2.3.253 Problems 25201 to 25300

Table 2.1037: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25201

7533

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

57.881

25202

13331

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

57.902

25203

3231

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

57.925

25204

192

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

58.067

25205

2881

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

58.076

25206

22341

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

58.167

25207

25653

\begin{align*} R^{\prime \prime }&=-\frac {k}{R^{2}} \\ \end{align*}

58.187

25208

2330

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

58.309

25209

13378

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

58.337

25210

10406

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

58.353

25211

12130

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

58.482

25212

788

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

58.489

25213

17995

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

58.571

25214

5568

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

58.631

25215

13425

\begin{align*} y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\ \end{align*}

58.656

25216

20128

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

58.864

25217

15555

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

58.968

25218

3247

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

59.023

25219

13471

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

59.145

25220

11924

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

59.308

25221

11790

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

59.384

25222

12034

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

59.385

25223

19074

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

59.456

25224

10375

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

59.479

25225

13845

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

59.504

25226

23888

\begin{align*} \frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\ \end{align*}

59.580

25227

13211

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

59.898

25228

4708

\begin{align*} y^{\prime }&=a +b y-\sqrt {A +B y} \\ \end{align*}

59.905

25229

47

\begin{align*} y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \\ \end{align*}

59.928

25230

607

\begin{align*} x^{\prime }&=3 x-4 y+z+t \\ y^{\prime }&=x-3 z+t^{2} \\ z^{\prime }&=6 y-7 z+t^{3} \\ \end{align*}

60.062

25231

25007

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

60.106

25232

9686

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\ x_{2}^{\prime }&=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\ x_{3}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\ x_{4}^{\prime }&=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\ x_{5}^{\prime }&=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \\ \end{align*}

60.178

25233

6259

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

60.315

25234

5112

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

60.319

25235

12993

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

60.328

25236

10376

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

60.365

25237

6369

\begin{align*} 2 y^{\prime \prime }&=1+12 y^{2} \\ \end{align*}

60.472

25238

12095

\begin{align*} y^{\prime }&=\frac {\left (-\sqrt {a}\, x^{3}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2} \\ \end{align*}

60.584

25239

13031

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

60.650

25240

4922

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

60.670

25241

10408

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

60.881

25242

1165

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

60.890

25243

24169

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

60.931

25244

11917

\begin{align*} y^{\prime }&=\frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\ \end{align*}

60.937

25245

12097

\begin{align*} y^{\prime }&=\frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \\ \end{align*}

61.002

25246

11992

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

61.076

25247

11810

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

61.135

25248

5514

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

61.306

25249

12050

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

61.467

25250

6532

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

61.667

25251

10023

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

61.681

25252

12107

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

61.725

25253

4113

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

61.748

25254

12557

\begin{align*} 144 x \left (x -1\right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y&=0 \\ \end{align*}

61.770

25255

2502

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

61.787

25256

12555

\begin{align*} 48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y&=0 \\ \end{align*}

61.806

25257

6266

\begin{align*} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} \left (b^{2}+x^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}

61.904

25258

6447

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

61.925

25259

13327

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

62.033

25260

13844

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

62.044

25261

21042

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

62.044

25262

13373

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

62.165

25263

13441

\begin{align*} y^{\prime } x&=\lambda \arctan \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arctan \left (x \right )^{n} \\ \end{align*}

62.167

25264

4707

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

62.179

25265

4877

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

62.256

25266

13834

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

62.309

25267

6171

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

62.431

25268

13374

\begin{align*} y^{\prime }&=a \sin \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\ \end{align*}

62.431

25269

1681

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

62.523

25270

5513

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

62.530

25271

21852

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

62.657

25272

196

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

62.662

25273

6167

\begin{align*} -\left (4 p^{2}+1\right ) y-8 y^{\prime } x +4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

62.736

25274

13412

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

62.855

25275

15630

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

62.865

25276

13862

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

62.914

25277

6279

\begin{align*} -\left (4 k^{2}+\left (-4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

62.954

25278

13505

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

63.031

25279

5515

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

63.120

25280

13528

\begin{align*} y^{\prime } y-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

63.123

25281

11776

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

63.178

25282

20457

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\ \end{align*}

63.197

25283

20744

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

63.257

25284

13598

\begin{align*} y^{\prime } y-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{3}/{5}}} \\ \end{align*}

63.414

25285

13601

\begin{align*} y^{\prime } y+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}} \\ \end{align*}

63.458

25286

11912

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

63.523

25287

6278

\begin{align*} -\left (4 k^{2}+\left (4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

63.582

25288

13433

\begin{align*} y^{\prime }&=\lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\ \end{align*}

63.766

25289

6146

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

63.827

25290

19720

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

63.859

25291

19275

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

63.872

25292

20742

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

64.002

25293

20683

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

64.064

25294

13549

\begin{align*} y^{\prime } y-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \\ \end{align*}

64.101

25295

13592

\begin{align*} y^{\prime } y-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (2+x \right )}{4 x^{4}} \\ \end{align*}

64.178

25296

11450

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

64.235

25297

7542

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

64.297

25298

13477

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

64.319

25299

19048

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+1 \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

64.401

25300

13215

\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m} \\ \end{align*}

64.591