2.3.117 Problems 11601 to 11700

Table 2.777: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11601

8995

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

0.875

11602

12457

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

0.875

11603

14802

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\)

N/A

N/A

N/A

0.875

11604

14925

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

0.875

11605

18358

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

0.875

11606

21171

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

0.875

11607

12310

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

0.876

11608

21692

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

0.876

11609

22482

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

0.876

11610

23610

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

0.876

11611

23811

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

0.876

11612

25831

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

0.876

11613

1747

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

0.877

11614

7960

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

0.877

11615

10421

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

0.877

11616

14294

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{8}+x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.877

11617

23713

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

0.877

11618

24771

\begin{align*} 3 v^{\prime }+2 v+w^{\prime }-6 w&=5 \,{\mathrm e}^{x} \\ 4 v^{\prime }+2 v+w^{\prime }-8 w&=5 \,{\mathrm e}^{x}+2 x -3 \\ \end{align*}

0.877

11619

25765

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

0.877

11620

1828

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

0.878

11621

1993

\begin{align*} 9 x^{2} \left (x +5\right ) y^{\prime \prime }+9 x \left (5+9 x \right ) y^{\prime }-\left (5-8 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.878

11622

4184

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

0.878

11623

6867

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

0.878

11624

8866

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

0.878

11625

9544

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

0.878

11626

13413

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

0.878

11627

13666

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

0.878

11628

14134

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

0.878

11629

15663

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

0.878

11630

16875

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

0.878

11631

21017

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

0.878

11632

1641

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

0.879

11633

9323

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

0.879

11634

21006

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

0.879

11635

22711

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

0.879

11636

23705

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

0.879

11637

9815

\begin{align*} 4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y&=0 \\ \end{align*}

0.880

11638

15279

\begin{align*} x^{\prime }&=-4 x+9 y+12 \,{\mathrm e}^{-t} \\ y^{\prime }&=-5 x+2 y \\ \end{align*}

0.880

11639

19517

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

0.880

11640

21051

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

0.880

11641

2802

\begin{align*} x^{\prime }&=-7 x+y-6 z \\ y^{\prime }&=10 x-4 y+12 z \\ z^{\prime }&=2 x-y+z \\ \end{align*}

0.881

11642

11791

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

0.881

11643

16668

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} \sin \left (3 x \right ) \\ \end{align*}

0.881

11644

16877

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

0.881

11645

17835

\begin{align*} x^{\prime \prime }+16 x&=t \sin \left (t \right ) \\ \end{align*}

0.881

11646

3955

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

0.882

11647

7663

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

0.882

11648

14815

\begin{align*} y^{\prime \prime }+4 y&=8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}
Using Laplace transform method.

0.882

11649

19603

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

0.882

11650

20986

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

0.882

11651

23933

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

0.882

11652

9649

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

0.883

11653

15232

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=39 \operatorname {Heaviside}\left (t \right )-507 \left (-2+t \right ) \operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.883

11654

19053

\begin{align*} x_{1}^{\prime }&=-7 x_{1}+9 x_{2}-6 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+11 x_{2}-7 x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+3 x_{2}-x_{3} \\ \end{align*}

0.883

11655

19504

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

0.883

11656

8770

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

0.884

11657

13063

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

0.884

11658

15682

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

0.884

11659

17303

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

0.884

11660

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 \(t=0\).

0.885

11661

12547

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (\ln \left (x \right )^{2} x^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}}&=0 \\ \end{align*}

0.885

11662

12892

\begin{align*} y^{\prime \prime } x +a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y}&=0 \\ \end{align*}

0.885

11663

4179

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

0.886

11664

6540

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

0.886

11665

12501

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

0.886

11666

14990

\begin{align*} x^{\prime }&=8 x+14 y \\ y^{\prime }&=7 x+y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.886

11667

19200

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

0.886

11668

21189

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

0.886

11669

14366

\begin{align*} x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-4 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.887

11670

17432

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

0.887

11671

18351

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

0.887

11672

23462

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=x^{2} {\mathrm e}^{5 x} \\ \end{align*}

0.887

11673

25094

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

0.887

11674

648

\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*}

0.888

11675

2063

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.888

11676

4539

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

0.888

11677

6521

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

0.888

11678

7975

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

0.888

11679

8884

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

0.888

11680

9238

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}

0.888

11681

14291

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

0.888

11682

16624

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \\ \end{align*}

0.888

11683

20182

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

0.888

11684

1952

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

0.889

11685

3698

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

0.889

11686

4456

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \\ \end{align*}

0.889

11687

7641

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

0.889

11688

9529

\begin{align*} \left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.889

11689

9750

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

0.889

11690

16266

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

0.889

11691

23688

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

0.889

11692

177

\begin{align*} x^{\prime }&=4 x \left (7-x\right ) \\ x \left (0\right ) &= 11 \\ \end{align*}

0.890

11693

10262

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

0.890

11694

19441

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

0.890

11695

21605

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

0.890

11696

23116

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

0.890

11697

25399

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

0.890

11698

5971

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

0.891

11699

6365

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

0.891

11700

9956

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

0.891