2.3.86 Problems 8501 to 8600

Table 2.745: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8501

14335

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

0.518

8502

16773

\begin{align*} y^{\prime \prime }+9 y&=27 t^{3} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.518

8503

16785

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

Using Laplace transform method.

0.518

8504

20901

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

Series expansion around \(x=\infty \).

0.518

8505

21471

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

0.518

8506

24026

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

0.518

8507

25271

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

0.518

8508

485

\begin{align*} 4 y^{\prime \prime } x +8 y^{\prime }+y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.519

8509

1788

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

0.519

8510

1889

\begin{align*} \left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.519

8511

2429

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

Series expansion around \(t=0\).

0.519

8512

2729

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

0.519

8513

5577

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

0.519

8514

5796

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\ \end{align*}

0.519

8515

6206

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

0.519

8516

6884

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

0.519

8517

7288

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=120 \sin \left (5 x \right ) \\ \end{align*}

0.519

8518

7295

\begin{align*} 5 y^{\prime \prime }+6 y^{\prime }+2 y&=x^{2}+6 x \\ \end{align*}

0.519

8519

7814

\begin{align*} y^{\prime \prime }-60 y^{\prime }-900 y&=5 \,{\mathrm e}^{10 x} \\ \end{align*}

0.519

8520

8563

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

Series expansion around \(x=0\).

0.519

8521

9067

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

0.519

8522

9674

\begin{align*} x^{\prime }&=10 x-5 y \\ y^{\prime }&=8 x-12 y \\ \end{align*}

0.519

8523

14618

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

0.519

8524

14804

\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.519

8525

18455

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

0.519

8526

19480

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

0.519

8527

20592

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

0.519

8528

23659

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t}+5 t \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

0.519

8529

23717

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

Series expansion around \(x=0\).

0.519

8530

1860

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

Series expansion around \(x=0\).

0.520

8531

7762

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \\ \end{align*}

0.520

8532

8271

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

0.520

8533

8393

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

0.520

8534

8479

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

Series expansion around \(x=1\).

0.520

8535

8528

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

Series expansion around \(x=0\).

0.520

8536

9376

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

Series expansion around \(x=0\).

0.520

8537

10203

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

Series expansion around \(x=0\).

0.520

8538

11738

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

0.520

8539

14741

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

Series expansion around \(x=1\).

0.520

8540

16072

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{3 t} \\ \end{align*}

0.520

8541

16161

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

0.520

8542

19835

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

0.520

8543

20344

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=15 x^{2} \\ \end{align*}

0.520

8544

23527

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

0.520

8545

23631

\begin{align*} y^{\prime \prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

Using Laplace transform method.

0.520

8546

23814

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

0.520

8547

23934

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

0.520

8548

24075

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

0.520

8549

25196

\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=2 t \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

0.520

8550

25522

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{i \omega t} \\ \end{align*}

0.520

8551

26070

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

0.520

8552

26432

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

0.520

8553

26492

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

0.520

8554

26556

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

0.520

8555

27772

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

Series expansion around \(x=0\).

0.520

8556

2543

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

0.521

8557

9748

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

0.521

8558

12804

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 y^{\prime \prime } x&=0 \\ \end{align*}

0.521

8559

16413

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

0.521

8560

16649

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}

0.521

8561

18673

\begin{align*} x^{\prime }&=\frac {3 x}{4}-2 y \\ y^{\prime }&=x-\frac {5 y}{4} \\ \end{align*}

0.521

8562

23092

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

With initial conditions

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

0.521

8563

23512

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

0.521

8564

23658

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=39 \,{\mathrm e}^{t} \sin \left (t \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

0.521

8565

23768

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

0.521

8566

24033

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x} x^{2} \\ \end{align*}

0.521

8567

25575

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

0.521

8568

633

\begin{align*} x_{1}^{\prime }&=5 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}

0.522

8569

3749

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

0.522

8570

7112

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

0.522

8571

7596

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

0.522

8572

10240

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=4 \sqrt {x}\, {\mathrm e}^{x} \\ \end{align*}

0.522

8573

15267

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

0.522

8574

16336

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

0.522

8575

16650

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

0.522

8576

19836

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

0.522

8577

25550

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

0.522

8578

25568

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

0.522

8579

584

\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=13 x+4 y \\ \end{align*}

With initial conditions

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

0.523

8580

617

\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*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 10 \\ x_{2} \left (0\right ) &= 12 \\ x_{3} \left (0\right ) &= -1 \\ \end{align*}

0.523

8581

1262

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

0.523

8582

2048

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

Series expansion around \(x=0\).

0.523

8583

3992

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

Series expansion around \(x=0\).

0.523

8584

7645

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

Series expansion around \(x=1\).

0.523

8585

7774

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=6 \sin \left (t \right ) \\ \end{align*}

0.523

8586

7821

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

Using Laplace transform method.

0.523

8587

9234

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

0.523

8588

10271

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

0.523

8589

11291

\begin{align*} y^{\prime \prime }&=\frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}} \\ \end{align*}

0.523

8590

12901

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

0.523

8591

12920

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

0.523

8592

14807

\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.523

8593

14875

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

0.523

8594

16007

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

With initial conditions

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

0.523

8595

16554

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

0.523

8596

16566

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

0.523

8597

16763

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

Using Laplace transform method.

0.523

8598

21151

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

0.523

8599

21630

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

Series expansion around \(x=1\).

0.523

8600

21891

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=2 \sin \left (x \right ) {\mathrm e}^{-x} \\ \end{align*}

0.523