2.3.111 Problems 11001 to 11100

Table 2.765: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11001

5950

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

0.797

11002

9562

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

0.797

11003

23580

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

0.797

11004

2467

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

0.798

11005

9181

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

0.798

11006

10145

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

0.798

11007

15811

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

0.798

11008

16657

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=x^{3} \sin \left (4 x \right ) \\ \end{align*}

0.798

11009

1729

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

0.799

11010

1830

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

0.799

11011

2245

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

0.799

11012

5465

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

0.799

11013

10469

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

0.799

11014

16063

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

0.799

11015

20354

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

0.799

11016

21257

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

0.799

11017

22914

\begin{align*} x^{\prime }+5 x+3 y^{\prime }-11 y&=0 \\ x^{\prime }+3 x+y^{\prime }-7 y&=0 \\ \end{align*}

0.799

11018

23055

\begin{align*} r^{\prime }&=-a \sin \left (\theta \right ) \\ r \left (0\right ) &= 2 a \\ \end{align*}

0.799

11019

1456

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

0.800

11020

1961

\begin{align*} 2 \left (x +3\right ) x^{2} y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.800

11021

3164

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

0.800

11022

4188

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

0.800

11023

6864

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

0.800

11024

7817

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

0.800

11025

9075

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

0.800

11026

18230

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

0.800

11027

21753

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

0.800

11028

6293

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

0.801

11029

7202

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

0.801

11030

12883

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

0.801

11031

14625

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=5 \,{\mathrm e}^{-2 x} x \\ \end{align*}

0.801

11032

20560

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

0.801

11033

24551

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

0.801

11034

24838

\begin{align*} 9 y^{2} {y^{\prime }}^{2}-3 y^{\prime } x +y&=0 \\ \end{align*}

0.801

11035

4056

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

0.802

11036

7803

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

0.802

11037

8331

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

0.802

11038

9684

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

0.802

11039

15390

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

0.802

11040

16897

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

0.802

11041

17692

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

0.802

11042

18995

\begin{align*} x_{1}^{\prime }&=-x_{3} \\ x_{2}^{\prime }&=2 x_{1} \\ x_{3}^{\prime }&=-x_{1}+2 x_{2}+4 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 7 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= 5 \\ \end{align*}

0.802

11043

19167

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

0.802

11044

20016

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

0.802

11045

23595

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

0.802

11046

1495

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.803

11047

2784

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

0.803

11048

3348

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

0.803

11049

4564

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

0.803

11050

6946

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

0.803

11051

13298

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

0.803

11052

14359

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

0.803

11053

19064

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

0.803

11054

20956

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

0.803

11055

22814

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

0.803

11056

24834

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

0.803

11057

3759

\begin{align*} y^{\prime \prime }+2 y^{\prime }+17 y&=\frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \\ \end{align*}

0.804

11058

5815

\begin{align*} b \,{\mathrm e}^{k x} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

0.804

11059

6422

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

0.804

11060

18681

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

0.804

11061

4053

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.805

11062

4595

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

0.805

11063

7180

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

0.805

11064

7773

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

0.805

11065

8264

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

0.805

11066

9847

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

0.805

11067

10118

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

0.805

11068

18242

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

0.805

11069

20624

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

0.805

11070

21640

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

0.805

11071

23599

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

0.805

11072

23632

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}
Using Laplace transform method.

0.805

11073

1501

\begin{align*} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.806

11074

2247

\begin{align*} y_{1}^{\prime }&=3 y_{1}+5 y_{2}+8 y_{3} \\ y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3} \\ \end{align*}

0.806

11075

2588

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

0.806

11076

5408

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

0.806

11077

9410

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

0.806

11078

15441

\begin{align*} y^{\prime \prime }+n^{2} y&=h \sin \left (r x \right ) \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= c \\ \end{align*}

0.806

11079

16038

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

0.806

11080

18828

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

0.806

11081

23794

\begin{align*} x^{\prime }&=4 x-6 y \\ y^{\prime }&=8 x-10 y \\ \end{align*}

0.806

11082

24577

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

0.806

11083

315

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\ \end{align*}

0.807

11084

7458

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

0.807

11085

12628

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

0.807

11086

14801

\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\)

N/A

N/A

N/A

0.807

11087

23438

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

0.807

11088

20651

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

0.808

11089

24717

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

0.808

11090

172

\begin{align*} x^{\prime }&=10 x-x^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}

0.809

11091

923

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

0.809

11092

1942

\begin{align*} \left (x +3\right ) x^{2} y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.809

11093

2248

\begin{align*} y_{1}^{\prime }&=y_{1}-y_{2}+2 y_{3} \\ y_{2}^{\prime }&=12 y_{1}-4 y_{2}+10 y_{3} \\ y_{3}^{\prime }&=-6 y_{1}+y_{2}-7 y_{3} \\ \end{align*}

0.809

11094

5466

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

0.809

11095

8591

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

0.809

11096

11822

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

0.809

11097

14611

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+37 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

0.809

11098

14807

\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.809

11099

16383

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

0.809

11100

16407

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

0.809