2.2.93 Problems 9201 to 9300

Table 2.199: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

9201

\begin{align*} x^{2} y^{\prime }-2 y&=3 x^{2} \\ y \left (1\right ) &= 2 \\ \end{align*}

[_linear]

1.696

9202

\begin{align*} y^{2} y^{\prime }&=x \\ y \left (-1\right ) &= 3 \\ \end{align*}

[_separable]

4.175

9203

\begin{align*} \csc \left (x \right ) y^{\prime }&=\csc \left (y\right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

[_separable]

2.417

9204

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ y \left (1\right ) &= 1 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12.103

9205

\begin{align*} y^{\prime }&=\frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

6.052

9206

\begin{align*} 2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

8.351

9207

\begin{align*} \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}&=0 \\ \end{align*}

[_separable]

1.899

9208

\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.470

9209

\begin{align*} y^{\prime \prime } x&=y^{\prime }-2 {y^{\prime }}^{3} \\ \end{align*}

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

1.397

9210

\begin{align*} y y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}

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

0.528

9211

\begin{align*} y^{\prime \prime } x -3 y^{\prime }&=5 x \\ \end{align*}

[[_2nd_order, _missing_y]]

0.861

9212

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.176

9213

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.237

9214

\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.213

9215

\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.209

9216

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.243

9217

\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.186

9218

\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.314

9219

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.247

9220

\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.756

9221

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.258

9222

\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.254

9223

\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.296

9224

\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*}

[[_2nd_order, _missing_x]]

1.073

9225

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.299

9226

\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.181

9227

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.223

9228

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.198

9229

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.191

9230

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (1\right ) &= {\mathrm e}^{2} \\ y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\ \end{align*}

[[_2nd_order, _missing_x]]

0.328

9231

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.336

9232

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.388

9233

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.352

9234

\begin{align*} y^{\prime \prime }+4 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2+3 \sqrt {2} \\ \end{align*}

[[_2nd_order, _missing_x]]

0.402

9235

\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.341

9236

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

1.113

9237

\begin{align*} 2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.812

9238

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.577

9239

\begin{align*} 4 x^{2} y^{\prime \prime }-3 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.204

9240

\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.774

9241

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\ \end{align*}

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.568

9242

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

1.104

9243

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.916

9244

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\ \end{align*}

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.822

9245

\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.325

9246

\begin{align*} 4 y+y^{\prime \prime }&=3 \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.392

9247

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=14 \,{\mathrm e}^{-5 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.415

9248

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.385

9249

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.339

9250

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.374

9251

\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.374

9252

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\ \end{align*}

[[_2nd_order, _missing_y]]

0.839

9253

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=6 \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.389

9254

\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.353

9255

\begin{align*} y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\ \end{align*}

[[_2nd_order, _missing_y]]

0.872

9256

\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.965

9257

\begin{align*} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

2.263

9258

\begin{align*} y^{\prime \prime }-3 y&={\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.339

9259

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.310

9260

\begin{align*} 4 y+y^{\prime \prime }&=\tan \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.592

9261

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \ln \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.497

9262

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.348

9263

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sec \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.547

9264

\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.300

9265

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.392

9266

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.362

9267

\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right )^{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.519

9268

\begin{align*} y^{\prime \prime }+y&=\cot \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.685

9269

\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) x \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.451

9270

\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.372

9271

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.476

9272

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.582

9273

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.350

9274

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.287

9275

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=\left (x^{2}-1\right )^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.871

9276

\begin{align*} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.786

9277

\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.021

9278

\begin{align*} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.700

9279

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

2.251

9280

\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.101

9281

\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.093

9282

\begin{align*} y^{\prime \prime } x +3 y^{\prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_y]]

0.095

9283

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.087

9284

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

[_Gegenbauer]

0.099

9285

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.105

9286

\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.100

9287

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.090

9288

\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.096

9289

\begin{align*} y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.321

9290

\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.094

9291

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.043

9292

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.056

9293

\begin{align*} y^{\prime \prime \prime }-y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.043

9294

\begin{align*} y^{\prime \prime \prime }+y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.046

9295

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.048

9296

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.058

9297

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.045

9298

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.059

9299

\begin{align*} y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.059

9300

\begin{align*} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.066