2.3.71 Problems 7001 to 7100

Table 2.673: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7001

4013

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

0.606

7002

7195

\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.606

7003

7965

\begin{align*} {y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y&=0 \\ \end{align*}

0.606

7004

8602

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

0.606

7005

10793

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

0.606

7006

16010

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

0.606

7007

19141

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

0.606

7008

20149

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

0.606

7009

8884

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

0.607

7010

9046

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

0.607

7011

10954

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

0.607

7012

10975

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

0.607

7013

14755

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

0.607

7014

462

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

0.608

7015

1904

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

0.608

7016

1912

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

0.608

7017

3242

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

0.608

7018

3986

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

0.608

7019

7622

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

0.608

7020

10667

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

0.608

7021

11103

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

0.608

7022

14891

\begin{align*} x^{\prime }+p x&=q \\ \end{align*}

0.608

7023

15732

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

0.608

7024

19516

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

0.608

7025

25464

\begin{align*} y^{\prime }&=a \left (t \right ) y+\delta \left (-t +s \right ) \\ \end{align*}

0.608

7026

1390

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

0.609

7027

4181

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

0.609

7028

10661

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

0.609

7029

10969

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

0.609

7030

16895

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

0.609

7031

23686

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

0.609

7032

25338

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

0.609

7033

4020

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (3 x +7\right ) y^{\prime }+\left (1+6 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.610

7034

4045

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

0.610

7035

17591

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

0.610

7036

22990

\begin{align*} p^{\prime }&=15-20 p \\ p \left (0\right ) &= {\frac {7}{10}} \\ \end{align*}

0.610

7037

23144

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

0.610

7038

25453

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

0.610

7039

1384

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

0.611

7040

1842

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

0.611

7041

3377

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

0.611

7042

14382

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

0.611

7043

14785

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

0.611

7044

16242

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

0.611

7045

17032

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

0.611

7046

17700

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

0.611

7047

21332

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

0.611

7048

24083

\begin{align*} 4 \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.611

7049

25454

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

0.611

7050

996

\begin{align*} x_{1}^{\prime }&=-20 x_{1}+11 x_{2}+13 x_{3} \\ x_{2}^{\prime }&=12 x_{1}-x_{2}-7 x_{3} \\ x_{3}^{\prime }&=-48 x_{1}+21 x_{2}+31 x_{3} \\ \end{align*}

0.612

7051

2004

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

0.612

7052

2639

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

0.612

7053

6969

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

0.612

7054

8895

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

0.612

7055

9506

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

0.612

7056

10477

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

0.612

7057

11187

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

0.612

7058

13300

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

0.612

7059

16842

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

0.612

7060

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*}

0.612

7061

21268

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

0.612

7062

22092

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

0.612

7063

1026

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }&=-4 x_{2}-x_{4} \\ \end{align*}

0.613

7064

19650

\begin{align*} x^{\prime }&=x+y-5 t +2 \\ y^{\prime }&=4 x-2 y-8 t -8 \\ \end{align*}

0.613

7065

20769

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

0.613

7066

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*}

0.614

7067

10519

\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*}

0.614

7068

10523

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\ \end{align*}

0.614

7069

10665

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

0.614

7070

10875

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

0.614

7071

486

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

0.615

7072

2284

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

0.615

7073

2703

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

0.615

7074

3814

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

0.615

7075

3993

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

0.615

7076

8477

\begin{align*} \left (x^{2}-25\right ) y^{\prime \prime }+2 y^{\prime } x +y&=0 \\ \end{align*}
Series expansion around \(x=1\).

0.615

7077

11080

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

0.615

7078

11150

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

0.615

7079

13109

\begin{align*} x^{\prime }&=-3 x+48 y-28 z \\ y^{\prime }&=-4 x+40 y-22 z \\ z^{\prime }&=-6 x+57 y-31 z \\ \end{align*}

0.615

7080

24002

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

0.615

7081

25401

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

0.615

7082

2401

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

0.616

7083

6852

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

0.616

7084

14115

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

0.616

7085

15978

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

0.616

7086

25109

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

0.616

7087

1920

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

0.617

7088

4576

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+27 t \\ x_{2}^{\prime }&=-x_{1}+4 x_{2} \\ \end{align*}

0.617

7089

6462

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

0.617

7090

7640

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

0.617

7091

9853

\begin{align*} \left (9 x^{2}+1\right ) y^{\prime \prime }-18 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.617

7092

9983

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

0.617

7093

14223

\begin{align*} y^{\prime }+y+\frac {1}{y}&=0 \\ \end{align*}

0.617

7094

16806

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

0.617

7095

19639

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

0.617

7096

21271

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

0.617

7097

1847

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

0.618

7098

2008

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

0.618

7099

2665

\begin{align*} t y^{\prime \prime }+y^{\prime }-4 y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.618

7100

2800

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

0.618