2.2.74 Problems 7301 to 7400

Table 2.149: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

7301

\[ {}y^{\prime \prime }+3 x y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.349

7302

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]
i.c.

[_Gegenbauer]

0.385

7303

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

[_separable]

0.487

7304

\[ {}\left (-2+x \right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.421

7305

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

[_Lienard]

0.597

7306

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

[[_Emden, _Fowler]]

1.071

7307

\[ {}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.655

7308

\[ {}x y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.330

7309

\[ {}y^{\prime \prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.360

7310

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

[_Lienard]

0.422

7311

\[ {}2 x \left (-1+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Jacobi]

0.707

7312

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

[[_2nd_order, _with_linear_symmetries]]

0.601

7313

\[ {}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.688

7314

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.691

7315

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.586

7316

\[ {}2 x \left (1-x \right ) y^{\prime \prime }-\left (1+6 x \right ) y^{\prime }-2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.730

7317

\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0 \]

[_Jacobi]

0.770

7318

\[ {}4 x y^{\prime \prime }+y^{\prime }+8 y = 0 \]

[[_Emden, _Fowler]]

0.691

7319

\[ {}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.583

7320

\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.477

7321

\[ {}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.326

7322

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{49}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.634

7323

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

[[_Emden, _Fowler]]

0.498

7324

\[ {}y^{\prime \prime }+\left ({\mathrm e}^{-2 x}-\frac {1}{9}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.720

7325

\[ {}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.700

7326

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.671

7327

\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+16 x \left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.483

7328

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-6\right ) y = 0 \]

[_Bessel]

0.656

7329

\[ {}x y^{\prime \prime }+5 y^{\prime }+x y = 0 \]

[_Lienard]

1.163

7330

\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (36 x^{4}-16\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.562

7331

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

[[_Emden, _Fowler]]

0.225

7332

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

[[_Emden, _Fowler]]

0.516

7333

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

[[_Emden, _Fowler]]

0.516

7334

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

[[_Emden, _Fowler]]

0.295

7335

\[ {}y^{\prime \prime }+k^{2} x^{4} y = 0 \]

[[_Emden, _Fowler]]

0.292

7336

\[ {}x y^{\prime \prime }-5 y^{\prime }+x y = 0 \]

[_Lienard]

1.102

7337

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

[[_2nd_order, _missing_x]]

0.389

7338

\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.628

7339

\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-\left (-1+x \right ) y^{\prime }-35 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.415

7340

\[ {}16 \left (x +1\right )^{2} y^{\prime \prime }+3 y = 0 \]

[[_Emden, _Fowler]]

0.389

7341

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y = 0 \]

[_Bessel]

0.682

7342

\[ {}x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.690

7343

\[ {}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0 \]

[_Laguerre]

0.646

7344

\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \]

[[_Emden, _Fowler]]

0.491

7345

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

[[_Emden, _Fowler]]

1.048

7346

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

[[_2nd_order, _with_linear_symmetries]]

0.404

7347

\[ {}y^{\prime }+\frac {26 y}{5} = \frac {97 \sin \left (2 t \right )}{5} \]
i.c.

[[_linear, ‘class A‘]]

0.535

7348

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

[_quadrature]

0.333

7349

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.293

7350

\[ {}y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.312

7351

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

[[_2nd_order, _missing_x]]

0.251

7352

\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.394

7353

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.339

7354

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

[[_2nd_order, _missing_x]]

0.294

7355

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.322

7356

\[ {}y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.189

7357

\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64 \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.339

7358

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.453

7359

\[ {}y^{\prime }-6 y = 0 \]
i.c.

[_quadrature]

0.429

7360

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.492

7361

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.401

7362

\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.196

7363

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.335

7364

\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.196

7365

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.960

7366

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

12.877

7367

\[ {}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.559

7368

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.072

7369

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.966

7370

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4.152

7371

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.901

7372

\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.739

7373

\[ {}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.780

7374

\[ {}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.743

7375

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.203

7376

\[ {}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.408

7377

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.963

7378

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.947

7379

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.555

7380

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.240

7381

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.928

7382

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

[_separable]

2.125

7383

\[ {}y^{\prime } = \frac {x^{2}}{y \left (x^{3}+1\right )} \]

[_separable]

1.873

7384

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

[_separable]

1.938

7385

\[ {}x y^{\prime } = \sqrt {1-y^{2}} \]

[_separable]

6.479

7386

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

[_separable]

1.295

7387

\[ {}x y y^{\prime } = \sqrt {1+y^{2}} \]

[_separable]

6.459

7388

\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y^{2} = 0 \]
i.c.

[_separable]

2.224

7389

\[ {}y^{\prime } = 3 y^{{2}/{3}} \]
i.c.

[_quadrature]

2.096

7390

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

[_separable]

2.645

7391

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

[_separable]

2.715

7392

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

[_separable]

2.451

7393

\[ {}\left (1+z^{\prime }\right ) {\mathrm e}^{-z} = 1 \]

[_quadrature]

1.851

7394

\[ {}y^{\prime } = \frac {3 x^{2}+4 x +2}{2 y-2} \]
i.c.

[_separable]

2.398

7395

\[ {}{\mathrm e}^{x}-\left ({\mathrm e}^{x}+1\right ) y y^{\prime } = 0 \]
i.c.

[_separable]

3.591

7396

\[ {}\frac {y}{-1+x}+\frac {x y^{\prime }}{y+1} = 0 \]

[_separable]

2.862

7397

\[ {}x +2 x^{3}+\left (y+2 y^{3}\right ) y^{\prime } = 0 \]

[_separable]

2.790

7398

\[ {}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0 \]

[_separable]

12.070

7399

\[ {}\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0 \]

[_separable]

41.108

7400

\[ {}2 x \sqrt {1-y^{2}}+y y^{\prime } = 0 \]

[_separable]

2.153