2.3.101 Problems 10001 to 10100

Table 2.751: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10001

17500

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

0.756

10002

20857

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

0.756

10003

24802

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

0.756

10004

2729

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

0.757

10005

3276

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

0.757

10006

6717

\begin{align*} 2 y x +2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=10 x^{2}+10 \\ \end{align*}

0.757

10007

7684

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

0.757

10008

10403

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

0.757

10009

12393

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

0.757

10010

14361

\begin{align*} x^{\prime \prime }+4 x&=\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.757

10011

14943

\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \\ \end{align*}

0.757

10012

17446

\begin{align*} y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \\ \end{align*}

0.757

10013

17484

\begin{align*} y^{\prime \prime }+16 y&=2 \cos \left (4 t \right ) \\ \end{align*}

0.757

10014

18194

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=8 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.757

10015

19039

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

0.757

10016

23995

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

0.757

10017

24459

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

0.757

10018

25571

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

0.757

10019

26036

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

0.757

10020

26574

\begin{align*} 5 y^{\prime \prime }-6 y^{\prime }+5 y&=13 \,{\mathrm e}^{x} \cosh \left (x \right ) \\ \end{align*}

0.757

10021

698

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

0.758

10022

6272

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

0.758

10023

9856

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

0.758

10024

12283

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

0.758

10025

14060

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

0.758

10026

14677

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

0.758

10027

1454

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

0.759

10028

1977

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.759

10029

3821

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

0.759

10030

15684

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \\ \end{align*}

0.759

10031

5464

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

0.760

10032

5482

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

0.760

10033

7090

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

0.760

10034

7294

\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \\ \end{align*}

0.760

10035

7599

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

0.760

10036

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 \(x=0\).

0.760

10037

9061

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

0.760

10038

18413

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

0.760

10039

18700

\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=8 x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -3 \\ \end{align*}

0.760

10040

20453

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

0.760

10041

25984

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

0.760

10042

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 \(x=0\).

0.761

10043

8961

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

0.761

10044

9849

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

0.761

10045

10041

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

0.761

10046

14301

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

0.761

10047

14787

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

0.761

10048

16011

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

0.761

10049

17681

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

0.761

10050

18667

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

0.761

10051

19370

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

0.761

10052

23922

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

0.761

10053

8537

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

0.762

10054

9838

\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.762

10055

14393

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

0.762

10056

17680

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

0.762

10057

1988

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.763

10058

8512

\begin{align*} y^{\prime \prime } x +y^{\prime }+10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.763

10059

9509

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

0.763

10060

14186

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

0.763

10061

15744

\(\left [\begin {array}{ccc} 7 & -1 & 6 \\ -10 & 4 & -12 \\ -2 & 1 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.763

10062

16881

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

0.763

10063

19704

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

0.763

10064

20709

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

0.763

10065

20999

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

0.763

10066

15

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

0.764

10067

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*}

0.764

10068

3846

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

0.764

10069

20415

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

0.764

10070

24432

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

0.764

10071

24465

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

0.764

10072

1850

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

0.765

10073

6206

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

0.765

10074

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*}

0.765

10075

8258

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

0.765

10076

8527

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

0.765

10077

17033

\begin{align*} y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\ y \left (0\right ) &= 0 \\ \end{align*}

0.765

10078

22862

\begin{align*} U^{\prime \prime }+\frac {2 U^{\prime }}{r}+a U&=0 \\ \end{align*}
Series expansion around \(r=0\).

0.765

10079

25563

\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&=0 \\ \end{align*}

0.765

10080

3907

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

0.766

10081

4498

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

0.766

10082

4558

\begin{align*} x^{\prime }-x-2 y&=0 \\ x-y^{\prime }&=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= x_{0} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

0.766

10083

7835

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

0.766

10084

8534

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

0.766

10085

10339

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

0.766

10086

17502

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{4}} \\ \end{align*}

0.766

10087

18018

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

0.766

10088

1528

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

0.767

10089

4553

\begin{align*} x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\ 2 x+y^{\prime }-y&=2 \cos \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= x_{0} \\ y \left (0\right ) &= y_{0} \\ \end{align*}

0.767

10090

5638

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

0.767

10091

7289

\begin{align*} 5 y^{\prime \prime }+12 y^{\prime }+20 y&=120 \sin \left (2 x \right ) \\ \end{align*}

0.767

10092

7290

\begin{align*} y^{\prime \prime }+9 y&=30 \sin \left (3 x \right ) \\ \end{align*}

0.767

10093

8608

\begin{align*} y^{\prime \prime } x +y^{\prime }+36 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.767

10094

12945

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

0.767

10095

13073

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

0.767

10096

14313

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

0.767

10097

19513

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

0.767

10098

22682

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

0.767

10099

1965

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

0.768

10100

7098

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

0.768