2.4.10 second order ode can be made integrable

Table 2.473: second order ode can be made integrable

#

ODE

ODE classification

Solved?

149

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

216

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

217

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

218

\[ {}y^{\prime \prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

271

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

311

\[ {}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y \]

[[_2nd_order, _missing_x]]

808

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

809

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

810

\[ {}y^{\prime \prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

842

\[ {}y^{\prime \prime }+2 y = 4 \]

[[_2nd_order, _missing_x]]

845

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

859

\[ {}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y \]

[[_2nd_order, _missing_x]]

1254

\[ {}4 y^{\prime \prime }-9 y = 0 \]

[[_2nd_order, _missing_x]]

1264

\[ {}4 y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1265

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1268

\[ {}4 y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1278

\[ {}4 y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

1286

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1355

\[ {}u^{\prime \prime }+2 u = 0 \]

[[_2nd_order, _missing_x]]

2364

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

2545

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

2564

\[ {}y^{\prime \prime }+w^{2} y = 0 \]

[[_2nd_order, _missing_x]]

2820

\[ {}z^{\prime \prime }+z^{3} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2821

\[ {}z^{\prime \prime }+z+z^{5} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2822

\[ {}z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2823

\[ {}z^{\prime \prime }+\frac {z}{1+z^{2}} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2824

\[ {}z^{\prime \prime }+z-2 z^{3} = 0 \]

[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]]

2835

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2836

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2837

\[ {}y^{\prime \prime }-\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2838

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2840

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3059

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

3245

\[ {}y^{\prime \prime } = k^{2} y \]

[[_2nd_order, _missing_x]]

3246

\[ {}x^{\prime \prime }+k^{2} x = 0 \]

[[_2nd_order, _missing_x]]

3266

\[ {}y^{\prime \prime } = y \]

[[_2nd_order, _missing_x]]

3558

\[ {}y^{\prime \prime }-25 y = 0 \]

[[_2nd_order, _missing_x]]

3559

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

3564

\[ {}y^{\prime \prime }-9 y = 0 \]

[[_2nd_order, _missing_x]]

3698

\[ {}y^{\prime \prime }-36 y = 0 \]

[[_2nd_order, _missing_x]]

4125

\[ {}y^{\prime \prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

5918

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

6002

\[ {}y^{\prime \prime } = \frac {3 k y^{2}}{2} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

6003

\[ {}y^{\prime \prime } = 2 k y^{3} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

6140

\[ {}y^{\prime \prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

6243

\[ {}y^{\prime \prime } = -4 y \]

[[_2nd_order, _missing_x]]

6245

\[ {}y^{\prime \prime } = y \]

[[_2nd_order, _missing_x]]

6388

\[ {}x^{\prime \prime }-\omega ^{2} x = 0 \]

[[_2nd_order, _missing_x]]

6504

\[ {}\frac {x^{\prime \prime }}{2} = -48 x \]
i.c.

[[_2nd_order, _missing_x]]

6575

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

6706

\[ {}y^{\prime \prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

6939

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6941

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6942

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6943

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6946

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6972

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6973

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6974

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

6986

\[ {}y^{\prime \prime }+9 y = 18 \]

[[_2nd_order, _missing_x]]

7008

\[ {}y^{\prime \prime }+9 y = 5 \]

[[_2nd_order, _missing_x]]

7585

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

7586

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

7587

\[ {}y^{\prime \prime }+k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

7612

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

7613

\[ {}3 y^{\prime \prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

7614

\[ {}y^{\prime \prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

7621

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7622

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7623

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7624

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7628

\[ {}y^{\prime \prime }+10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

7650

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

7651

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

7762

\[ {}y^{\prime \prime }+k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

7777

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

7778

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

7907

\[ {}y^{\prime \prime }-k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

7939

\[ {}y^{\prime \prime }+8 y = 0 \]

[[_2nd_order, _missing_x]]

7945

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

7949

\[ {}y^{\prime \prime } = 4 y \]

[[_2nd_order, _missing_x]]

8047

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

8070

\[ {}y^{\prime \prime } = -3 y \]
i.c.

[[_2nd_order, _missing_x]]

8071

\[ {}y^{\prime \prime }+\sin \left (y\right ) = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

8219

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

8221

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

8307

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

8500

\[ {}y^{\prime \prime }+\beta ^{2} y = 0 \]

[[_2nd_order, _missing_x]]

8962

\[ {}y^{\prime \prime } = A y^{{2}/{3}} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

8983

\[ {}y^{\prime \prime }+{\mathrm e}^{y} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

9109

\[ {}y^{\prime \prime }+y = 1 \]

[[_2nd_order, _missing_x]]

9128

\[ {}y^{\prime } y^{\prime \prime }+y^{2} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

9129

\[ {}y^{\prime } y^{\prime \prime }+y^{n} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

10998

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

11002

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

11005

\[ {}y^{\prime \prime }+l y = 0 \]

[[_2nd_order, _missing_x]]

11551

\[ {}y^{\prime \prime }-y^{2} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

11552

\[ {}y^{\prime \prime }-6 y^{2} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

11554

\[ {}y^{\prime \prime }-6 y^{2}+4 y = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

11557

\[ {}y^{\prime \prime }-a y^{3} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

11560

\[ {}y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

11562

\[ {}y^{\prime \prime }+6 a^{10} y^{11}-y = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

11564

\[ {}y^{\prime \prime }-{\mathrm e}^{y} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

11567

\[ {}y^{\prime \prime }+a \sin \left (y\right ) = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

12422

\[ {}y^{\prime \prime }+a y = 0 \]

[[_2nd_order, _missing_x]]

12924

\[ {}2 y^{\prime \prime } = {\mathrm e}^{y} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

13051

\[ {}x^{\prime \prime }+9 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13052

\[ {}x^{\prime \prime }-12 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13346

\[ {}y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

13347

\[ {}4 y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

13607

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13608

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13609

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13610

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

13691

\[ {}y^{\prime \prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

14078

\[ {}y^{\prime \prime }+\alpha ^{2} y = 0 \]

[[_2nd_order, _missing_x]]

14079

\[ {}y^{\prime \prime }-\alpha ^{2} y = 0 \]

[[_2nd_order, _missing_x]]

14157

\[ {}y^{\prime \prime } = a^{2} y \]

[[_2nd_order, _missing_x]]

14166

\[ {}y^{\prime \prime } = 9 y \]

[[_2nd_order, _missing_x]]

14167

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

14168

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

14233

\[ {}x^{\prime \prime }+x-x^{3} = 0 \]

[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]]

14234

\[ {}x^{\prime \prime }+x+x^{3} = 0 \]

[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]]

14237

\[ {}x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

14266

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

14415

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

14416

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

14435

\[ {}y^{\prime \prime }+\alpha y = 0 \]

[[_2nd_order, _missing_x]]

14825

\[ {}y^{\prime \prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15225

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15238

\[ {}y^{\prime \prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15246

\[ {}y^{\prime \prime }-25 y = 0 \]

[[_2nd_order, _missing_x]]

15248

\[ {}4 y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

15253

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15255

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15268

\[ {}y^{\prime \prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

15273

\[ {}4 y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

15274

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15276

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

15464

\[ {}y^{\prime \prime }+36 y = 0 \]

[[_2nd_order, _missing_x]]

15467

\[ {}y^{\prime \prime }-36 y = 0 \]

[[_2nd_order, _missing_x]]

15473

\[ {}y^{\prime \prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

16106

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

16109

\[ {}y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

16111

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16116

\[ {}y^{\prime \prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

16142

\[ {}4 y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

16143

\[ {}y^{\prime \prime }+16 y = 0 \]

[[_2nd_order, _missing_x]]

16144

\[ {}y^{\prime \prime }+8 y = 0 \]

[[_2nd_order, _missing_x]]

16145

\[ {}y^{\prime \prime }+7 y = 0 \]

[[_2nd_order, _missing_x]]

16156

\[ {}y^{\prime \prime }+36 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16157

\[ {}y^{\prime \prime }+100 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16175

\[ {}y^{\prime \prime }-16 y = 0 \]

[[_2nd_order, _missing_x]]

16237

\[ {}y^{\prime \prime }+4 y = 1 \]

[[_2nd_order, _missing_x]]

16521

\[ {}y^{\prime \prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16552

\[ {}4 x^{\prime \prime }+9 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16553

\[ {}9 x^{\prime \prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16554

\[ {}x^{\prime \prime }+64 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16555

\[ {}x^{\prime \prime }+100 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16556

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16557

\[ {}x^{\prime \prime }+4 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16558

\[ {}x^{\prime \prime }+16 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16559

\[ {}x^{\prime \prime }+256 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16560

\[ {}x^{\prime \prime }+9 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16561

\[ {}10 x^{\prime \prime }+\frac {x}{10} = 0 \]
i.c.

[[_2nd_order, _missing_x]]

16840

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

16881

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

16918

\[ {}y^{\prime \prime }+k^{2} y = k \]

[[_2nd_order, _missing_x]]

16941

\[ {}y^{\prime \prime }+9 y = 9 \]

[[_2nd_order, _missing_x]]

17038

\[ {}y^{\prime \prime }-y = 1 \]

[[_2nd_order, _missing_x]]

17109

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17110

\[ {}y^{\prime \prime }+\lambda y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17111

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17115

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17120

\[ {}y^{\prime \prime }+\lambda ^{2} y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17121

\[ {}y^{\prime \prime }+\lambda ^{2} y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17481

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17482

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17496

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

17525

\[ {}4 y^{\prime \prime }-9 y = 0 \]

[[_2nd_order, _missing_x]]

17534

\[ {}4 y^{\prime \prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

17547

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17554

\[ {}4 y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17570

\[ {}m y^{\prime \prime }+k y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

17934

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

17989

\[ {}y^{\prime \prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

17990

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

18118

\[ {}y^{\prime \prime }-k y = 0 \]

[[_2nd_order, _missing_x]]

18191

\[ {}y^{\prime \prime }-y = 0 \]

[[_2nd_order, _missing_x]]

18219

\[ {}y^{\prime \prime }+8 y = 0 \]

[[_2nd_order, _missing_x]]

18229

\[ {}y^{\prime \prime } = 4 y \]

[[_2nd_order, _missing_x]]

18494

\[ {}\theta ^{\prime \prime } = -p^{2} \theta \]

[[_2nd_order, _missing_x]]

18509

\[ {}\theta ^{\prime \prime }-p^{2} \theta = 0 \]

[[_2nd_order, _missing_x]]

18510

\[ {}y^{\prime \prime }+y = 0 \]

[[_2nd_order, _missing_x]]

18512

\[ {}r^{\prime \prime }-a^{2} r = 0 \]

[[_2nd_order, _missing_x]]

18528

\[ {}y^{\prime \prime } = -m^{2} y \]

[[_2nd_order, _missing_x]]

18612

\[ {}e y^{\prime \prime } = P \left (-y+a \right ) \]

[[_2nd_order, _missing_x]]

18629

\[ {}y^{\prime \prime } = -a^{2} y \]

[[_2nd_order, _missing_x]]

18655

\[ {}y^{\prime \prime }-k^{2} y = 0 \]

[[_2nd_order, _missing_x]]

18797

\[ {}y^{\prime \prime }-m^{2} y = 0 \]

[[_2nd_order, _missing_x]]

18886

\[ {}y^{\prime \prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

19088

\[ {}y^{\prime \prime }-n^{2} y = 0 \]

[[_2nd_order, _missing_x]]

19303

\[ {}y^{\prime \prime } = y \]

[[_2nd_order, _missing_x]]

19305

\[ {}y^{\prime \prime }-a^{2} y = 0 \]

[[_2nd_order, _missing_x]]

19307

\[ {}y^{\prime \prime } = y^{3}-y \]

[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]]

19308

\[ {}y^{\prime \prime } = {\mathrm e}^{2 y} \]
i.c.

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

19350

\[ {}y^{\prime \prime } = {\mathrm e}^{y} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

19351

\[ {}y^{\prime \prime }+a^{2} y = 0 \]

[[_2nd_order, _missing_x]]