2.3.150 Problems 14901 to 15000

Table 2.873: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14901

13730

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

1.712

14902

2400

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

1.713

14903

8293

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (-6\right ) &= 0 \\ \end{align*}

1.714

14904

23146

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

1.714

14905

14172

\begin{align*} x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y&=0 \\ \end{align*}

1.715

14906

9758

\begin{align*} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\ \end{align*}

1.716

14907

6403

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

1.717

14908

9638

\begin{align*} 2 y^{\prime \prime }+t y^{\prime }-2 y&=10 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.717

14909

20420

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

1.717

14910

3316

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

1.719

14911

9416

\begin{align*} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y&=0 \\ \end{align*}

Series expansion around \(x=3\).

1.719

14912

22879

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ y \left (\frac {1}{2}\right ) &= 10 \\ \end{align*}

Series expansion around \(x={\frac {1}{2}}\).

1.719

14913

26192

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

1.719

14914

6498

\begin{align*} x y y^{\prime \prime }&=y \left (\operatorname {a2} +\operatorname {a3} y^{2}\right )+x \left (\operatorname {a0} +\operatorname {a1} y^{4}\right )-y y^{\prime }+{y^{\prime }}^{2} x \\ \end{align*}

1.720

14915

103

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

1.721

14916

25684

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

1.722

14917

1499

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

Using Laplace transform method.

1.723

14918

3439

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

1.724

14919

9025

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

1.724

14920

18095

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

1.725

14921

21936

\begin{align*} x y^{\prime \prime }+y^{\prime }&=16 x^{3} \\ \end{align*}

1.725

14922

23032

\begin{align*} y^{\prime \prime }-9 y&=5 \\ \end{align*}

1.725

14923

153

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

1.726

14924

15109

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

1.726

14925

22484

\begin{align*} y^{\prime } y^{\prime \prime }&=1 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.726

14926

20437

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

1.727

14927

3956

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

Using Laplace transform method.

1.728

14928

18729

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

1.728

14929

809

\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

1.729

14930

26882

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

1.729

14931

5895

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

1.730

14932

9341

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

1.730

14933

14983

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

Series expansion around \(x=0\).

1.730

14934

25559

\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&={\mathrm e}^{c t} \\ \end{align*}

1.730

14935

26162

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

1.730

14936

26222

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

1.730

14937

1264

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

1.731

14938

2435

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

1.731

14939

5594

\begin{align*} 9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y&=0 \\ \end{align*}

1.731

14940

9871

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

Series expansion around \(x=0\).

1.731

14941

15305

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.731

14942

14186

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

1.732

14943

25411

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

1.732

14944

5642

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

1.733

14945

17394

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

1.733

14946

17667

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

1.733

14947

21923

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x&=0 \\ y \left (0\right ) &= -{\frac {2}{3}} \\ y \left (1\right ) &= 2 \,{\mathrm e}^{-1}+\frac {1}{3} \\ \end{align*}

1.734

14948

19003

\begin{align*} x_{1}^{\prime }&=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\ x_{2}^{\prime }&=-3 x_{2} \\ x_{3}^{\prime }&=x_{1}-x_{3}-x_{5} \\ x_{4}^{\prime }&=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\ x_{5}^{\prime }&=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \\ \end{align*}

1.735

14949

27491

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

1.735

14950

2746

\begin{align*} x_{1}^{\prime }&=2 x_{2} \\ x_{2}^{\prime }&=-2 x_{1} \\ x_{3}^{\prime }&=-3 x_{4} \\ x_{4}^{\prime }&=3 x_{3} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 0 \\ \end{align*}

1.736

14951

7604

\begin{align*} 3 z^{\prime }+11 z&=0 \\ \end{align*}

1.736

14952

457

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

Series expansion around \(x=0\).

1.737

14953

13749

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

1.737

14954

15944

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

1.737

14955

16717

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

1.737

14956

13694

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

1.738

14957

13750

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

1.738

14958

14114

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

1.738

14959

3300

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

1.739

14960

1117

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

1.740

14961

10224

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

Series expansion around \(x=0\).

1.740

14962

10415

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

1.740

14963

24993

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

1.741

14964

15288

\begin{align*} x^{\prime }&=3 x-2 y+24 \sin \left (t \right ) \\ y^{\prime }&=9 x-3 y+12 \cos \left (t \right ) \\ \end{align*}

With initial conditions

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

1.742

14965

25518

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

1.742

14966

9038

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

1.744

14967

17469

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

1.744

14968

130

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

1.745

14969

9910

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

Series expansion around \(x=0\).

1.745

14970

17136

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

1.745

14971

7194

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

Series expansion around \(x=0\).

1.746

14972

9862

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

Series expansion around \(x=0\).

1.746

14973

27207

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

1.746

14974

670

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

1.747

14975

25233

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

1.747

14976

26365

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

1.747

14977

13699

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

1.748

14978

23351

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

1.748

14979

11661

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

1.749

14980

14135

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

1.749

14981

14977

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

Series expansion around \(x=0\).

1.749

14982

22859

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

Series expansion around \(x=0\).

1.749

14983

27297

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

1.749

14984

494

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

Series expansion around \(x=0\).

1.750

14985

2564

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

1.750

14986

3529

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

1.750

14987

7359

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

1.750

14988

9948

\begin{align*} 2 \left (5+x \right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.750

14989

14350

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

1.750

14990

17468

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.750

14991

18112

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

1.750

14992

25412

\begin{align*} y+y^{\prime }&=\operatorname {Heaviside}\left (t -10\right ) \\ \end{align*}

1.750

14993

26129

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

1.750

14994

7624

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

Series expansion around \(x=0\).

1.751

14995

23962

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

1.751

14996

2633

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

1.752

14997

8414

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (0\right ) &= 2 \\ \end{align*}

1.753

14998

13686

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

1.753

14999

23931

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

1.754

15000

2684

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

Using Laplace transform method.

1.755