2.3.90 Problems 8901 to 9000

Table 2.753: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8901

3331

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

0.654

8902

3921

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

0.654

8903

3995

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.654

8904

9513

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

Series expansion around \(x=0\).

0.654

8905

9589

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

Series expansion around \(x=0\).

0.654

8906

9836

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.654

8907

10249

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

Series expansion around \(x=0\).

0.654

8908

12406

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

0.654

8909

14407

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

0.654

8910

14837

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

0.654

8911

14871

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

0.654

8912

15111

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

With initial conditions

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

0.654

8913

15725

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

Using Laplace transform method.

0.654

8914

16081

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.654

8915

16092

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=-8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.654

8916

16748

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

0.654

8917

20839

\begin{align*} 8 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.654

8918

21233

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

0.654

8919

24725

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

0.654

8920

24733

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

0.654

8921

25552

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

0.654

8922

26642

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

0.654

8923

354

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

0.655

8924

1748

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}

0.655

8925

1939

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

Series expansion around \(x=1\).

0.655

8926

3181

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

0.655

8927

7811

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\ \end{align*}

0.655

8928

9379

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

Series expansion around \(x=0\).

0.655

8929

9674

\begin{align*} x^{\prime }&=10 x-5 y \\ y^{\prime }&=8 x-12 y \\ \end{align*}

0.655

8930

15432

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

0.655

8931

17704

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

Series expansion around \(x=0\).

0.655

8932

18788

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.655

8933

19786

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

0.655

8934

21800

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

0.655

8935

22838

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

Series expansion around \(x=0\).

0.655

8936

23475

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

0.655

8937

24091

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

Series expansion around \(x=0\).

0.655

8938

25140

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

0.655

8939

25270

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

0.655

8940

25578

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

0.655

8941

27719

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

0.655

8942

2704

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

With initial conditions

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

0.656

8943

8793

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

0.656

8944

10180

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

Series expansion around \(x=0\).

0.656

8945

10219

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

Series expansion around \(x=0\).

0.656

8946

10586

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

0.656

8947

11828

\begin{align*} 16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\ \end{align*}

0.656

8948

14380

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

0.656

8949

18281

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

0.656

8950

20616

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

0.656

8951

26748

\begin{align*} 2 x^{\prime }&=6 x-y-6 t^{2}-t +3 \\ y^{\prime }&=2 y-2 t -1 \\ \end{align*}

With initial conditions

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

0.656

8952

886

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

0.657

8953

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 \(x=0\).

0.657

8954

4133

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

0.657

8955

4172

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 3 \\ y_{2} \left (0\right ) &= 7 \\ \end{align*}

0.657

8956

9673

\begin{align*} x^{\prime }&=-\frac {5 x}{2}+2 y \\ y^{\prime }&=\frac {3 x}{4}-2 y \\ \end{align*}

0.657

8957

16193

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

0.657

8958

20580

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

0.657

8959

21142

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

0.657

8960

24713

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

0.657

8961

25960

\begin{align*} y^{\prime \prime }+16 y&=14 \cos \left (3 x \right ) \\ \end{align*}

0.657

8962

27530

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

0.657

8963

373

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

0.658

8964

2052

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

Series expansion around \(x=0\).

0.658

8965

3803

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

0.658

8966

6765

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

0.658

8967

10122

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

0.658

8968

12322

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

0.658

8969

17428

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

0.658

8970

17505

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

0.658

8971

18657

\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-5 x+4 y \\ \end{align*}

0.658

8972

19883

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

0.658

8973

20140

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

0.658

8974

21580

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

0.658

8975

22262

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

With initial conditions

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

0.658

8976

25333

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

Series expansion around \(t=0\).

0.658

8977

25817

\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \\ \end{align*}

0.658

8978

25971

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

0.658

8979

26630

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

0.658

8980

495

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

Series expansion around \(x=0\).

0.659

8981

513

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

Series expansion around \(x=0\).

0.659

8982

3134

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

0.659

8983

5801

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

0.659

8984

14928

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

0.659

8985

17689

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

Series expansion around \(x=0\).

0.659

8986

21725

\begin{align*} w^{\prime }+y&=\sin \left (t \right ) \\ y^{\prime }-z&={\mathrm e}^{t} \\ w+y+z^{\prime }&=1 \\ \end{align*}

With initial conditions

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

0.659

8987

22199

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

Series expansion around \(x=0\).

0.659

8988

27656

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \\ \end{align*}

0.659

8989

912

\begin{align*} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\ \end{align*}

0.660

8990

2279

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

0.660

8991

3377

\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.660

8992

10469

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

0.660

8993

17459

\begin{align*} y^{\prime \prime }-4 y&=32 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.660

8994

20738

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

0.660

8995

22821

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

Series expansion around \(x=0\).

0.660

8996

24898

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

0.660

8997

470

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

Series expansion around \(x=0\).

0.661

8998

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*}

0.661

8999

2642

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

Series expansion around \(t=0\).

0.661

9000

7882

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

0.661