957

7167

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

1.483

13958

7171

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

1.483

13959

9734

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

1.483

13960

17136

\begin{align*} y^{\prime }&=12+4 y-y^{2} \\ \end{align*}

1.483

13961

25808

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

1.483

13962

7689

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

1.484

13963

10159

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

1.484

13964

17664

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

1.484

13965

24062

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

1.484

13966

24772

\begin{align*} 2 y^{\prime }+2 y+w^{\prime }-w&=x +1 \\ y^{\prime }+3 y+w^{\prime }+w&=4 x +14 \\ \end{align*}

1.484

13967

1223

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

1.485

13968

663

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

1.486

13969

22507

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

1.486

13970

23379

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

1.486

13971

2091

\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.487

13972

12979

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

1.487

13973

18867

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

1.487

13974

19876

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

1.487

13975

23978

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

1.487

13976

710

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

1.488

13977

3305

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

1.488

13978

18148

\begin{align*} y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\ \end{align*}

1.488

13979

1827

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

1.490

13980

7195

\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.490

13981

9918

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

1.490

13982

15945

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

1.490

13983

168

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

1.491

13984

842

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

1.491

13985

15236

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \\ y \left (0\right ) &= -6 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.491

13986

18840

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=2 t^{2}+4 \,{\mathrm e}^{2 t} t +t \sin \left (2 t \right ) \\ \end{align*}

1.492

13987

3629

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

1.493

13988

9584

\begin{align*} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\ \end{align*}

1.493

13989

15247

\begin{align*} 10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right ) \\ Q \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.493

13990

23316

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

1.493

13991

16499

\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}

1.494

13992

19196

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

1.494

13993

5067

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

1.495

13994

9859

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

1.495

13995

25494

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

1.495

13996

5364

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

1.496

13997

6391

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

1.496

13998

6764

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

1.496

13999

6803

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

1.496

14000

7166

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

1.496