2.3.254 Problems 25301 to 25400

Table 2.1039: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25301

11644

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

64.763

25302

13594

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

64.847

25303

6836

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

64.977

25304

6261

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

65.009

25305

13600

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

65.237

25306

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*}

65.270

25307

11770

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

65.312

25308

4346

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

65.411

25309

12094

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

65.412

25310

6105

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

65.460

25311

9781

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

65.632

25312

11771

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

65.664

25313

4744

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

65.720

25314

7547

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

65.737

25315

11548

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

66.010

25316

6196

\begin{align*} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

66.060

25317

19333

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

66.096

25318

24162

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

66.120

25319

12090

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

66.151

25320

22559

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

66.686

25321

7422

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

66.697

25322

2890

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

66.776

25323

13619

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

66.837

25324

12262

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

66.949

25325

13040

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

67.201

25326

13581

\begin{align*} y^{\prime } y+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}} \\ \end{align*}

67.211

25327

21433

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

67.268

25328

13478

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

67.315

25329

19922

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

67.564

25330

6090

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

67.635

25331

12634

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

67.661

25332

21833

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

67.674

25333

13341

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

67.758

25334

20443

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

67.817

25335

13405

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

67.869

25336

6446

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

67.993

25337

2909

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

68.079

25338

13580

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

68.094

25339

13484

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

68.117

25340

13426

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

68.152

25341

13614

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

68.372

25342

12503

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

68.530

25343

21817

\begin{align*} 4 x -2 y+3+\left (5 y-2 x +7\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

68.536

25344

24064

\begin{align*} y^{\left (10\right )}+y&=x^{10} \\ \end{align*}

68.570

25345

6197

\begin{align*} \operatorname {a2} y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

68.713

25346

14897

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

68.906

25347

12549

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

69.241

25348

22466

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

69.257

25349

21361

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

69.263

25350

21836

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

69.504

25351

6132

\begin{align*} 6 y-4 \left (x +a \right ) y^{\prime }+\left (\operatorname {a0} +x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

69.626

25352

20733

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

69.634

25353

7966

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

69.691

25354

12027

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

69.697

25355

13622

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

69.732

25356

12520

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

69.780

25357

13448

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

70.153

25358

12533

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

70.156

25359

6198

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

70.237

25360

13579

\begin{align*} y^{\prime } y+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}} \\ \end{align*}

70.296

25361

14267

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

70.299

25362

12047

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

70.527

25363

5005

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

70.642

25364

12278

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

70.760

25365

18342

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

70.891

25366

13506

\begin{align*} y^{\prime } y-y&=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \\ \end{align*}

70.907

25367

21827

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

70.973

25368

2912

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

71.117

25369

13536

\begin{align*} y^{\prime } y-y&=\frac {63 x}{4}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}

71.146

25370

13382

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

71.203

25371

12532

\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*}

71.237

25372

13595

\begin{align*} y^{\prime } y-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -13\right )}{26 x^{4}} \\ \end{align*}

71.263

25373

21838

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

71.394

25374

14541

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

71.405

25375

15976

\begin{align*} p^{\prime }&=3 p-2 q-7 r \\ q^{\prime }&=-2 p+6 r \\ r^{\prime }&=\frac {73 q}{100}+2 r \\ \end{align*}

71.455

25376

21756

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

71.490

25377

13437

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

71.620

25378

11792

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

71.691

25379

19114

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

71.784

25380

20468

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

71.869

25381

13421

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

72.003

25382

12597

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

72.224

25383

16210

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

72.385

25384

12631

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

72.447

25385

6172

\begin{align*} \left (c \,x^{2}+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*}

72.539

25386

12017

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

72.546

25387

6258

\begin{align*} -\left (k^{2}-p \left (1+p \right ) \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*}

72.848

25388

22770

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

72.934

25389

11549

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

73.111

25390

21453

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

73.200

25391

13582

\begin{align*} y^{\prime } y+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\ \end{align*}

73.239

25392

13596

\begin{align*} y^{\prime } y-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{{11}/{5}}} \\ \end{align*}

73.265

25393

21384

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

73.323

25394

17919

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

73.326

25395

13263

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

73.343

25396

13922

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

73.459

25397

13593

\begin{align*} y^{\prime } y+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \\ \end{align*}

73.490

25398

19658

\begin{align*} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5}&=0 \\ \end{align*}

73.641

25399

10195

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

73.871

25400

13275

\begin{align*} x \left (a \,x^{k}+b \right ) y^{\prime }&=\alpha \,x^{n} y^{2}+\left (\beta -a n \,x^{k}\right ) y+\gamma \,x^{-n} \\ \end{align*}

74.086