2.3.116 Problems 11501 to 11600

Table 2.763: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11501

17513

\begin{align*} y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \\ \end{align*}

0.628

11502

17680

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

0.628

11503

18447

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

0.628

11504

18805

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}

0.628

11505

21623

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

0.628

11506

22789

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

0.628

11507

3319

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

0.629

11508

5983

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

0.629

11509

9682

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

0.629

11510

15161

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

0.629

11511

18254

\begin{align*} 9 y+6 y^{\prime }+y^{\prime \prime }&=18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \\ \end{align*}

0.629

11512

25348

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

0.629

11513

2014

\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.630

11514

6598

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

0.630

11515

8541

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

0.630

11516

9811

\begin{align*} x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y&=0 \\ \end{align*}

0.630

11517

14960

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

0.630

11518

18289

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}

0.630

11519

18453

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

0.630

11520

21547

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

0.630

11521

21653

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

0.630

11522

1958

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

0.631

11523

2260

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

0.631

11524

6038

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

0.631

11525

7166

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

0.631

11526

9428

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

0.631

11527

9877

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

0.631

11528

17446

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

0.631

11529

19502

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

0.631

11530

21004

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

0.631

11531

21886

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

0.631

11532

25303

\begin{align*} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.631

11533

14682

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

0.632

11534

16431

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

0.632

11535

17653

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

0.632

11536

17895

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

0.632

11537

20403

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

0.632

11538

20549

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

0.632

11539

22772

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

0.632

11540

23743

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

0.632

11541

25412

\begin{align*} y+y^{\prime }&=\operatorname {Heaviside}\left (t -10\right ) \\ \end{align*}

0.632

11542

641

\begin{align*} x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\ \end{align*}

0.633

11543

2454

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

0.633

11544

6188

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

0.633

11545

6469

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

0.633

11546

11818

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

0.633

11547

18950

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.633

11548

19882

\begin{align*} y^{\prime }+3 y+z&=0 \\ z^{\prime }+3 y+5 z&=0 \\ \end{align*}

0.633

11549

23083

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

0.633

11550

25487

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

0.633

11551

147

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

0.634

11552

1755

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

0.634

11553

1959

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

0.634

11554

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 \(x=0\).

0.634

11555

2019

\begin{align*} x^{2} \left (9+4 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.634

11556

2251

\begin{align*} y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3} \\ y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3} \\ y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3} \\ \end{align*}

0.634

11557

2252

\begin{align*} y_{1}^{\prime }&=3 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }&=3 y_{1}+5 y_{2}+y_{3} \\ y_{3}^{\prime }&=-6 y_{1}+2 y_{2}+4 y_{3} \\ \end{align*}

0.634

11558

2684

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

0.634

11559

4538

\begin{align*} y_{1}^{\prime }-2 y_{1}+3 y_{2}-3 y_{3}&=0 \\ -4 y_{1}+y_{2}^{\prime }+5 y_{2}-3 y_{3}&=0 \\ -4 y_{1}+4 y_{2}+y_{3}^{\prime }-2 y_{3}&=0 \\ \end{align*}

0.634

11560

7215

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

0.634

11561

10174

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

0.634

11562

10189

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

0.634

11563

16498

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

0.634

11564

16881

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

0.634

11565

16943

\begin{align*} x^{\prime }&=8 x+2 y+7 \,{\mathrm e}^{2 t} \\ y^{\prime }&=4 x+y-7 \,{\mathrm e}^{2 t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.634

11566

23081

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

0.634

11567

23723

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

0.634

11568

25199

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

0.634

11569

25346

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

0.634

11570

2280

\begin{align*} y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3} \\ y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3} \\ y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3} \\ \end{align*}

0.635

11571

3162

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

0.635

11572

3959

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

0.635

11573

4431

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

0.635

11574

6395

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

0.635

11575

8616

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

0.635

11576

9408

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

0.635

11577

9743

\begin{align*} x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y&=0 \\ \end{align*}

0.635

11578

11033

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*}

0.635

11579

14176

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

0.635

11580

16387

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

0.635

11581

17515

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

0.635

11582

17603

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

0.635

11583

17819

\begin{align*} x^{\prime \prime }+x&=\cos \left (\frac {7 t}{10}\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.635

11584

17835

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

0.635

11585

19193

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

0.635

11586

23732

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

0.635

11587

1035

\begin{align*} x_{1}^{\prime }&=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }&=17 x_{1}+7 x_{2}+5 x_{3} \\ \end{align*}

0.636

11588

1357

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u&=3 \cos \left (\frac {t}{4}\right ) \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.636

11589

1493

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.636

11590

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 \(x=0\).

0.636

11591

2408

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

0.636

11592

7203

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

0.636

11593

10082

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

0.636

11594

13292

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

0.636

11595

17508

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 t} \ln \left (2 t \right ) \\ \end{align*}

0.636

11596

18723

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

0.636

11597

20930

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

0.636

11598

22488

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

0.636

11599

22725

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

0.636

11600

25381

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

0.636