2.3.70 Problems 6901 to 7000

Table 2.683: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6901

23271

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

0.444

6902

24695

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

0.444

6903

24704

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

0.444

6904

25167

\begin{align*} y_{1}^{\prime }-3 y_{1}&=-4 y_{2} \\ y_{2}^{\prime }+y_{2}&=y_{1} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}

0.444

6905

127

\begin{align*} y^{\prime } x +6 y&=3 x y^{{4}/{3}} \\ \end{align*}

0.445

6906

1872

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

0.445

6907

6109

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

0.445

6908

7279

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

0.445

6909

8288

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}

0.445

6910

9265

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

0.445

6911

9799

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

0.445

6912

10939

\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}

0.445

6913

13170

\(\left [\begin {array}{ccc} 32 & -67 & 47 \\ 7 & -14 & 13 \\ -7 & 15 & -6 \end {array}\right ]\)

N/A

N/A

N/A

0.445

6914

15986

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

0.445

6915

16151

\begin{align*} y^{\prime \prime }+16 y&=t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.445

6916

16606

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x} \\ \end{align*}

0.445

6917

16850

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

0.445

6918

18270

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

0.445

6919

19623

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

0.445

6920

20150

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

0.445

6921

20704

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

0.445

6922

20905

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

0.445

6923

22200

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

0.445

6924

22763

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

0.445

6925

25989

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

0.445

6926

3134

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

0.446

6927

5637

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

0.446

6928

5720

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

0.446

6929

6080

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

0.446

6930

7852

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

0.446

6931

7914

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

0.446

6932

14830

\begin{align*} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x&=0 \\ \end{align*}

0.446

6933

15435

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

0.446

6934

16617

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=18 x^{2}+3 x +4 \\ \end{align*}

0.446

6935

16741

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=81 \,{\mathrm e}^{3 x} \\ \end{align*}

0.446

6936

17021

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

0.446

6937

17617

\begin{align*} 4 x^{2} y^{\prime \prime }+17 y&=0 \\ \end{align*}

0.446

6938

18638

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

0.446

6939

19019

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

0.446

6940

24548

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=50 x +13 \,{\mathrm e}^{3 x} \\ \end{align*}

0.446

6941

24791

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

0.446

6942

25552

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

0.446

6943

2232

\begin{align*} 4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-y^{\prime } x +y&=6 x \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 4 \\ y^{\prime \prime \prime }\left (1\right ) &= -{\frac {37}{4}} \\ \end{align*}

0.447

6944

3428

\begin{align*} y^{\prime }&=\sin \left (t \right )^{2} \\ y \left (\frac {\pi }{6}\right ) &= 3 \\ \end{align*}

0.447

6945

3509

\begin{align*} \left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*}
Series expansion around \(z=0\).

0.447

6946

3814

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

0.447

6947

4064

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

0.447

6948

5742

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

0.447

6949

8185

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

0.447

6950

8476

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

0.447

6951

9457

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

0.447

6952

10453

\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.447

6953

12363

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

0.447

6954

13061

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

0.447

6955

15433

\begin{align*} y^{\prime \prime }+9 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}

0.447

6956

18093

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

0.447

6957

18792

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

0.447

6958

18863

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

0.447

6959

20552

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

0.447

6960

21656

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

0.447

6961

23393

\begin{align*} x^{5} y^{\left (5\right )}+3 x^{3} y^{\prime \prime \prime }-9 x^{2} y^{\prime \prime }+18 y^{\prime } x -18 y&=0 \\ \end{align*}

0.447

6962

24651

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

0.447

6963

24653

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

0.447

6964

483

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

0.448

6965

3429

\begin{align*} y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\ y \left (0\right ) &= 12 \\ \end{align*}

0.448

6966

3828

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

0.448

6967

8164

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

0.448

6968

8488

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

0.448

6969

9607

\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.448

6970

10029

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

0.448

6971

10460

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

0.448

6972

12369

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

0.448

6973

16820

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

0.448

6974

17425

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=-{\mathrm e}^{-9 t} \\ \end{align*}

0.448

6975

25181

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

0.448

6976

25590

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

0.448

6977

632

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

0.449

6978

2401

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

0.449

6979

8892

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ \end{align*}

0.449

6980

15571

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

0.449

6981

16072

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{3 t} \\ \end{align*}

0.449

6982

16183

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

0.449

6983

18704

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

0.449

6984

21499

\begin{align*} y^{\prime \prime }-\frac {6 y^{\prime }}{5}+\frac {9 y}{25}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.449

6985

24581

\begin{align*} y^{\prime \prime }+9 y&=18 x -3+20 \,{\mathrm e}^{x} \\ \end{align*}

0.449

6986

25110

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.449

6987

25121

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

0.449

6988

1927

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

0.450

6989

1928

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

0.450

6990

3510

\begin{align*} \left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*}
Series expansion around \(z=0\).

0.450

6991

3731

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

0.450

6992

6096

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

0.450

6993

6644

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

0.450

6994

9347

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

0.450

6995

9363

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

0.450

6996

9447

\begin{align*} L i^{\prime }+R i&=E_{0} \sin \left (\omega t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.450

6997

14779

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

0.450

6998

15998

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

0.450

6999

16631

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=10 \,{\mathrm e}^{3 x} \\ \end{align*}

0.450

7000

16825

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

0.450