2.2.193 Problems 19201 to 19300

Table 2.403: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

19201

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

[[_3rd_order, _with_linear_symmetries]]

0.381

19202

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

[[_2nd_order, _linear, _nonhomogeneous]]

8.155

19203

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

[[_2nd_order, _with_linear_symmetries]]

0.950

19204

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

[_Lienard]

0.554

19205

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

[_Lienard]

2.398

19206

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

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

1.672

19207

\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.040

19208

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.365

19209

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

system_of_ODEs

2.356

19210

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

system_of_ODEs

0.681

19211

\begin{align*} y^{\prime }&=\frac {y^{2}}{z} \\ z^{\prime }&=\frac {y}{2} \\ \end{align*}

system_of_ODEs

0.035

19212

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

system_of_ODEs

0.045

19213

\begin{align*} y^{\prime }&=-z \\ z^{\prime }&=y \\ \end{align*}
With initial conditions
\begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 0 \\ \end{align*}

system_of_ODEs

0.460

19214

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

[NONE]

0.642

19215

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

[[_2nd_order, _missing_x], [_Emden, _modified]]

79.006

19216

\begin{align*} y^{\prime }&=\frac {z^{2}}{y} \\ z^{\prime }&=\frac {y^{2}}{z} \\ \end{align*}

system_of_ODEs

0.038

19217

\begin{align*} y^{\prime }&=\frac {y^{2}}{z} \\ z^{\prime }&=\frac {z^{2}}{y} \\ \end{align*}

system_of_ODEs

0.040

19218

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

system_of_ODEs

0.631

19219

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

system_of_ODEs

0.860

19220

\begin{align*} x^{\prime }+5 x+y&=7 \,{\mathrm e}^{t}-27 \\ -2 x+y^{\prime }+3 y&=-3 \,{\mathrm e}^{t}+12 \\ \end{align*}

system_of_ODEs

1.303

19221

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

system_of_ODEs

0.048

19222

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

system_of_ODEs

0.836

19223

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

system_of_ODEs

0.038

19224

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

system_of_ODEs

0.040

19225

\begin{align*} t x^{\prime }+6 x-y-3 z&=0 \\ y^{\prime } t +23 x-6 y-9 z&=0 \\ t z^{\prime }+x+y-2 z&=0 \\ \end{align*}

system_of_ODEs

0.052

19226

\begin{align*} x^{\prime }+5 x+y&={\mathrm e}^{t} \\ y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\ \end{align*}

system_of_ODEs

0.720

19227

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

[_quadrature]

0.986

19228

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

[_separable]

4.720

19229

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

[_separable]

3.589

19230

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

[_quadrature]

1.546

19231

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

[[_2nd_order, _missing_x]]

1.625

19232

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

[[_2nd_order, _missing_x]]

1.773

19233

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

26.466

19234

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

[[_homogeneous, ‘class D‘], _rational, _Riccati]

2.537

19235

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

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

8.848

19236

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

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

12.470

19237

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

[[_homogeneous, ‘class G‘], _rational]

1.964

19238

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

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

65.835

19239

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

[[_1st_order, _with_linear_symmetries]]

3.802

19240

\begin{align*} 1+y^{2}+y^{2} y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.536

19241

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

[_quadrature]

0.380

19242

\begin{align*} y^{\prime } x&=1 \\ \end{align*}

[_quadrature]

0.581

19243

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

[_quadrature]

0.363

19244

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

[_quadrature]

0.329

19245

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

[_quadrature]

0.491

19246

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

[_quadrature]

0.452

19247

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

[_quadrature]

0.622

19248

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

[_quadrature]

0.401

19249

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

[_separable]

6.437

19250

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

[_separable]

9.604

19251

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

[_separable]

3.228

19252

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

[_separable]

3.540

19253

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

[_separable]

2.674

19254

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

[_quadrature]

0.724

19255

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

[_separable]

3.454

19256

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

[_separable]

3.690

19257

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

[_separable]

4.347

19258

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

[_separable]

5.597

19259

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_quadrature]

0.506

19260

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

[_quadrature]

1.566

19261

\begin{align*} y^{\prime }&=\ln \left (x \right ) \\ y \left ({\mathrm e}\right ) &= 0 \\ \end{align*}

[_quadrature]

0.615

19262

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

[_quadrature]

0.692

19263

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

[_quadrature]

0.809

19264

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

[_quadrature]

0.769

19265

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

4.096

19266

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

[_quadrature]

0.614

19267

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

[_separable]

3.394

19268

\begin{align*} 3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\ \end{align*}

[_separable]

6.000

19269

\begin{align*} y^{\prime }&={\mathrm e}^{x} \cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.669

19270

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

[_separable]

4.555

19271

\begin{align*} y^{\prime }&=2 y x +1 \\ \end{align*}

[_linear]

1.912

19272

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.208

19273

\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.078

19274

\begin{align*} v^{\prime }&=g -\frac {k v^{2}}{m} \\ \end{align*}

[_quadrature]

5.256

19275

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

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

51.957

19276

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

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

10.951

19277

\begin{align*} x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\ \end{align*}

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

11.264

19278

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

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

20.945

19279

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

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

9.000

19280

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

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

18.922

19281

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

[_linear]

6.122

19282

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

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

20.612

19283

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

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

6.938

19284

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

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

10.760

19285

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

[[_homogeneous, ‘class C‘], _Riccati]

2.224

19286

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

[[_homogeneous, ‘class C‘], _dAlembert]

5.504

19287

\begin{align*} y^{\prime }&=\frac {x +y+4}{x -y-6} \\ \end{align*}

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

19.774

19288

\begin{align*} y^{\prime }&=\frac {x +y+4}{x +y-6} \\ \end{align*}

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

9.664

19289

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

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

12.484

19290

\begin{align*} y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\ \end{align*}

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

238.646

19291

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

[_linear]

4.431

19292

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

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

5.757

19293

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

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

7.553

19294

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

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

45.257

19295

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

[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

45.270

19296

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

[‘y=_G(x,y’)‘]

27.674

19297

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

[_exact, _rational]

2.724

19298

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

[_separable]

0.185

19299

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

[_separable]

0.635

19300

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

[_exact]

29.821