2.3.136 Problems 13501 to 13600

Table 2.845: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13501

13900

\begin{align*} x^{6} y^{\prime \prime }+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+b y&=0 \\ \end{align*}

2.437

13502

4641

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

2.438

13503

16994

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

2.438

13504

21675

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

Series expansion around \(x=0\).

2.438

13505

27657

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

2.438

13506

1172

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

2.441

13507

17157

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

2.441

13508

23657

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=3 t^{3}-9 t^{2}-5 t +1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

Using Laplace transform method.

2.441

13509

17115

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

2.442

13510

18400

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

2.442

13511

4955

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

2.443

13512

17889

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

2.443

13513

11698

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

2.444

13514

26109

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

2.444

13515

6535

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

2.445

13516

6026

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

2.447

13517

10396

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

2.447

13518

11763

\begin{align*} 9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\ \end{align*}

2.447

13519

22761

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

2.447

13520

9546

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

Series expansion around \(x=0\).

2.448

13521

17786

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=8 x \\ \end{align*}

2.448

13522

23671

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

Series expansion around \(x=0\).

2.448

13523

23701

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

Series expansion around \(x=3\).

2.448

13524

2476

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

2.450

13525

10218

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

Series expansion around \(x=0\).

2.450

13526

20526

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

2.451

13527

21769

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

2.451

13528

5667

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

2.452

13529

17168

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

2.452

13530

23684

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

Series expansion around \(x=0\).

2.452

13531

5758

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

2.453

13532

18790

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

2.453

13533

23439

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

Series expansion around \(x=0\).

2.453

13534

17783

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

2.454

13535

21381

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

2.454

13536

21525

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

2.454

13537

2689

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

2.455

13538

7207

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

2.455

13539

8558

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

Series expansion around \(x=0\).

2.455

13540

9552

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

Series expansion around \(x=0\).

2.455

13541

15656

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

2.455

13542

2481

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

2.456

13543

4631

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

2.456

13544

8995

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

Series expansion around \(x=0\).

2.456

13545

10393

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

2.456

13546

23493

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

2.456

13547

2518

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

2.457

13548

13699

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

2.457

13549

20564

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

2.457

13550

22836

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

Series expansion around \(x=1\).

2.457

13551

709

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

2.458

13552

8515

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

Series expansion around \(x=0\).

2.458

13553

16385

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

2.458

13554

2323

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

2.459

13555

8590

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

Series expansion around \(x=0\).

2.459

13556

19854

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

2.459

13557

4094

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

2.460

13558

11765

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

2.460

13559

16050

\begin{align*} x^{\prime }&=-10 x+10 y \\ y^{\prime }&=28 x-y \\ z^{\prime }&=-\frac {8 z}{3} \\ \end{align*}

2.460

13560

27120

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

N/A

N/A

N/A

2.460

13561

1150

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

2.461

13562

13874

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

2.461

13563

15779

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

2.461

13564

15888

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

2.461

13565

21244

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

2.461

13566

21674

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

Series expansion around \(x=0\).

2.461

13567

3227

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

2.462

13568

18537

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

2.462

13569

24067

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

2.462

13570

756

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

2.463

13571

23597

\begin{align*} c_{1}^{\prime }&=-\frac {k c_{1}}{V_{1}}+\frac {k c_{2}}{V_{1}} \\ c_{2}^{\prime }&=\frac {k c_{1}}{V_{2}}-\frac {k c_{2}}{V_{2}} \\ \end{align*}

2.463

13572

24901

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

2.463

13573

22309

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

2.464

13574

14172

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

2.466

13575

16875

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

Series expansion around \(x=0\).

2.466

13576

1254

\begin{align*} 4 y^{\prime \prime }-9 y&=0 \\ \end{align*}

2.467

13577

11624

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

2.467

13578

15173

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

2.467

13579

22323

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

2.467

13580

4108

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

2.470

13581

16402

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

2.470

13582

16884

\begin{align*} \left (-1+x \right )^{2} y^{\prime \prime }-5 \left (-1+x \right ) y^{\prime }+9 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

2.471

13583

23433

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

Series expansion around \(x=0\).

2.471

13584

25369

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

With initial conditions

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

2.471

13585

9542

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

Series expansion around \(x=0\).

2.472

13586

6249

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

2.473

13587

11706

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

2.473

13588

17191

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

2.473

13589

17251

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

2.473

13590

25382

\begin{align*} y_{1}^{\prime }&=5 y_{1}+2 y_{2}+t \\ y_{2}^{\prime }&=-8 y_{1}-3 y_{2}-2 t \\ \end{align*}

With initial conditions

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

2.473

13591

8020

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

2.474

13592

15526

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

2.474

13593

23708

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

Series expansion around \(x=0\).

2.474

13594

24465

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

2.474

13595

16861

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

Series expansion around \(x=2\).

2.475

13596

27577

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

2.475

13597

8078

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

Series expansion around \(x=0\).

2.476

13598

15318

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

2.476

13599

26646

\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=\frac {2 x^{3}+x^{2}-4 x -6}{x^{4}} \\ \end{align*}

2.476

13600

2655

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

Series expansion around \(t=0\).

2.477