2.3.96 Problems 9501 to 9600

Table 2.723: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9501

16584

\begin{align*} 4 y+y^{\prime \prime }&=24 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.483

9502

17460

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

0.483

9503

18030

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

0.483

9504

20076

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

0.483

9505

21723

\begin{align*} x^{\prime }-6 x+3 y&=8 \,{\mathrm e}^{t} \\ y^{\prime }-2 x-y&=4 \,{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.483

9506

22703

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

0.483

9507

24730

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

0.483

9508

873

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

0.484

9509

2031

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

0.484

9510

3136

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.484

9511

6561

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

0.484

9512

7727

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

0.484

9513

8621

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

0.484

9514

14741

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

0.484

9515

14919

\begin{align*} z^{\prime \prime }-4 z^{\prime }+13 z&=0 \\ z \left (0\right ) &= 7 \\ z^{\prime }\left (0\right ) &= 42 \\ \end{align*}

0.484

9516

17461

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=3 t \\ y \left (0\right ) &= {\frac {23}{12}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{2}} \\ \end{align*}

0.484

9517

18264

\begin{align*} y^{\prime \prime }+9 y&=36 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.484

9518

20926

\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=-5 x \\ \end{align*}

0.484

9519

22858

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

0.484

9520

25265

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

0.484

9521

1807

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

0.485

9522

3962

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

0.485

9523

4739

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

0.485

9524

16098

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

0.485

9525

18334

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

0.485

9526

20704

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

0.485

9527

22214

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

0.485

9528

22224

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

0.485

9529

22918

\begin{align*} x^{\prime }+x+2 y^{\prime }+3 y&=0 \\ x^{\prime }-2 x+5 y^{\prime }&=0 \\ \end{align*}

0.485

9530

25141

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

0.485

9531

346

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

0.486

9532

1512

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

0.486

9533

1937

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

0.486

9534

2052

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

0.486

9535

2422

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

0.486

9536

6445

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

0.486

9537

7660

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

0.486

9538

10947

\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}

0.486

9539

13190

\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ -2 & 4 & -1 \\ -4 & 4 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.486

9540

14178

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

0.486

9541

14618

\begin{align*} y^{\prime \prime }-3 y^{\prime }+8 y&=4 x^{2} \\ \end{align*}

0.486

9542

14805

\(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\)

N/A

N/A

N/A

0.486

9543

15995

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

0.486

9544

16108

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

0.486

9545

18393

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

0.486

9546

19593

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

0.486

9547

21647

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

0.486

9548

22156

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

0.486

9549

22872

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

0.486

9550

23080

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

0.486

9551

24002

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

0.486

9552

24670

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

0.486

9553

24731

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

0.486

9554

25698

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

0.486

9555

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 \(x=0\).

0.487

9556

5623

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

0.487

9557

6034

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

0.487

9558

6111

\begin{align*} -6 y-2 \left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}

0.487

9559

6352

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

0.487

9560

8003

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

0.487

9561

9698

\begin{align*} x^{\prime }&=z \\ y^{\prime }&=y \\ z^{\prime }&=x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 5 \\ \end{align*}

0.487

9562

12575

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

0.487

9563

13028

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

0.487

9564

14184

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

0.487

9565

14638

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

0.487

9566

14769

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

0.487

9567

15095

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

0.487

9568

15435

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

0.487

9569

16091

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=10 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.487

9570

16142

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

0.487

9571

18036

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

0.487

9572

18233

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

0.487

9573

18321

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

0.487

9574

18881

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

0.487

9575

20475

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

0.487

9576

20765

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

0.487

9577

23079

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

0.487

9578

24751

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

0.487

9579

25284

\begin{align*} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=f \left (t \right ) \\ \end{align*}
Using Laplace transform method.

0.487

9580

5656

\begin{align*} x^{6} {y^{\prime }}^{3}-y^{\prime } x -y&=0 \\ \end{align*}

0.488

9581

7781

\begin{align*} x^{\prime \prime }+5 x^{\prime }+6 x&=\cos \left (t \right ) \\ x \left (0\right ) &= {\frac {1}{10}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.488

9582

9764

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

0.488

9583

13000

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

0.488

9584

14803

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

N/A

N/A

N/A

0.488

9585

15836

\begin{align*} v^{\prime }&=\frac {K -v}{R C} \\ \end{align*}

0.488

9586

17687

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

0.488

9587

21916

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

0.488

9588

22855

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

0.488

9589

22860

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

0.488

9590

24095

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

0.488

9591

25159

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

0.488

9592

349

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

0.489

9593

1446

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

0.489

9594

3428

\begin{align*} y^{\prime }&=\sin \left (t \right )^{2} \\ y \left (\frac {\pi }{6}\right ) &= 3 \\ \end{align*}

0.489

9595

5539

\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}

0.489

9596

6596

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

0.489

9597

7085

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

0.489

9598

8989

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

0.489

9599

18834

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

0.489

9600

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*}

0.489