2.2.243 Problems 24201 to 24300

Table 2.503: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

24201

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

[_linear]

3.864

24202

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

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

23.599

24203

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

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

11.218

24204

\begin{align*} 3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

6.798

24205

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

[_exact]

6.289

24206

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

[_exact]

4.769

24207

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

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

9.253

24208

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

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

11.261

24209

\begin{align*} x^{3} y^{3}+1+x^{4} y^{2} y^{\prime }&=0 \\ \end{align*}

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

4.322

24210

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

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

12.249

24211

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

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

7.610

24212

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

[_separable]

12.860

24213

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

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

10.044

24214

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

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

5.805

24215

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

[_exact, _rational]

3.212

24216

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

[_rational]

3.067

24217

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

[[_1st_order, _with_linear_symmetries], _rational]

4.259

24218

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

[NONE]

3.843

24219

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

3.487

24220

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

[_rational]

19.808

24221

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

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

109.472

24222

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

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

4.692

24223

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

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

4.625

24224

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

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

8.223

24225

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

[_exact, _rational]

3.750

24226

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

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

17.737

24227

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

[_rational]

6.442

24228

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

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

11.868

24229

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

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

12.813

24230

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

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

6.603

24231

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

[_rational, _Bernoulli]

2.935

24232

\begin{align*} 2 x^{5} y^{\prime }&=y \left (3 x^{4}+y^{2}\right ) \\ \end{align*}

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

25.582

24233

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

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

24.211

24234

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

[_rational]

28.105

24235

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

[_linear]

4.891

24236

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

[_linear]

3.735

24237

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

[_linear]

2.470

24238

\begin{align*} x^{\prime } t&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \\ \end{align*}

[_linear]

4.068

24239

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

[[_linear, ‘class A‘]]

1.777

24240

\begin{align*} \left (3 x -1\right ) y^{\prime }&=6 y-10 \left (3 x -1\right )^{{1}/{3}} \\ \end{align*}

[_linear]

4.786

24241

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

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

133.786

24242

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

[_linear]

3.237

24243

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

[_separable]

3.394

24244

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

[_linear]

3.688

24245

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

[_linear]

5.018

24246

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

[_linear]

3.292

24247

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

[[_linear, ‘class A‘]]

1.708

24248

\begin{align*} y^{\prime }-m_{2} y&=c \,{\mathrm e}^{m_{1} x} \\ \end{align*}

[[_linear, ‘class A‘]]

2.980

24249

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

11.454

24250

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

[_linear]

2.533

24251

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

[_linear]

3.451

24252

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

[_linear]

6.717

24253

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

[_linear]

2.292

24254

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

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

2.716

24255

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

[_linear]

5.165

24256

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

[_linear]

2.358

24257

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

[_linear]

6.108

24258

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

[_linear]

5.126

24259

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

[_quadrature]

0.475

24260

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

[_linear]

2.987

24261

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

[_linear]

3.932

24262

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

[_linear]

3.509

24263

\begin{align*} L i^{\prime }+R i&=e \\ i \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

2.173

24264

\begin{align*} L i^{\prime }+R i&=e \sin \left (w t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}

[[_linear, ‘class A‘]]

2.806

24265

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

[[_linear, ‘class A‘]]

5.171

24266

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

[[_linear, ‘class A‘]]

2.023

24267

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

[_linear]

4.599

24268

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

[_separable]

3.276

24269

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

[_linear]

6.018

24270

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

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

59.910

24271

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

[_separable]

2.989

24272

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

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

55.164

24273

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

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

11.404

24274

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

[_separable]

3.052

24275

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

[_linear]

3.493

24276

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

[_linear]

3.265

24277

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

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

15.683

24278

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

[_separable]

3.207

24279

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

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

405.438

24280

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

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

9.700

24281

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

[_separable]

4.507

24282

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

[[_homogeneous, ‘class A‘]]

42.677

24283

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

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

44.437

24284

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

[_quadrature]

1.339

24285

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

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

25.851

24286

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

[_separable]

3.983

24287

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

[_exact]

28.444

24288

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

[_linear]

2.590

24289

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

[_exact, _rational]

3.537

24290

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

[_linear]

2.640

24291

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

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

19.693

24292

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

[_separable]

5.727

24293

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

[_linear]

3.894

24294

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

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

15.902

24295

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

[_linear]

16.082

24296

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

[_separable]

17.394

24297

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

[_separable]

17.764

24298

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

[_separable]

15.612

24299

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

[_separable]

14.724

24300

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

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

3.198