2.3.116 Problems 11501 to 11600

Table 2.781: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11501

4052

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

0.946

11502

9893

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

0.946

11503

12608

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

0.946

11504

17101

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

0.946

11505

20101

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

0.946

11506

21920

\begin{align*} y^{\prime \prime }+4 y&=t \sin \left (t \right ) \\ y \left (0\right ) &= {\frac {7}{9}} \\ y^{\prime }\left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}
Using Laplace transform method.

0.946

11507

3867

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

0.947

11508

7898

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

0.947

11509

16171

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

0.947

11510

18435

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

0.947

11511

18678

\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=a x+\frac {5 y}{4} \\ \end{align*}

0.947

11512

2741

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

0.948

11513

6293

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

0.948

11514

15756

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

0.948

11515

17682

\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+16 \left (2+x \right ) y^{\prime }-y&=0 \\ \end{align*}
Series expansion around \(x=1\).

0.948

11516

21752

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

0.948

11517

21886

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

0.948

11518

2590

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

0.949

11519

7954

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

0.949

11520

14775

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

0.949

11521

25529

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

0.949

11522

1945

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

0.950

11523

2263

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

0.950

11524

2600

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=\left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t} \\ \end{align*}

0.950

11525

3372

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

0.950

11526

6403

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

0.950

11527

7647

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

0.950

11528

8353

\begin{align*} q^{\prime }&=k \left (q-70\right ) \\ \end{align*}

0.950

11529

9533

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

0.950

11530

14781

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

0.950

11531

20738

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

0.950

11532

1007

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

0.951

11533

2806

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

0.951

11534

12624

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

0.951

11535

25527

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

0.951

11536

15447

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

0.952

11537

16385

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

0.952

11538

17506

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \\ \end{align*}

0.953

11539

18831

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

0.953

11540

26430

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

0.953

11541

3502

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

0.954

11542

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 \(x=0\).

0.954

11543

24766

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

0.954

11544

25419

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

0.954

11545

26507

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

0.954

11546

2645

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

0.955

11547

4024

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

0.955

11548

6042

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

0.955

11549

6434

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

0.955

11550

6586

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

0.955

11551

7085

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

0.955

11552

10449

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

0.955

11553

14959

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

0.955

11554

19437

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

0.955

11555

19518

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

0.955

11556

991

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

0.956

11557

1949

\begin{align*} x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.956

11558

7565

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

0.956

11559

16229

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

0.956

11560

19862

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

0.956

11561

23565

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

0.956

11562

25530

\begin{align*} y^{\prime \prime }&={\mathrm e}^{i \omega t} \\ \end{align*}

0.956

11563

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*}

0.957

11564

2084

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.957

11565

2587

\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*}

0.957

11566

4025

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

0.957

11567

6076

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

0.957

11568

8562

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

0.957

11569

10082

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

0.957

11570

15169

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

0.957

11571

20522

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

0.957

11572

21126

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

0.957

11573

22638

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

0.957

11574

24547

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=7+75 \sin \left (2 x \right ) \\ \end{align*}

0.957

11575

26554

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

0.957

11576

2640

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

0.958

11577

3808

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

0.958

11578

14336

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{t}&=a \\ \end{align*}

0.958

11579

21531

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=2 x -40 \cos \left (2 x \right ) \\ \end{align*}

0.958

11580

23622

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

0.958

11581

26461

\begin{align*} \sqrt {-x^{2}+1}\, y^{\prime \prime }+\sqrt {1-{y^{\prime }}^{2}}&=0 \\ \end{align*}

0.958

11582

2067

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

0.959

11583

2457

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

0.959

11584

3830

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

0.959

11585

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*}

0.959

11586

6135

\begin{align*} 2 \left (x +5\right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}

0.959

11587

6273

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

0.959

11588

15305

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

0.959

11589

17719

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

0.959

11590

21243

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

0.959

11591

21753

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

0.959

11592

24102

\begin{align*} 6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.959

11593

3769

\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=F \left (x \right ) \\ \end{align*}

0.960

11594

4485

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

0.960

11595

11735

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

0.960

11596

12281

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

0.960

11597

14960

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

0.960

11598

17718

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

0.960

11599

22807

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

0.960

11600

25087

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

0.960