2.4.10 second order ode can be made integrable

Table 2.465: 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]]

6940

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

[[_2nd_order, _missing_x]]

6941

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

[[_2nd_order, _missing_x]]

6943

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

6947

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

[[_2nd_order, _missing_x]]

6973

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

[[_2nd_order, _missing_x]]

6975

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

[[_2nd_order, _missing_x]]

6976

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

[[_2nd_order, _missing_x]]

7363

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

[[_2nd_order, _missing_x]]

7364

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

[[_2nd_order, _missing_x]]

7365

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

[[_2nd_order, _missing_x]]

7390

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

[[_2nd_order, _missing_x]]

7391

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

[[_2nd_order, _missing_x]]

7392

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

[[_2nd_order, _missing_x]]

7393

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

[[_2nd_order, _quadrature]]

7400

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

[[_2nd_order, _missing_x]]

7401

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

[[_2nd_order, _missing_x]]

7402

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

[[_2nd_order, _missing_x]]

7406

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

[[_2nd_order, _missing_x]]

7428

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

[[_2nd_order, _missing_x]]

7429

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

[[_2nd_order, _missing_x]]

7540

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

[[_2nd_order, _missing_x]]

7544

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

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

7545

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

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

7546

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

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

7555

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

[[_2nd_order, _missing_x]]

7556

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

[[_2nd_order, _missing_x]]

7685

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

[[_2nd_order, _missing_x]]

7717

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

[[_2nd_order, _missing_x]]

7723

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

[[_2nd_order, _missing_x]]

7727

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

[[_2nd_order, _missing_x]]

7825

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

[[_2nd_order, _missing_x]]

7848

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

[[_2nd_order, _missing_x]]

7849

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

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

7997

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

[[_2nd_order, _missing_x]]

7999

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

[[_2nd_order, _missing_x]]

8085

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

[[_2nd_order, _missing_x]]

8278

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

[[_2nd_order, _missing_x]]

8284

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

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

8285

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

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

8286

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

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

8544

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

[[_2nd_order, _quadrature]]

8545

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

[[_2nd_order, _quadrature]]

8547

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

[[_2nd_order, _quadrature]]

8551

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

[[_2nd_order, _quadrature]]

8555

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

[[_2nd_order, _quadrature]]

8560

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

[[_2nd_order, _quadrature]]

8740

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

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

8761

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

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

8850

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

[[_2nd_order, _quadrature]]

8853

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

[[_2nd_order, _quadrature]]

8856

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

[[_2nd_order, _quadrature]]

8857

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

[[_2nd_order, _quadrature]]

8887

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

[[_2nd_order, _missing_x]]

8906

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

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

8907

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

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

10789

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

[[_2nd_order, _quadrature]]

10790

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

[[_2nd_order, _missing_x]]

10794

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

[[_2nd_order, _missing_x]]

10797

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

[[_2nd_order, _missing_x]]

11368

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

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

11369

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

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

11371

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

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

11374

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

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

11377

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

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

11379

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

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

11381

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

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

11384

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

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

12279

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

[[_2nd_order, _missing_x]]

12773

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

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

12901

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

[[_2nd_order, _missing_x]]

13045

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

[[_2nd_order, _missing_x]]

13195

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

[[_2nd_order, _missing_x]]

13196

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

[[_2nd_order, _missing_x]]

13456

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

[[_2nd_order, _missing_x]]

13457

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

[[_2nd_order, _missing_x]]

13458

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

[[_2nd_order, _missing_x]]

13533

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

[[_2nd_order, _missing_x]]

13540

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

[[_2nd_order, _missing_x]]

13542

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

[[_2nd_order, _missing_x]]

13927

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

[[_2nd_order, _missing_x]]

13928

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

[[_2nd_order, _missing_x]]

14004

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

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

14006

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

[[_2nd_order, _missing_x]]

14012

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

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

14015

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

[[_2nd_order, _missing_x]]

14016

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

[[_2nd_order, _missing_x]]

14017

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

[[_2nd_order, _missing_x]]

14082

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

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

14083

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

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

14086

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

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

14115

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

[[_2nd_order, _missing_x]]

14264

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

[[_2nd_order, _missing_x]]

14265

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

[[_2nd_order, _missing_x]]

14268

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

[[_2nd_order, _missing_x]]

14271

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

[[_2nd_order, _missing_x]]

14284

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

[[_2nd_order, _missing_x]]

14674

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

[[_2nd_order, _missing_x]]

14994

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

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

15013

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

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

15074

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

[[_2nd_order, _missing_x]]

15075

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

[[_2nd_order, _missing_x]]

15087

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

[[_2nd_order, _missing_x]]

15095

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

[[_2nd_order, _missing_x]]

15097

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

[[_2nd_order, _missing_x]]

15102

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

[[_2nd_order, _missing_x]]

15103

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

[[_2nd_order, _missing_x]]

15104

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

[[_2nd_order, _missing_x]]

15117

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

[[_2nd_order, _missing_x]]

15122

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

[[_2nd_order, _missing_x]]

15124

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

[[_2nd_order, _missing_x]]

15125

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

[[_2nd_order, _missing_x]]

15193

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

[[_2nd_order, _missing_x]]

15313

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

[[_2nd_order, _missing_x]]

15316

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

[[_2nd_order, _missing_x]]

15322

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

[[_2nd_order, _missing_x]]

15955

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

[[_2nd_order, _missing_x]]

15958

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

[[_2nd_order, _missing_x]]

15960

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

[[_2nd_order, _missing_x]]

15965

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

[[_2nd_order, _missing_x]]

15984

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

[[_2nd_order, _quadrature]]

15991

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

[[_2nd_order, _missing_x]]

15992

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

[[_2nd_order, _missing_x]]

15993

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

[[_2nd_order, _missing_x]]

15994

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

[[_2nd_order, _missing_x]]

16005

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

[[_2nd_order, _missing_x]]

16006

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

[[_2nd_order, _missing_x]]

16024

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

[[_2nd_order, _missing_x]]

16063

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

[[_2nd_order, _missing_x]]

16086

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

[[_2nd_order, _missing_x]]

16369

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

[[_2nd_order, _missing_x]]

16402

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

[[_2nd_order, _missing_x]]

16403

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

[[_2nd_order, _missing_x]]

16404

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

[[_2nd_order, _missing_x]]

16405

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

[[_2nd_order, _missing_x]]

16406

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

[[_2nd_order, _missing_x]]

16407

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

[[_2nd_order, _missing_x]]

16408

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

[[_2nd_order, _missing_x]]

16409

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

[[_2nd_order, _missing_x]]

16410

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

[[_2nd_order, _missing_x]]

16689

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

[[_2nd_order, _missing_x]]

16727

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

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

16730

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

[[_2nd_order, _missing_x]]

16767

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

[[_2nd_order, _missing_x]]

16790

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

[[_2nd_order, _missing_x]]

16887

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

[[_2nd_order, _missing_x]]

16959

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

[[_2nd_order, _missing_x]]

16960

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

[[_2nd_order, _missing_x]]

16964

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

[[_2nd_order, _missing_x]]

16970

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

[[_2nd_order, _missing_x]]

17345

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

[[_2nd_order, _missing_x]]

17374

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

[[_2nd_order, _missing_x]]

17383

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

[[_2nd_order, _missing_x]]

17388

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

[[_2nd_order, _missing_x]]

17396

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

[[_2nd_order, _missing_x]]

17403

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

[[_2nd_order, _missing_x]]

17417

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

[[_2nd_order, _missing_x]]

17419

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

[[_2nd_order, _missing_x]]

17783

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

[[_2nd_order, _missing_x]]

17838

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

[[_2nd_order, _missing_x]]

17839

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

[[_2nd_order, _missing_x]]

17967

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

[[_2nd_order, _missing_x]]

18040

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

[[_2nd_order, _missing_x]]

18068

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

[[_2nd_order, _missing_x]]

18078

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

[[_2nd_order, _missing_x]]

18300

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

[[_2nd_order, _missing_x]]

18343

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

[[_2nd_order, _missing_x]]

18346

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

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

18358

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

[[_2nd_order, _missing_x]]

18359

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

[[_2nd_order, _missing_x]]

18361

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

[[_2nd_order, _missing_x]]

18377

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

[[_2nd_order, _missing_x]]

18461

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

[[_2nd_order, _missing_x]]

18478

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

[[_2nd_order, _missing_x]]

18504

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

[[_2nd_order, _missing_x]]

18646

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

[[_2nd_order, _missing_x]]

18735

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

[[_2nd_order, _missing_x]]

18736

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

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

18937

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

[[_2nd_order, _missing_x]]

19152

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

[[_2nd_order, _missing_x]]

19154

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

[[_2nd_order, _missing_x]]

19156

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

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

19157

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

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

19199

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

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

19200

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

[[_2nd_order, _missing_x]]

19204

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

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