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]

2.137

9202

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

[_separable]

5.671

9203

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

[_separable]

3.154

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‘]]

20.934

9205

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

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

13.405

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]

17.444

9207

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

[_separable]

3.702

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]]

4.444

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]]

12.261

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]]

1.481

9211

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

[[_2nd_order, _missing_y]]

3.185

9212

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

[[_2nd_order, _missing_x]]

4.901

9213

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

[[_2nd_order, _missing_x]]

7.033

9214

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

[[_2nd_order, _missing_x]]

4.882

9215

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

[[_2nd_order, _missing_x]]

5.231

9216

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

[[_2nd_order, _missing_x]]

5.517

9217

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

[[_2nd_order, _missing_x]]

5.491

9218

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

[[_2nd_order, _missing_x]]

18.295

9219

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

[[_2nd_order, _missing_x]]

8.293

9220

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

[[_2nd_order, _missing_x]]

1.795

9221

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

[[_2nd_order, _missing_x]]

7.625

9222

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

[[_2nd_order, _missing_x]]

7.888

9223

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

[[_2nd_order, _missing_x]]

16.656

9224

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

[[_2nd_order, _missing_x]]

2.863

9225

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

[[_2nd_order, _missing_x]]

14.920

9226

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

[[_2nd_order, _missing_x]]

5.840

9227

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

[[_2nd_order, _missing_x]]

5.843

9228

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

[[_2nd_order, _missing_x]]

3.628

9229

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

[[_2nd_order, _missing_x]]

5.524

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]]

16.793

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]]

1.262

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]]

7.089

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]]

7.227

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]]

1.368

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]]

14.340

9236

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

[[_Emden, _Fowler]]

7.033

9237

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

[[_Emden, _Fowler]]

7.662

9238

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

[[_Emden, _Fowler]]

2.221

9239

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

[[_Emden, _Fowler]]

1.772

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)]‘]]

2.944

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)]‘]]

1.762

9242

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

[[_Emden, _Fowler]]

4.310

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)]‘]]

5.816

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)]‘]]

2.688

9245

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

[[_2nd_order, _with_linear_symmetries]]

31.565

9246

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

[[_2nd_order, _linear, _nonhomogeneous]]

28.118

9247

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

[[_2nd_order, _with_linear_symmetries]]

25.770

9248

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

[[_2nd_order, _with_linear_symmetries]]

31.699

9249

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

[[_2nd_order, _with_linear_symmetries]]

32.257

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]]

34.938

9251

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.800

9252

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

[[_2nd_order, _missing_y]]

4.022

9253

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

[[_2nd_order, _with_linear_symmetries]]

21.295

9254

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

[[_2nd_order, _linear, _nonhomogeneous]]

31.340

9255

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

[[_2nd_order, _missing_y]]

5.724

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]]

29.503

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]]

32.191

9258

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

[[_2nd_order, _with_linear_symmetries]]

25.966

9259

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

[[_3rd_order, _missing_y]]

0.335

9260

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

[[_2nd_order, _linear, _nonhomogeneous]]

29.619

9261

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

[[_2nd_order, _linear, _nonhomogeneous]]

32.833

9262

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

[[_2nd_order, _linear, _nonhomogeneous]]

36.251

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]]

29.323

9264

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

[[_2nd_order, _with_linear_symmetries]]

33.497

9265

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

[[_2nd_order, _linear, _nonhomogeneous]]

33.344

9266

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.860

9267

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.958

9268

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.309

9269

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

[[_2nd_order, _linear, _nonhomogeneous]]

27.662

9270

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.572

9271

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

[[_2nd_order, _linear, _nonhomogeneous]]

9.218

9272

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.248

9273

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

[[_2nd_order, _with_linear_symmetries]]

19.855

9274

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

[[_2nd_order, _with_linear_symmetries]]

30.062

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]]

69.148

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]]

67.730

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]]

19.713

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]]

5.634

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]]

8.434

9280

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

[[_2nd_order, _missing_x]]

0.174

9281

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

[[_2nd_order, _missing_x]]

0.188

9282

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

[[_2nd_order, _missing_y]]

0.129

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)]‘]]

0.135

9284

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

[_Gegenbauer]

0.161

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]]

0.159

9286

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

[[_2nd_order, _with_linear_symmetries]]

0.140

9287

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

[[_Emden, _Fowler]]

0.134

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]]

0.152

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]]

6.589

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]]

0.150

9291

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

[[_3rd_order, _missing_x]]

0.069

9292

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

[[_3rd_order, _missing_x]]

0.099

9293

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

[[_3rd_order, _missing_x]]

0.059

9294

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

[[_3rd_order, _missing_x]]

0.052

9295

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

[[_3rd_order, _missing_x]]

0.076

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]]

0.083

9297

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

[[_high_order, _missing_x]]

0.056

9298

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

[[_high_order, _missing_x]]

0.084

9299

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

[[_high_order, _missing_x]]

0.086

9300

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

[[_high_order, _missing_x]]

0.093