Chapter 1
Lookup tables for all problems in current book

1.1 section 1
1.2 section 2 (system of first order odes)
1.3 section 3. First order odes solved using Laplace method
1.4 section 4. First order odes solved using series method

1.1 section 1

Table 1.1: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

10259

1

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=0 \end {array} \]

10260

2

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a \end {array} \]

10261

3

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \end {array} \]

10262

4

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1 \end {array} \]

10263

5

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x \end {array} \]

10264

6

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x y \end {array} \]

10265

7

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x +y \end {array} \]

10266

8

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x +b y \end {array} \]

10267

9

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \end {array} \]

10268

10

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=b y \end {array} \]

10269

11

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x +b y^{2} \end {array} \]

10270

12

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=0 \end {array} \]

10271

13

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a \end {array} \]

10272

14

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a x \end {array} \]

10273

15

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a x +y \end {array} \]

10274

16

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a x +b y \end {array} \]

10275

17

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=y \end {array} \]

10276

18

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=b y \end {array} \]

10277

19

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a x +b y^{2} \end {array} \]

10278

20

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=\frac {a x +b y^{2}}{r} \end {array} \]

10279

21

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=\frac {a x +b y^{2}}{r x} \end {array} \]

10280

22

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=\frac {a x +b y^{2}}{r \,x^{2}} \end {array} \]

10281

23

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=\frac {a x +b y^{2}}{y} \end {array} \]

10282

24

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \sin \left (x \right ) y x y^{\prime }&=0 \end {array} \]

10283

25

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi& =0 \end {array} \]

10284

26

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sin \left (x \right )+y \end {array} \]

10285

27

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sin \left (x \right )+y^{2} \end {array} \]

10286

28

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \end {array} \]

10287

29

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\cos \left (x \right )+\frac {y^{2}}{x} \end {array} \]

10288

30

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x +y+b y^{2} \end {array} \]

10289

31

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }&=0 \end {array} \]

10290

32

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime }&=0 \end {array} \]

10291

33

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e} y^{\prime }&=0 \end {array} \]

10292

34

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \pi y^{\prime }&=0 \end {array} \]

10293

35

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime }&=0 \end {array} \]

10294

36

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f \left (x \right ) y^{\prime }&=0 \end {array} \]

10295

37

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }&=1 \end {array} \]

10296

38

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }&=\sin \left (x \right ) \end {array} \]

10297

39

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime }&=0 \end {array} \]

10298

40

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=0 \end {array} \]

10299

41

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y y^{\prime }&=0 \end {array} \]

10300

42

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y \sin \left (x \right ) y^{\prime }&=0 \end {array} \]

10301

43

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \pi y \sin \left (x \right ) y^{\prime }&=0 \end {array} \]

10302

44

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \sin \left (x \right ) y^{\prime }&=0 \end {array} \]

10303

45

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \sin \left (x \right ) {y^{\prime }}^{2}&=0 \end {array} \]

10304

46

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}&=0 \end {array} \]

10305

47

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{n}&=0 \end {array} \]

10306

48

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{n}&=0 \end {array} \]

10307

49

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=x \end {array} \]

10308

50

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=x +y \end {array} \]

10309

51

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {y}{x} \end {array} \]

10310

52

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {y^{2}}{x} \end {array} \]

10311

53

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {y^{3}}{x} \end {array} \]

10312

54

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}&=\frac {y^{2}}{x} \end {array} \]

10313

55

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {1}{y x} \end {array} \]

10314

56

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {1}{x y^{3}} \end {array} \]

10315

57

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \end {array} \]

10316

58

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{4}&=\frac {1}{x y^{3}} \end {array} \]

10317

59

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {1}{x^{3} y^{4}} \end {array} \]

10318

60

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {1+6 x +y} \end {array} \]

10319

61

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \end {array} \]

10320

62

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \end {array} \]

10321

63

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (a +b x +y\right )^{4} \end {array} \]

10322

64

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \end {array} \]

10323

65

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (a +b x +c y\right )^{6} \end {array} \]

10324

66

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]

10325

67

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=10+{\mathrm e}^{x +y} \end {array} \]

10326

68

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \end {array} \]

10327

69

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \end {array} \]

10328

70

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \end {array} \]

1.2 section 2 (system of first order odes)

Table 1.3: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

10329

1

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )&=t +y \left (t \right )\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}\\ \end {array} \]

10330

2

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )&=t +y \left (t \right )\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}\\ \end {array} \]

10331

3

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )&=y \left (t \right )+t +\sin \left (t \right )+\cos \left (t \right )\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}\\ \end {array} \]

1.3 section 3. First order odes solved using Laplace method

Table 1.5: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

10332

1

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=t\\ y \left (0\right )&=5\\ \end {array} \]

Using Laplace transform method.

10333

2

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y t&=0\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

10334

3

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

10335

4

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0\\ y \left (0\right )&=y_{0}\\ \end {array} \]

Using Laplace transform method.

10336

5

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0\\ y \left (x_{0} \right )&=y_{0}\\ \end {array} \]

Using Laplace transform method.

10337

6

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0 \end {array} \]

Using Laplace transform method.

10338

7

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0\\ y \left (1\right )&=5\\ \end {array} \]

Using Laplace transform method.

10339

8

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=\sin \left (t \right )\\ y \left (1\right )&=0\\ \end {array} \]

Using Laplace transform method.

10340

9

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=t\\ y \left (1\right )&=0\\ \end {array} \]

Using Laplace transform method.

10341

10

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=t\\ y \left (1\right )&=1\\ \end {array} \]

Using Laplace transform method.

10342

11

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y+y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

10343

12

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a t +1\right ) y^{\prime }+y&=t\\ y \left (1\right )&=0\\ \end {array} \]

Using Laplace transform method.

10344

13

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\left (a t +b t \right ) y&=0\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

10345

14

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\left (a t +b t \right ) y&=0\\ y \left (-3\right )&=0\\ \end {array} \]

Using Laplace transform method.

1.4 section 4. First order odes solved using series method

Table 1.7: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

10346

1

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y x&=x \end {array} \]

Series expansion around \(x=0\).

10347

2

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=\sin \left (x \right ) \end {array} \]

Series expansion around \(x=0\).

10348

3

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=0\\ y \left (0\right )&=1\\ \end {array} \]

Series expansion around \(x=0\).

10349

4

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=x \end {array} \]

Series expansion around \(x=0\).

10350

5

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=1 \end {array} \]

Series expansion around \(x=0\).

10351

6

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=\sin \left (x \right ) \end {array} \]

Series expansion around \(x=0\).

10352

7

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=2 x^{4}+x^{3}+x \end {array} \]

Series expansion around \(x=0\).

10353

8

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=\frac {1}{x^{3}} \end {array} \]

Series expansion around \(x=0\).

10354

9

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+2 y x&=\sqrt {x} \end {array} \]

Series expansion around \(x=0\).

10355

10

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {y}{x}&=0 \end {array} \]

Series expansion around \(x=0\).

10356

11

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x \end {array} \]

Series expansion around \(x=0\).

10357

12

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x +\sin \left (x \right ) \end {array} \]

Series expansion around \(x=0\).

10358

13

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=\tan \left (x \right ) \end {array} \]

Series expansion around \(x=0\).

10359

14

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=\cos \left (x \right )+\sin \left (x \right ) \end {array} \]

Series expansion around \(x=0\).