2.3.118 Problems 11701 to 11800

Table 2.779: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11701

14677

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

0.891

11702

17705

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

0.891

11703

21471

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

0.891

11704

23607

\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=12 x-7 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 3 \\ \end{align*}

0.891

11705

4176

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

0.892

11706

19602

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

0.892

11707

22704

\begin{align*} i^{\prime \prime }+9 i&=12 \cos \left (3 t \right ) \\ i \left (0\right ) &= 4 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.892

11708

3360

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

0.893

11709

8046

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

0.893

11710

15163

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

0.893

11711

21769

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

0.893

11712

175

\begin{align*} x^{\prime }&=3 x \left (5-x\right ) \\ x \left (0\right ) &= 8 \\ \end{align*}

0.894

11713

3915

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

0.894

11714

10366

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

0.894

11715

14837

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

0.894

11716

19731

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

0.894

11717

992

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+9 x_{4} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4} \\ x_{3}^{\prime }&=-x_{3}+8 x_{4} \\ x_{4}^{\prime }&=x_{4} \\ \end{align*}

0.895

11718

10240

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\ \end{align*}

0.895

11719

12377

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

0.895

11720

13775

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

0.895

11721

14635

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

0.895

11722

15173

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

0.895

11723

22277

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+9 \,{\mathrm e}^{-t} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

0.895

11724

22826

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

0.895

11725

2102

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.896

11726

4185

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

0.896

11727

9480

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

0.896

11728

9768

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

0.896

11729

16674

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \\ \end{align*}

0.896

11730

17791

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

0.896

11731

19193

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

0.896

11732

20062

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

0.896

11733

24860

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

0.896

11734

24880

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

0.896

11735

14628

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y&=5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \\ \end{align*}

0.897

11736

14663

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

0.897

11737

16992

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

0.897

11738

18354

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

0.897

11739

22945

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

0.897

11740

25376

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

0.897

11741

1950

\begin{align*} 8 x^{2} y^{\prime \prime }-2 x \left (-x^{2}-4 x +3\right ) y^{\prime }+\left (x^{2}+6 x +3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.898

11742

3013

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

0.898

11743

5464

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

0.898

11744

8910

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

0.898

11745

11355

\begin{align*} y^{\prime }-a^{n} f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right )&=0 \\ \end{align*}

0.898

11746

11760

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

0.898

11747

3575

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ \end{align*}

0.899

11748

4183

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

0.899

11749

8312

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

0.900

11750

8863

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

0.900

11751

15806

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

0.900

11752

16899

\begin{align*} \left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x +10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.900

11753

21269

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

0.900

11754

23444

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

0.900

11755

23510

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

0.900

11756

1968

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.901

11757

2080

\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.901

11758

3743

\begin{align*} y^{\prime \prime }+16 y&=34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \\ \end{align*}

0.901

11759

10294

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

0.901

11760

14789

\begin{align*} x^{\prime }&=5 x+3 y \\ y^{\prime }&=4 x+y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 8 \\ \end{align*}

0.901

11761

16385

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

0.901

11762

17775

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

0.901

11763

19420

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

0.901

11764

2738

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

0.902

11765

6514

\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*}

0.902

11766

9890

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

0.902

11767

14401

\begin{align*} x^{\prime }&=-5 x+3 y \\ y^{\prime }&=2 x-10 y \\ \end{align*}

0.902

11768

16388

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

0.902

11769

20541

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

0.902

11770

22940

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

0.902

11771

23562

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

0.902

11772

25027

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

0.902

11773

6018

\begin{align*} \operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

0.903

11774

6579

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

0.903

11775

8217

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

0.903

11776

18871

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

0.903

11777

18992

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

0.903

11778

18996

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

0.903

11779

1832

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (3+2 x \right ) y&=x^{{5}/{2}} {\mathrm e}^{x} \\ \end{align*}

0.904

11780

2406

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=t^{{5}/{2}} {\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.904

11781

7672

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

0.904

11782

9141

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

0.904

11783

9982

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

0.904

11784

15485

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

0.904

11785

16414

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

0.904

11786

22904

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

0.904

11787

25892

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

0.904

11788

9430

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

0.905

11789

14604

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.905

11790

24949

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

0.905

11791

6852

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

0.906

11792

9404

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

0.906

11793

20135

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

0.906

11794

1947

\begin{align*} 4 x^{2} y^{\prime \prime }+x \left (4 x^{2}+2 x +7\right ) y^{\prime }-\left (-7 x^{2}-4 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.907

11795

2398

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

0.907

11796

2463

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

0.907

11797

10219

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

0.907

11798

12447

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

0.907

11799

16404

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

0.907

11800

1441

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

0.908