2.3.116 Problems 11501 to 11600

Table 2.805: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11501

27380

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

0.913

11502

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*}

0.914

11503

6432

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

0.914

11504

8846

\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*}

0.914

11505

13160

\(\left [\begin {array}{cccc} 1 & 2 & 2 & 2 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 0 & 4 \end {array}\right ]\)

N/A

N/A

N/A

0.914

11506

14685

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

0.914

11507

14936

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

0.914

11508

15561

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

0.914

11509

16261

\begin{align*} y^{\prime }&=4 y+8 \\ \end{align*}

0.914

11510

17584

\begin{align*} y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y&=t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right ) \\ \end{align*}

0.914

11511

26535

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

0.914

11512

6307

\begin{align*} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3} \\ \end{align*}

0.915

11513

8524

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

Series expansion around \(x=0\).

0.915

11514

9847

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

Series expansion around \(x=0\).

0.915

11515

14727

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

Series expansion around \(x=0\).

0.915

11516

19601

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

Series expansion around \(x=0\).

0.915

11517

23244

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

0.915

11518

3691

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

0.916

11519

26141

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

0.916

11520

1960

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

Series expansion around \(x=0\).

0.917

11521

8599

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

Series expansion around \(x=0\).

0.917

11522

13881

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

0.917

11523

20997

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

0.917

11524

21460

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

0.917

11525

3381

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

Series expansion around \(x=0\).

0.918

11526

8580

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

Series expansion around \(x=0\).

0.918

11527

15719

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

Using Laplace transform method.

0.918

11528

15750

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

0.918

11529

16657

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

0.918

11530

24884

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

0.918

11531

26938

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

0.918

11532

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*}

0.919

11533

10393

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

0.919

11534

12399

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

0.919

11535

13007

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

0.919

11536

17432

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

0.919

11537

3629

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

0.920

11538

8597

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{49}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.920

11539

10233

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

0.920

11540

12850

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

0.920

11541

14100

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

0.920

11542

14557

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 7 \\ \end{align*}

0.920

11543

18978

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

0.920

11544

19598

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

Series expansion around \(x=0\).

0.920

11545

19867

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

0.920

11546

21630

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

Series expansion around \(x=1\).

0.920

11547

653

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

0.921

11548

2274

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= -4 \\ y_{2} \left (0\right ) &= 1 \\ y_{3} \left (0\right ) &= -3 \\ \end{align*}

0.921

11549

5575

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

0.921

11550

9333

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

0.921

11551

16406

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

0.921

11552

16668

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

0.921

11553

20615

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

0.921

11554

20714

\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*}

0.921

11555

20747

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

0.921

11556

21907

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

Series expansion around \(x=0\).

0.921

11557

1528

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

0.922

11558

1962

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

Series expansion around \(x=0\).

0.922

11559

4028

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

Series expansion around \(x=0\).

0.922

11560

5931

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

0.922

11561

6472

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

0.922

11562

7123

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

0.922

11563

22192

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

Series expansion around \(x=0\).

0.922

11564

22843

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

Series expansion around \(x=0\).

0.922

11565

2650

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

Series expansion around \(t=0\).

0.923

11566

6885

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

0.923

11567

7153

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

0.923

11568

10181

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

Series expansion around \(x=0\).

0.923

11569

14642

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.923

11570

15843

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

0.923

11571

16426

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

0.923

11572

1038

\begin{align*} x_{1}^{\prime }&=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\ x_{2}^{\prime }&=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\ x_{3}^{\prime }&=-10 x_{1}+3 x_{2}-9 x_{4} \\ x_{4}^{\prime }&=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \\ \end{align*}

0.924

11573

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 \(x=0\).

0.924

11574

2759

\begin{align*} x_{1}^{\prime }&=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

0.924

11575

4030

\begin{align*} x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.924

11576

7261

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

0.924

11577

8078

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

Series expansion around \(x=0\).

0.924

11578

9327

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

0.924

11579

9522

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

Series expansion around \(x=0\).

0.924

11580

16893

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

Series expansion around \(x=0\).

0.924

11581

18453

\begin{align*} x^{\prime }&=2 x-4 y+1 \\ y^{\prime }&=-x+5 y \\ \end{align*}

0.924

11582

18865

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

0.924

11583

21999

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

0.924

11584

24702

\begin{align*} 4 y+y^{\prime \prime }&=20 \,{\mathrm e}^{x}-20 \cos \left (2 x \right ) \\ \end{align*}

0.924

11585

1942

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

Series expansion around \(x=0\).

0.925

11586

1955

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

Series expansion around \(x=0\).

0.925

11587

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*}

0.925

11588

2648

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

Series expansion around \(t=0\).

0.925

11589

6947

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

0.925

11590

8541

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.925

11591

9076

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

0.925

11592

9794

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

0.925

11593

9840

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

Series expansion around \(x=0\).

0.925

11594

12326

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

0.925

11595

14335

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

0.925

11596

18275

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

0.925

11597

20033

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\ \end{align*}

0.925

11598

20907

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

Series expansion around \(x=0\).

0.925

11599

26031

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

Series expansion around \(x=0\).

0.925

11600

619

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= -7 \\ x_{3} \left (0\right ) &= 11 \\ \end{align*}

0.926