2.2.243 Problems 24201 to 24300

Table 2.499: 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]

2.897

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‘]]

7.124

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‘]]

5.505

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‘]]

1.856

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]

6.041

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]

3.105

24207

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

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

5.251

24208

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

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

5.949

24209

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

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

2.439

24210

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

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

6.274

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]

5.694

24212

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

[_separable]

6.738

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]

5.931

24214

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

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

5.972

24215

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

[_exact, _rational]

2.364

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]

2.100

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]

2.648

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]

2.956

24219

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

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

2.379

24220

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

[_rational]

3.356

24221

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

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

54.400

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)]‘]]

5.872

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)]‘]]

1.867

24224

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

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

7.139

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]

2.827

24226

\begin{align*} y \left (y+x^{2}\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‘]]

6.337

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]

4.269

24228

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

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

7.410

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]

6.993

24230

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

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

6.191

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]

2.113

24232

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

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

14.217

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]

15.375

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]

34.420

24235

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

[_linear]

2.682

24236

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

[_linear]

2.447

24237

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

[_linear]

1.708

24238

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

[_linear]

2.836

24239

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

[[_linear, ‘class A‘]]

1.008

24240

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

[_linear]

3.450

24241

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

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

30.679

24242

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

[_linear]

2.383

24243

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

[_separable]

2.058

24244

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

[_linear]

2.830

24245

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

[_linear]

2.949

24246

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

[_linear]

1.946

24247

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

[[_linear, ‘class A‘]]

1.306

24248

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

[[_linear, ‘class A‘]]

2.058

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‘]]

1.618

24250

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

[_linear]

1.733

24251

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

[_linear]

1.993

24252

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

[_linear]

3.852

24253

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

[_linear]

1.608

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]‘]]

1.876

24255

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

[_linear]

6.760

24256

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

[_linear]

1.689

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]

6.445

24258

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

[_linear]

3.067

24259

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

[_quadrature]

0.355

24260

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

[_linear]

2.180

24261

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

[_linear]

2.949

24262

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

[_linear]

2.271

24263

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

[_quadrature]

1.244

24264

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

[[_linear, ‘class A‘]]

2.157

24265

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

[[_linear, ‘class A‘]]

2.695

24266

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

[[_linear, ‘class A‘]]

1.049

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]

3.173

24268

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

[_separable]

1.829

24269

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

[_linear]

2.925

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‘]]

43.328

24271

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

[_separable]

2.569

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]

49.009

24273

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

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

6.928

24274

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

[_separable]

2.215

24275

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

[_linear]

2.632

24276

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

[_linear]

2.172

24277

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

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

8.354

24278

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

[_separable]

2.409

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]

11.558

24280

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

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

6.119

24281

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

[_separable]

2.896

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‘]]

13.110

24283

\begin{align*} y \left (y^{2}+x^{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]

16.891

24284

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

[_quadrature]

0.678

24285

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

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

7.528

24286

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

[_separable]

2.729

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]

32.605

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]

1.804

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]

2.306

24290

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

[_linear]

1.505

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‘]]

11.513

24292

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

[_separable]

4.073

24293

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

[_linear]

2.869

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‘]]

11.215

24295

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

[_linear]

5.430

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]

17.085

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]

15.712

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]

8.968

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]

8.558

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]‘]]

2.121