2.3.140 Problems 13901 to 14000

Table 2.853: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13901

9680

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

1.385

13902

14757

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

Series expansion around \(x=0\).

1.385

13903

15881

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

1.385

13904

18196

\begin{align*} 7 y^{\prime \prime }-y^{\prime }&=14 x \\ \end{align*}

1.385

13905

9962

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

Series expansion around \(x=0\).

1.386

13906

22172

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

Series expansion around \(x=0\).

1.386

13907

8312

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

1.387

13908

8992

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

Series expansion around \(x=0\).

1.387

13909

12401

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

1.387

13910

6549

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

1.388

13911

8800

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

1.388

13912

20168

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

1.389

13913

20569

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

1.389

13914

13850

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

1.390

13915

6091

\begin{align*} -12 y-8 x y^{\prime }+\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}

1.391

13916

8591

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

Series expansion around \(x=0\).

1.391

13917

9939

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

Series expansion around \(x=0\).

1.391

13918

14876

\begin{align*} x^{\prime }&=\sec \left (t \right )^{2} \\ x \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

1.391

13919

25964

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

1.391

13920

26736

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

1.391

13921

2608

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

1.392

13922

6268

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

1.392

13923

9959

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

Series expansion around \(x=0\).

1.392

13924

6957

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

1.393

13925

7964

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

1.393

13926

20876

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

1.393

13927

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*}

1.393

13928

24880

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

1.393

13929

25949

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

1.393

13930

4483

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

1.394

13931

12308

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

1.394

13932

18252

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

1.394

13933

20561

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

1.394

13934

6396

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

1.395

13935

7440

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

1.395

13936

9826

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

1.395

13937

12650

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

1.395

13938

19491

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=0 \\ \end{align*}

1.395

13939

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*}

1.396

13940

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 \(x=0\).

1.396

13941

22057

\begin{align*} y^{\prime }-3 y&=6 \\ \end{align*}

1.396

13942

22865

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

Series expansion around \(x=0\).

1.396

13943

2635

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

1.397

13944

9414

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

Series expansion around \(x=0\).

1.397

13945

4523

\begin{align*} y^{\prime \prime }+4 y&=8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

1.398

13946

6165

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

1.398

13947

11882

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

1.398

13948

18389

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

1.398

13949

21614

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=1 \\ \end{align*}

1.398

13950

21676

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

Series expansion around \(x=0\).

1.398

13951

904

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

1.400

13952

8764

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

1.400

13953

19854

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

1.400

13954

23836

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

1.400

13955

6430

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

1.401

13956

6884

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

1.401

13957

7373

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

1.401

13958

13033

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

1.401

13959

21528

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

1.401

13960

3847

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\ x_{3}^{\prime }&=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\ x_{4}^{\prime }&=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \\ \end{align*}

1.403

13961

3698

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

1.404

13962

5382

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

1.404

13963

9354

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

1.404

13964

15878

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

1.404

13965

20877

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

1.404

13966

22696

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

1.404

13967

27551

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

1.404

13968

16556

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\ \end{align*}

1.405

13969

17679

\begin{align*} 6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y&=0 \\ y \left (1\right ) &= a \\ y^{\prime }\left (1\right ) &= b \\ \end{align*}

1.406

13970

20204

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

1.406

13971

7118

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

1.407

13972

3441

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

1.408

13973

6521

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

1.408

13974

7595

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

1.408

13975

17895

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

1.408

13976

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*}

1.408

13977

18992

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }&=-8 x_{1}-5 x_{2}-3 x_{3} \\ \end{align*}

1.408

13978

9884

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=0 \\ \end{align*}

1.409

13979

9899

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

Series expansion around \(x=4\).

1.409

13980

11565

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

1.409

13981

1505

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

Using Laplace transform method.

1.410

13982

4575

\begin{align*} x_{1}^{\prime }&=-x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )} \\ \end{align*}

1.410

13983

10035

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

1.410

13984

12494

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

1.410

13985

3607

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

1.411

13986

8248

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

1.411

13987

22836

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

Series expansion around \(x=1\).

1.411

13988

10444

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

1.412

13989

14775

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

1.412

13990

8181

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

1.413

13991

10418

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

1.413

13992

11355

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

1.413

13993

3234

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y&=\cos \left (\ln \left (x \right )\right ) \\ \end{align*}

1.414

13994

7662

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

Series expansion around \(x=0\).

1.414

13995

13294

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

1.414

13996

20478

\begin{align*} 8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \\ \end{align*}

1.414

13997

1796

\begin{align*} 6 y^{\prime }+6 y^{2}-y-1&=0 \\ \end{align*}

1.415

13998

7954

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

1.415

13999

9861

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

Series expansion around \(x=0\).

1.415

14000

17444

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \\ \end{align*}

1.415