2.2.163 Problems 16201 to 16300

Table 2.327: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

16201

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.687

16202

\[ {}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.814

16203

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.616

16204

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.162

16205

\[ {}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

0.455

16206

\[ {}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.635

16207

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.553

16208

\[ {}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \]

[[_2nd_order, _missing_y]]

1.344

16209

\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \]

[[_2nd_order, _missing_y]]

1.294

16210

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]

[[_2nd_order, _missing_y]]

1.320

16211

\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \]

[[_2nd_order, _missing_y]]

1.283

16212

\[ {}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \]

[[_2nd_order, _quadrature]]

1.185

16213

\[ {}y^{\prime \prime }+3 y^{\prime } = 18 \]
i.c.

[[_2nd_order, _missing_x]]

1.549

16214

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

[[_2nd_order, _missing_x]]

1.339

16215

\[ {}y^{\prime \prime }-4 y = 32 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.672

16216

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

[[_2nd_order, _missing_x]]

0.633

16217

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

[[_2nd_order, _with_linear_symmetries]]

0.671

16218

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 4 \]
i.c.

[[_2nd_order, _missing_x]]

0.797

16219

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.699

16220

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = -1 \]
i.c.

[[_2nd_order, _missing_x]]

0.859

16221

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

[[_2nd_order, _missing_y]]

1.644

16222

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

[[_2nd_order, _missing_y]]

1.555

16223

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

[[_2nd_order, _missing_y]]

1.403

16224

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _missing_y]]

1.690

16225

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

[[_2nd_order, _missing_y]]

2.022

16226

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.080

16227

\[ {}y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

8.693

16228

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.590

16229

\[ {}y^{\prime }-4 y = t^{2} \]

[[_linear, ‘class A‘]]

1.000

16230

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

[[_linear, ‘class A‘]]

1.521

16231

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

[[_linear, ‘class A‘]]

1.298

16232

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

[[_linear, ‘class A‘]]

1.258

16233

\[ {}y^{\prime }+4 y = t \,{\mathrm e}^{-4 t} \]

[[_linear, ‘class A‘]]

1.563

16234

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.664

16235

\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.953

16236

\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.873

16237

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

[[_2nd_order, _missing_x]]

1.651

16238

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

[[_2nd_order, _missing_y]]

1.109

16239

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t} \]

[[_2nd_order, _with_linear_symmetries]]

0.501

16240

\[ {}y^{\prime \prime }+16 y = 2 \cos \left (4 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.736

16241

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.662

16242

\[ {}y^{\prime \prime }+\frac {y}{4} = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.195

16243

\[ {}y^{\prime \prime }+16 y = \csc \left (4 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.378

16244

\[ {}y^{\prime \prime }+16 y = \cot \left (4 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.696

16245

\[ {}y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.854

16246

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.028

16247

\[ {}y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.936

16248

\[ {}y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.739

16249

\[ {}y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.901

16250

\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.891

16251

\[ {}y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.724

16252

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.749

16253

\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.632

16254

\[ {}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.811

16255

\[ {}y^{\prime \prime }-y = 2 \sinh \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.752

16256

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.579

16257

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.697

16258

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.622

16259

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.673

16260

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.655

16261

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{t}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.711

16262

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.748

16263

\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \sqrt {-t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.706

16264

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.766

16265

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t} \arctan \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.759

16266

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1} \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.657

16267

\[ {}y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.264

16268

\[ {}y^{\prime \prime }+9 y = \tan \left (3 t \right )^{2} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.335

16269

\[ {}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.064

16270

\[ {}y^{\prime \prime }+9 y = \tan \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.152

16271

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.071

16272

\[ {}y^{\prime \prime }+16 y = \tan \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.965

16273

\[ {}y^{\prime \prime }+4 y = \tan \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.891

16274

\[ {}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \tan \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.450

16275

\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right ) \tan \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.443

16276

\[ {}y^{\prime \prime }+9 y = \frac {\csc \left (3 t \right )}{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.109

16277

\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )^{2} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.890

16278

\[ {}y^{\prime \prime }-16 y = 16 t \,{\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.738

16279

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.382

16280

\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )+\tan \left (2 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.629

16281

\[ {}y^{\prime \prime }+9 y = \csc \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

2.097

16282

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 65 \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

0.611

16283

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.633

16284

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

[[_2nd_order, _with_linear_symmetries]]

1.585

16285

\[ {}t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y = 2 \ln \left (t \right ) \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.364

16286

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

[[_2nd_order, _with_linear_symmetries]]

0.678

16287

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.845

16288

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

[[_2nd_order, _with_linear_symmetries]]

0.127

16289

\[ {}t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y = t^{3}+2 t \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.094

16290

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

[_Lienard]

0.138

16291

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

[[_2nd_order, _with_linear_symmetries]]

1.069

16292

\[ {}4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (16 t^{2}-1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.124

16293

\[ {}4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.277

16294

\[ {}t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-y^{\prime } t +y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

1.433

16295

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

[[_2nd_order, _with_linear_symmetries]]

2.404

16296

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

[[_3rd_order, _quadrature]]

0.075

16297

\[ {}y^{\prime \prime \prime }-10 y^{\prime \prime }+25 y^{\prime } = 0 \]

[[_3rd_order, _missing_x]]

0.083

16298

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

[[_3rd_order, _missing_x]]

0.081

16299

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

[[_high_order, _missing_x]]

0.083

16300

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

[[_3rd_order, _missing_x]]

0.079