2.2.53 Problems 5201 to 5300

Table 2.123: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

5201

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

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

243.663

5202

\begin{align*} 8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4}&=0 \\ \end{align*}

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

94.512

5203

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

[_separable]

22.490

5204

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

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

14.707

5205

\begin{align*} x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\ \end{align*}

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

49.641

5206

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

[_separable]

7.938

5207

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

[_separable]

15.631

5208

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

[_separable]

4.247

5209

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

[_separable]

4.056

5210

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

[_exact, _rational]

4.191

5211

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

[_exact, _rational]

3.665

5212

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

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

22.639

5213

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

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

20.928

5214

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

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

32.967

5215

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

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

4.480

5216

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

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

2.583

5217

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

[[_1st_order, _with_linear_symmetries], _rational]

4.915

5218

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

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

3.789

5219

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

[_exact, _rational]

4.343

5220

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

[_rational]

4.198

5221

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

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

25.152

5222

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

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

11.840

5223

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

[_separable]

4.334

5224

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

[_rational]

13.826

5225

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

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

4.357

5226

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

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

3.753

5227

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

[[_1st_order, _with_linear_symmetries], _rational]

7.032

5228

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

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

27.965

5229

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

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

12.620

5230

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

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

26.311

5231

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

[[_homogeneous, ‘class C‘], _rational]

9.748

5232

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

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

59.697

5233

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

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

28.484

5234

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

[[_homogeneous, ‘class C‘], _rational]

10.787

5235

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

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

3.973

5236

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

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

50.755

5237

\begin{align*} \left (1-3 x -y\right )^{2} y^{\prime }&=\left (-2 y+1\right ) \left (3-6 x -4 y\right ) \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational]

14.933

5238

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

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

46.066

5239

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

[_rational, _Bernoulli]

4.503

5240

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

[_exact, _rational]

4.046

5241

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

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

23.954

5242

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

[‘y=_G(x,y’)‘]

5.540

5243

\begin{align*} \left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\ \end{align*}

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

3.901

5244

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

[[_homogeneous, ‘class C‘], _rational]

16.602

5245

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

[_exact, _rational]

4.282

5246

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

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

4.177

5247

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

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

22.651

5248

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

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

108.831

5249

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

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

89.385

5250

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

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

145.987

5251

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

[_separable]

8.415

5252

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

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

18.645

5253

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

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

5.562

5254

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

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

13.083

5255

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

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

21.872

5256

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

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

28.632

5257

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

[[_1st_order, _with_linear_symmetries], _rational]

12.956

5258

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

[_separable]

9.602

5259

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

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

67.832

5260

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

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

33.581

5261

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

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

21.852

5262

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

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

36.772

5263

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

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

37.041

5264

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

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

34.059

5265

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

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

25.797

5266

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

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

9.994

5267

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

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

5.044

5268

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

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

11.555

5269

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

[_rational]

4.642

5270

\begin{align*} x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime }&=6 y^{3} \\ \end{align*}

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

5.813

5271

\begin{align*} 6 x y^{2} y^{\prime }+x +2 y^{3}&=0 \\ \end{align*}

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

8.723

5272

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

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

14.771

5273

\begin{align*} x \left (x^{2}-6 y^{2}\right ) y^{\prime }&=4 \left (x^{2}+3 y^{2}\right ) y \\ \end{align*}

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

42.397

5274

\begin{align*} x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y&=0 \\ \end{align*}

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

15.355

5275

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

[_separable]

5.012

5276

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

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

13.039

5277

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

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

1.545

5278

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

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

8.285

5279

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

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

50.504

5280

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

[_separable]

5.252

5281

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

[_separable]

15.275

5282

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

[_separable]

6.086

5283

\begin{align*} \left (1-x^{3}+6 x^{2} y^{2}\right ) y^{\prime }&=\left (6+3 y x -4 y^{3}\right ) x \\ \end{align*}

[_exact, _rational]

4.954

5284

\begin{align*} x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y&=0 \\ \end{align*}

[_exact, _rational]

5.895

5285

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

[_separable]

12.274

5286

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

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

8.730

5287

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

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

15.575

5288

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

[_exact, _rational]

4.065

5289

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

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

4.977

5290

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

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

3.839

5291

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

[_exact, _rational]

4.795

5292

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

[_rational]

5.805

5293

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

[_exact, _rational]

4.573

5294

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

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

49.789

5295

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

[_rational]

96.299

5296

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

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

3.888

5297

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

[_separable]

5.084

5298

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

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

47.866

5299

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

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

4.105

5300

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

[_rational]

9.586