2.3.90 Problems 8901 to 9000

Table 2.723: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8901

7762

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \\ \end{align*}

0.584

8902

7823

\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.584

8903

23497

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

0.584

8904

24070

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

0.584

8905

26056

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

0.584

8906

2286

\begin{align*} y_{1}^{\prime }&=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-26 y_{1}+9 y_{2} \\ \end{align*}

0.585

8907

2751

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

0.585

8908

3740

\begin{align*} y^{\prime \prime }-4 y&=100 \,{\mathrm e}^{x} \sin \left (x \right ) x \\ \end{align*}

0.585

8909

3859

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

0.585

8910

5734

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

0.585

8911

6272

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

0.585

8912

7904

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

0.585

8913

13103

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

0.585

8914

14309

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

0.585

8915

14581

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

0.585

8916

16013

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

0.585

8917

18730

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

0.585

8918

22701

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

0.585

8919

23344

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

0.585

8920

23507

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

0.585

8921

1902

\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -2 \\ \end{align*}
Series expansion around \(x=1\).

0.586

8922

1903

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

0.586

8923

2625

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

0.586

8924

3434

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

0.586

8925

4750

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

0.586

8926

6301

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

0.586

8927

7291

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

0.586

8928

8943

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

0.586

8929

9183

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

0.586

8930

12370

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

0.586

8931

16837

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

0.586

8932

17117

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

0.586

8933

17751

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

0.586

8934

19519

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

0.586

8935

19965

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

0.586

8936

22304

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

0.586

8937

22726

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

0.586

8938

8024

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \\ \end{align*}

0.587

8939

10167

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

0.587

8940

13843

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

0.587

8941

18677

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

0.587

8942

18987

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

0.587

8943

21658

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

0.587

8944

2032

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

0.588

8945

2416

\begin{align*} t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}
Series expansion around \(t=1\).

0.588

8946

2594

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=t \,{\mathrm e}^{\alpha t} \\ \end{align*}

0.588

8947

3896

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

0.588

8948

5873

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

0.588

8949

7293

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+5 y&=40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \\ \end{align*}

0.588

8950

8548

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

0.588

8951

10141

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

0.588

8952

17014

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

0.588

8953

18251

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

0.588

8954

18401

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{3} \\ \end{align*}

0.588

8955

22841

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

0.588

8956

25519

\begin{align*} y^{\prime \prime }+4 y&=F \cos \left (\omega t \right ) \\ \end{align*}

0.588

8957

1900

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

0.589

8958

3836

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

0.589

8959

4560

\begin{align*} 2 x^{\prime }+x-5 y^{\prime }-4 y&=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right ) \\ 3 x^{\prime }-2 x-4 y^{\prime }+y&=0 \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.589

8960

6203

\begin{align*} 4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

0.589

8961

7360

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

0.589

8962

8520

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

0.589

8963

18096

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

0.589

8964

18348

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

0.589

8965

18855

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (2 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.589

8966

19885

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

0.589

8967

22269

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

0.589

8968

23559

\begin{align*} x^{\prime }&=5 x-6 y \\ y^{\prime }&=6 x-7 y \\ \end{align*}

0.589

8969

25525

\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right )-\sin \left (\omega t \right ) \\ \end{align*}

0.589

8970

1919

\begin{align*} \left (4 x^{2}-4 x +1\right ) y^{\prime \prime }-\left (8-16 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.590

8971

3850

\begin{align*} x_{1}^{\prime }&=-x_{1}-6 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+5 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.590

8972

5492

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

0.590

8973

7287

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

0.590

8974

7821

\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.590

8975

8084

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

0.590

8976

8257

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

0.590

8977

14997

\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.590

8978

16984

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

0.590

8979

17492

\begin{align*} y^{\prime \prime }+12 y^{\prime }+37 y&={\mathrm e}^{-6 t} \csc \left (t \right ) \\ \end{align*}

0.590

8980

19510

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

0.590

8981

21302

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

0.590

8982

23016

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

0.590

8983

24862

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

0.590

8984

24871

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

0.590

8985

25245

\begin{align*} t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \\ \end{align*}
Using Laplace transform method.

0.590

8986

2720

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

0.591

8987

2825

\begin{align*} x_{1}^{\prime }&=-x_{2} \\ x_{2}^{\prime }&=8 x_{1}-6 x_{2} \\ \end{align*}

0.591

8988

8542

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.591

8989

9747

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

0.591

8990

13705

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

0.591

8991

16981

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

0.591

8992

19606

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

0.591

8993

21679

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

0.591

8994

348

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

0.592

8995

909

\begin{align*} x^{\prime \prime }+4 x&=5 \sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.592

8996

3921

\begin{align*} x_{1}^{\prime }&=5 x_{1}+9 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}-x_{2} \\ \end{align*}

0.592

8997

4006

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

0.592

8998

7134

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

0.592

8999

7522

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

0.592

9000

12964

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

0.592