2.4.10 second order ode can be made integrable

Table 2.445: 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]]

6389

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

[[_2nd_order, _missing_x]]

6576

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

[[_2nd_order, _missing_x]]

6707

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

[[_2nd_order, _missing_x]]

7261

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

[[_2nd_order, _missing_x]]

7262

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

[[_2nd_order, _missing_x]]

7263

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

[[_2nd_order, _missing_x]]

7288

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

[[_2nd_order, _missing_x]]

7289

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

[[_2nd_order, _missing_x]]

7290

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

[[_2nd_order, _missing_x]]

7291

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

[[_2nd_order, _quadrature]]

7298

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

[[_2nd_order, _missing_x]]

7299

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

[[_2nd_order, _missing_x]]

7300

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

[[_2nd_order, _missing_x]]

7304

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

[[_2nd_order, _missing_x]]

7326

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

[[_2nd_order, _missing_x]]

7327

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

[[_2nd_order, _missing_x]]

7438

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

[[_2nd_order, _missing_x]]

7442

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

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

7443

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

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

7444

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

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

7453

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

[[_2nd_order, _missing_x]]

7454

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

[[_2nd_order, _missing_x]]

7583

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

[[_2nd_order, _missing_x]]

7615

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

[[_2nd_order, _missing_x]]

7621

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

[[_2nd_order, _missing_x]]

7625

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

[[_2nd_order, _missing_x]]

7723

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

[[_2nd_order, _missing_x]]

7746

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

[[_2nd_order, _missing_x]]

7747

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

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

7895

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

[[_2nd_order, _missing_x]]

7897

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

[[_2nd_order, _missing_x]]

7983

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

[[_2nd_order, _missing_x]]

8176

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

[[_2nd_order, _missing_x]]

8182

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

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

8183

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

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

8184

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

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

8442

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

[[_2nd_order, _quadrature]]

8443

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

[[_2nd_order, _quadrature]]

8445

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

[[_2nd_order, _quadrature]]

8638

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

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

8659

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

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

8748

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

[[_2nd_order, _quadrature]]

8751

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

[[_2nd_order, _quadrature]]

8754

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

[[_2nd_order, _quadrature]]

8785

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

[[_2nd_order, _missing_x]]

8804

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

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

8805

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

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

10687

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

[[_2nd_order, _quadrature]]

10688

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

[[_2nd_order, _missing_x]]

10692

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

[[_2nd_order, _missing_x]]

10695

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

[[_2nd_order, _missing_x]]

11266

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

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

11267

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

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

11269

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

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

11272

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

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

11275

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

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

11277

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

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

11279

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

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

11282

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

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

12177

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

[[_2nd_order, _missing_x]]

12671

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

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

12799

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

[[_2nd_order, _missing_x]]

12943

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

[[_2nd_order, _missing_x]]

13093

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

[[_2nd_order, _missing_x]]

13094

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

[[_2nd_order, _missing_x]]

13354

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

[[_2nd_order, _missing_x]]

13355

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

[[_2nd_order, _missing_x]]

13356

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

[[_2nd_order, _missing_x]]

13431

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

[[_2nd_order, _missing_x]]

13438

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

[[_2nd_order, _missing_x]]

13440

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

[[_2nd_order, _missing_x]]

13825

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

[[_2nd_order, _missing_x]]

13826

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

[[_2nd_order, _missing_x]]

13902

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

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

13904

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

[[_2nd_order, _missing_x]]

13910

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

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

13913

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

[[_2nd_order, _missing_x]]

13914

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

[[_2nd_order, _missing_x]]

13915

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

[[_2nd_order, _missing_x]]

13980

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

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

13981

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

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

13984

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

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

14013

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

[[_2nd_order, _missing_x]]

14162

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

[[_2nd_order, _missing_x]]

14163

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

[[_2nd_order, _missing_x]]

14166

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

[[_2nd_order, _missing_x]]

14169

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

[[_2nd_order, _missing_x]]

14182

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

[[_2nd_order, _missing_x]]

14572

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

[[_2nd_order, _missing_x]]

14892

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

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

14911

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

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

14972

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

[[_2nd_order, _missing_x]]

14973

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

[[_2nd_order, _missing_x]]

14985

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

[[_2nd_order, _missing_x]]

14993

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

[[_2nd_order, _missing_x]]

14995

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

[[_2nd_order, _missing_x]]

15000

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

[[_2nd_order, _missing_x]]

15001

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

[[_2nd_order, _missing_x]]

15002

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

[[_2nd_order, _missing_x]]

15015

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

[[_2nd_order, _missing_x]]

15020

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

[[_2nd_order, _missing_x]]

15022

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

[[_2nd_order, _missing_x]]

15023

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

[[_2nd_order, _missing_x]]

15091

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

[[_2nd_order, _missing_x]]

15211

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

[[_2nd_order, _missing_x]]

15214

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

[[_2nd_order, _missing_x]]

15220

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

[[_2nd_order, _missing_x]]

15853

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

[[_2nd_order, _missing_x]]

15856

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

[[_2nd_order, _missing_x]]

15858

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

[[_2nd_order, _missing_x]]

15863

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

[[_2nd_order, _missing_x]]

15882

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

[[_2nd_order, _quadrature]]

15889

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

[[_2nd_order, _missing_x]]

15890

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

[[_2nd_order, _missing_x]]

15891

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

[[_2nd_order, _missing_x]]

15892

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

[[_2nd_order, _missing_x]]

15903

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

[[_2nd_order, _missing_x]]

15904

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

[[_2nd_order, _missing_x]]

15922

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

[[_2nd_order, _missing_x]]

15961

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

[[_2nd_order, _missing_x]]

15984

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

[[_2nd_order, _missing_x]]

16267

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

[[_2nd_order, _missing_x]]

16300

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

[[_2nd_order, _missing_x]]

16301

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

[[_2nd_order, _missing_x]]

16302

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

[[_2nd_order, _missing_x]]

16303

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

[[_2nd_order, _missing_x]]

16304

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

[[_2nd_order, _missing_x]]

16305

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

[[_2nd_order, _missing_x]]

16306

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

[[_2nd_order, _missing_x]]

16307

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

[[_2nd_order, _missing_x]]

16308

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

[[_2nd_order, _missing_x]]

16587

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

[[_2nd_order, _missing_x]]

16625

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

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

16628

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

[[_2nd_order, _missing_x]]

16665

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

[[_2nd_order, _missing_x]]

16688

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

[[_2nd_order, _missing_x]]

16785

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

[[_2nd_order, _missing_x]]

16857

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

[[_2nd_order, _missing_x]]

16858

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

[[_2nd_order, _missing_x]]

16862

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

[[_2nd_order, _missing_x]]

16868

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

[[_2nd_order, _missing_x]]

17243

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

[[_2nd_order, _missing_x]]

17272

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

[[_2nd_order, _missing_x]]

17281

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

[[_2nd_order, _missing_x]]

17286

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

[[_2nd_order, _missing_x]]

17294

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

[[_2nd_order, _missing_x]]

17301

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

[[_2nd_order, _missing_x]]

17315

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

[[_2nd_order, _missing_x]]

17317

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

[[_2nd_order, _missing_x]]

17681

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

[[_2nd_order, _missing_x]]

17736

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

[[_2nd_order, _missing_x]]

17737

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

[[_2nd_order, _missing_x]]

17865

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

[[_2nd_order, _missing_x]]

17938

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

[[_2nd_order, _missing_x]]

17966

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

[[_2nd_order, _missing_x]]

17976

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

[[_2nd_order, _missing_x]]

18198

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

[[_2nd_order, _missing_x]]

18241

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

[[_2nd_order, _missing_x]]

18244

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

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

18256

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

[[_2nd_order, _missing_x]]

18257

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

[[_2nd_order, _missing_x]]

18259

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

[[_2nd_order, _missing_x]]

18275

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

[[_2nd_order, _missing_x]]

18359

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

[[_2nd_order, _missing_x]]

18376

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

[[_2nd_order, _missing_x]]

18402

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

[[_2nd_order, _missing_x]]