2.4.10 second order ode can be made integrable

Table 2.469: second order ode can be made integrable

#

ODE

CAS classification

Solved?

11

\[ {}x^{\prime \prime } = 50 \]
i.c.

[[_2nd_order, _quadrature]]

12

\[ {}x^{\prime \prime } = -20 \]
i.c.

[[_2nd_order, _quadrature]]

149

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

[[_2nd_order, _missing_x]]

215

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

[[_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]]

258

\[ {}y^{\prime \prime }-4 y = 12 \]
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]]

807

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

[[_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]]

839

\[ {}y^{\prime \prime }-4 y = 12 \]
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]]

1283

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

[[_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]]

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]]

3089

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

[[_2nd_order, _quadrature]]

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]]

3273

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

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

3282

\[ {}x^{\prime \prime }-k^{2} x = 0 \]
i.c.

[[_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]]

4127

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

[[_2nd_order, _quadrature]]

5918

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

[[_2nd_order, _missing_x]]

5945

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

[[_2nd_order, _quadrature]]

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]]

6013

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

[[_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]]

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]]

6940

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

6944

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

[[_2nd_order, _missing_x]]

6945

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

6974

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

[[_2nd_order, _missing_x]]

6975

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

7615

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

[[_2nd_order, _quadrature]]

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]]

7766

\[ {}y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}} \]
i.c.

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]

7767

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

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

7768

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

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

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]]

8506

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

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

8507

\[ {}2 y^{\prime \prime } = \sin \left (2 y\right ) \]
i.c.

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

8508

\[ {}2 y^{\prime \prime } = \sin \left (2 y\right ) \]
i.c.

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

8766

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

[[_2nd_order, _quadrature]]

8767

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

[[_2nd_order, _quadrature]]

8769

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

[[_2nd_order, _quadrature]]

8773

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

[[_2nd_order, _quadrature]]

8777

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

[[_2nd_order, _quadrature]]

8782

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

[[_2nd_order, _quadrature]]

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]]

9072

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

[[_2nd_order, _quadrature]]

9075

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

[[_2nd_order, _quadrature]]

9078

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

[[_2nd_order, _quadrature]]

9079

\[ {}{y^{\prime \prime }}^{2} = 1 \]

[[_2nd_order, _quadrature]]

9109

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

[[_2nd_order, _missing_x]]

9128

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

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

9129

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

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

11011

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

[[_2nd_order, _quadrature]]

11012

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

[[_2nd_order, _missing_x]]

11016

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

[[_2nd_order, _missing_x]]

11019

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

[[_2nd_order, _missing_x]]

11590

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

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

11591

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

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

11593

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

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

11596

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

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

11599

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

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

11601

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

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

11603

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

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

11606

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

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

12501

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

[[_2nd_order, _missing_x]]

12995

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

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

13123

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

[[_2nd_order, _missing_x]]

13267

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

[[_2nd_order, _missing_x]]

13417

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

[[_2nd_order, _missing_x]]

13418

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

[[_2nd_order, _missing_x]]

13678

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

[[_2nd_order, _missing_x]]

13679

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

[[_2nd_order, _missing_x]]

13680

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

[[_2nd_order, _missing_x]]

13755

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

[[_2nd_order, _missing_x]]

13762

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

[[_2nd_order, _missing_x]]

13764

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

[[_2nd_order, _missing_x]]

14149

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

[[_2nd_order, _missing_x]]

14150

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

[[_2nd_order, _missing_x]]

14226

\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]

14228

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

[[_2nd_order, _missing_x]]

14234

\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]

14237

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

[[_2nd_order, _missing_x]]

14238

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

[[_2nd_order, _missing_x]]

14239

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

[[_2nd_order, _missing_x]]

14304

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

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

14305

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

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

14308

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

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

14337

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

[[_2nd_order, _missing_x]]

14486

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

[[_2nd_order, _missing_x]]

14487

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

[[_2nd_order, _missing_x]]

14490

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

[[_2nd_order, _missing_x]]

14493

\[ {}y^{\prime \prime }-4 y = 31 \]
i.c.

[[_2nd_order, _missing_x]]

14506

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

[[_2nd_order, _missing_x]]

14896

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

[[_2nd_order, _missing_x]]

15216

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]

15235

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

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]

15296

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

[[_2nd_order, _missing_x]]

15297

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

[[_2nd_order, _missing_x]]

15309

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

[[_2nd_order, _missing_x]]

15317

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

[[_2nd_order, _missing_x]]

15319

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

[[_2nd_order, _missing_x]]

15324

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

[[_2nd_order, _missing_x]]

15325

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

[[_2nd_order, _missing_x]]

15326

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

[[_2nd_order, _missing_x]]

15339

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

[[_2nd_order, _missing_x]]

15344

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

[[_2nd_order, _missing_x]]

15346

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

[[_2nd_order, _missing_x]]

15347

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

[[_2nd_order, _missing_x]]

15415

\[ {}y^{\prime \prime }-9 y = 36 \]
i.c.

[[_2nd_order, _missing_x]]

15535

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

[[_2nd_order, _missing_x]]

15538

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

[[_2nd_order, _missing_x]]

15544

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

[[_2nd_order, _missing_x]]

16177

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

[[_2nd_order, _missing_x]]

16180

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

[[_2nd_order, _missing_x]]

16182

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

[[_2nd_order, _missing_x]]

16187

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

[[_2nd_order, _missing_x]]

16206

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

[[_2nd_order, _quadrature]]

16213

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

[[_2nd_order, _missing_x]]

16214

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

[[_2nd_order, _missing_x]]

16215

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

[[_2nd_order, _missing_x]]

16216

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

[[_2nd_order, _missing_x]]

16227

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

[[_2nd_order, _missing_x]]

16228

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

[[_2nd_order, _missing_x]]

16246

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

[[_2nd_order, _missing_x]]

16285

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

[[_2nd_order, _missing_x]]

16308

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

[[_2nd_order, _missing_x]]

16591

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

[[_2nd_order, _missing_x]]

16624

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

[[_2nd_order, _missing_x]]

16625

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

[[_2nd_order, _missing_x]]

16626

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

[[_2nd_order, _missing_x]]

16627

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

[[_2nd_order, _missing_x]]

16628

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

[[_2nd_order, _missing_x]]

16629

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

[[_2nd_order, _missing_x]]

16630

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

[[_2nd_order, _missing_x]]

16631

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

[[_2nd_order, _missing_x]]

16632

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

[[_2nd_order, _missing_x]]

16911

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

[[_2nd_order, _missing_x]]

16949

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

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

16952

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

[[_2nd_order, _missing_x]]

16989

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

[[_2nd_order, _missing_x]]

17012

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

[[_2nd_order, _missing_x]]

17109

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

[[_2nd_order, _missing_x]]

17181

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

[[_2nd_order, _missing_x]]

17182

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

[[_2nd_order, _missing_x]]

17186

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

[[_2nd_order, _missing_x]]

17192

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

[[_2nd_order, _missing_x]]

17567

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

[[_2nd_order, _missing_x]]

17596

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

[[_2nd_order, _missing_x]]

17605

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

[[_2nd_order, _missing_x]]

17610

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

[[_2nd_order, _missing_x]]

17618

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

[[_2nd_order, _missing_x]]

17625

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

[[_2nd_order, _missing_x]]

17639

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

[[_2nd_order, _missing_x]]

17641

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

[[_2nd_order, _missing_x]]

18005

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

[[_2nd_order, _missing_x]]

18060

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

[[_2nd_order, _missing_x]]

18061

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

[[_2nd_order, _missing_x]]

18189

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

[[_2nd_order, _missing_x]]

18262

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

[[_2nd_order, _missing_x]]

18290

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

[[_2nd_order, _missing_x]]

18300

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

[[_2nd_order, _missing_x]]

18522

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

[[_2nd_order, _missing_x]]

18565

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

[[_2nd_order, _missing_x]]

18568

\[ {}\phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]

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

18580

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

[[_2nd_order, _missing_x]]

18581

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

[[_2nd_order, _missing_x]]

18583

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

[[_2nd_order, _missing_x]]

18599

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

[[_2nd_order, _missing_x]]

18683

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

[[_2nd_order, _missing_x]]

18700

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

[[_2nd_order, _missing_x]]

18726

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

[[_2nd_order, _missing_x]]

18868

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

[[_2nd_order, _missing_x]]

18957

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

[[_2nd_order, _missing_x]]

18958

\[ {}y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]

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

19159

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

[[_2nd_order, _missing_x]]

19374

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

[[_2nd_order, _missing_x]]

19376

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

[[_2nd_order, _missing_x]]

19378

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

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

19379

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

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

19421

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

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

19422

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

[[_2nd_order, _missing_x]]

19426

\[ {}y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]

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