2.3.235 Problems 23401 to 23500

Table 2.1001: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23401

17893

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

10.022

23402

20978

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

10.027

23403

13556

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

10.029

23404

23133

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

10.030

23405

21436

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

10.046

23406

17881

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

10.059

23407

11566

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

10.063

23408

15174

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

10.063

23409

21069

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

10.066

23410

46

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

10.072

23411

5585

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

10.072

23412

12223

\begin{align*} y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 y^{2} x^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \\ \end{align*}

10.078

23413

5141

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

10.082

23414

13640

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

10.082

23415

20221

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

10.083

23416

12201

\begin{align*} y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\ \end{align*}

10.115

23417

17916

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

10.116

23418

13276

\begin{align*} x^{2} \left (a \,x^{n}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (p \,x^{n}+q \right ) x y+r \,x^{n}+s&=0 \\ \end{align*}

10.117

23419

11647

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

10.132

23420

12098

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

10.132

23421

5780

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

10.135

23422

19293

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

10.136

23423

7018

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

10.138

23424

21373

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

10.140

23425

13435

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

10.141

23426

11987

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

10.147

23427

11979

\begin{align*} y^{\prime }&=\frac {y \ln \left (x -1\right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (x -1\right ) x} \\ \end{align*}

10.148

23428

12269

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

10.156

23429

15639

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

10.156

23430

15880

\begin{align*} w^{\prime }&=3 w^{3}-12 w^{2} \\ \end{align*}

10.159

23431

7723

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

10.161

23432

6000

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

10.167

23433

13221

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

10.168

23434

19748

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

10.169

23435

15017

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

10.182

23436

24171

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

10.205

23437

4308

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

10.213

23438

5072

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

10.216

23439

20295

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

10.228

23440

19722

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

10.238

23441

18719

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

10.247

23442

15846

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

10.250

23443

5017

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

10.260

23444

12184

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

10.277

23445

21863

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

10.277

23446

25010

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

10.283

23447

21456

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

10.292

23448

7879

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

10.306

23449

13313

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

10.312

23450

21070

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

10.314

23451

19944

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

10.318

23452

12152

\begin{align*} y^{\prime }&=\frac {-30 x^{3} y+12 x^{6}+70 x^{{7}/{2}}-30 x^{3}-25 \sqrt {x}\, y+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\ \end{align*}

10.332

23453

25508

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

10.343

23454

17093

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

10.355

23455

19872

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

10.367

23456

23220

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

10.381

23457

6917

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

10.382

23458

13338

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

10.401

23459

8726

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

10.402

23460

20323

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

10.436

23461

12259

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

10.452

23462

12268

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

10.454

23463

13436

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

10.454

23464

24159

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

10.457

23465

11941

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

10.464

23466

2327

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

10.465

23467

24373

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

10.477

23468

12463

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

10.480

23469

11876

\begin{align*} y^{\prime }&=\frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}} \\ \end{align*}

10.490

23470

21065

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

10.493

23471

2911

\begin{align*} 2 x +y+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\ y \left (-\frac {1}{6}\right ) &= 0 \\ \end{align*}

10.509

23472

6335

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

10.513

23473

24353

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

10.514

23474

24164

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

10.522

23475

4948

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

10.528

23476

17309

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

10.529

23477

12194

\begin{align*} y^{\prime }&=\frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\ \end{align*}

10.535

23478

17048

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

10.545

23479

12003

\begin{align*} y^{\prime }&=\frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \\ \end{align*}

10.546

23480

3655

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

10.549

23481

11963

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

10.549

23482

24151

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

10.551

23483

5256

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

10.568

23484

21303

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

10.573

23485

12134

\begin{align*} y^{\prime }&=\frac {14 y x +12+2 x +x^{3} y^{3}+6 y^{2} x^{2}}{x^{2} \left (y x +2+x \right )} \\ \end{align*}

10.576

23486

8268

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

10.593

23487

23156

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

10.604

23488

21398

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

10.610

23489

12253

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

10.626

23490

23878

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

10.627

23491

6370

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

10.632

23492

13427

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

10.638

23493

8678

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

10.644

23494

13328

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

10.646

23495

19317

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

10.654

23496

20814

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

10.683

23497

21801

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

10.701

23498

13342

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

10.704

23499

18583

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

10.707

23500

12261

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

10.708