2.3.227 Problems 22601 to 22700

Table 2.997: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22601

4889

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

11.180

22602

9147

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

11.184

22603

12079

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

11.185

22604

20092

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

11.198

22605

18572

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

11.205

22606

6816

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

11.206

22607

13629

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

11.207

22608

1727

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

11.210

22609

5596

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

11.215

22610

25757

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

11.215

22611

1647

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

11.220

22612

19820

\begin{align*} \left (x -3 y+4\right ) y^{\prime }&=2 x -6 y+7 \\ \end{align*}

11.222

22613

25745

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

11.226

22614

14481

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

11.227

22615

4726

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

11.228

22616

3037

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

11.229

22617

200

\begin{align*} y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\ \end{align*}

11.232

22618

2882

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

11.232

22619

13483

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

11.248

22620

5866

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

11.252

22621

23672

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

11.253

22622

17107

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

11.256

22623

23858

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

11.257

22624

17957

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

11.263

22625

19277

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

11.264

22626

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*}

11.266

22627

1803

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

11.272

22628

24356

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

11.281

22629

4738

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

11.283

22630

5326

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

11.284

22631

23140

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

11.296

22632

14495

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

11.301

22633

5907

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

11.302

22634

7199

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

11.303

22635

19315

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

11.310

22636

3466

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

11.315

22637

11526

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

11.319

22638

17940

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

11.320

22639

7218

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

11.325

22640

14433

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

11.325

22641

12042

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

11.326

22642

17982

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

11.328

22643

20829

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

11.328

22644

4278

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

11.340

22645

7502

\begin{align*} y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\ \end{align*}

11.340

22646

21403

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

11.346

22647

8780

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

11.347

22648

25899

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

11.352

22649

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*}

11.355

22650

13443

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

11.359

22651

2537

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

11.360

22652

13993

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

11.362

22653

6916

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

11.365

22654

5330

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

11.367

22655

2690

\begin{align*} y^{\prime \prime }+y^{\prime }+7 y&=\left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

11.376

22656

7315

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

11.378

22657

22593

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

11.382

22658

15894

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

11.393

22659

22377

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

11.397

22660

17100

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

11.398

22661

17886

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

11.424

22662

21397

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

11.434

22663

3435

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

11.436

22664

24168

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

11.436

22665

5918

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

11.454

22666

1592

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

11.456

22667

6031

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

11.484

22668

6912

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

11.484

22669

8378

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

11.487

22670

12307

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

11.494

22671

13761

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

11.496

22672

2854

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

11.497

22673

7681

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

11.499

22674

10279

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

11.499

22675

14898

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

11.502

22676

17885

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

11.504

22677

22557

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

11.513

22678

19335

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

11.514

22679

7336

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

11.519

22680

19913

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

11.519

22681

5318

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

11.521

22682

7412

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

11.522

22683

16354

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

11.534

22684

17223

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

11.534

22685

7228

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

11.536

22686

1628

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

11.541

22687

4690

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

11.542

22688

13487

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

11.545

22689

12156

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

11.552

22690

12257

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

11.555

22691

3652

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

11.556

22692

23238

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

11.556

22693

14459

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

11.558

22694

4855

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

11.564

22695

23060

\begin{align*} r^{\prime } \left (1+\frac {\cos \left (\theta \right )}{2}\right )-r \sin \left (\theta \right )&=0 \\ r \left (\frac {\pi }{2}\right ) &= 2 a \\ \end{align*}

11.564

22696

1200

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

11.574

22697

7923

\begin{align*} \left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \\ \end{align*}

11.582

22698

23895

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

11.584

22699

11344

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

11.586

22700

5917

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

11.588