2.3.247 Problems 24601 to 24700

Table 2.1043: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24601

3655

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

25.851

24602

2898

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

25.880

24603

8712

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

25.881

24604

22343

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

25.955

24605

24344

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

25.964

24606

2945

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

25.973

24607

12263

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

25.978

24608

11608

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

25.997

24609

13541

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

26.022

24610

26316

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

26.036

24611

12081

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

26.050

24612

4745

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

26.061

24613

24226

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

26.062

24614

14867

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

26.088

24615

5193

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

26.090

24616

22025

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

26.127

24617

21420

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

26.128

24618

20821

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

26.129

24619

5149

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

26.133

24620

11369

\begin{align*} y^{\prime }-\sqrt {\frac {a y^{4}+b y^{2}+1}{x^{4} a +b \,x^{2}+1}}&=0 \\ \end{align*}

26.134

24621

14084

\begin{align*} 8 \left (1+y^{\prime }\right )^{3}&=27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \\ \end{align*}

26.139

24622

4348

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

26.189

24623

11994

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

26.199

24624

18572

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

26.207

24625

20449

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

26.215

24626

8870

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

26.224

24627

5877

\begin{align*} \left (\operatorname {a0} +4 \operatorname {a1} \cosh \left (x \right )^{2}-\operatorname {a2} \operatorname {sech}\left (x \right )^{2}\right ) y+\tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

26.235

24628

5357

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

26.244

24629

1147

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

26.257

24630

1718

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

26.266

24631

13999

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

26.269

24632

11679

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

26.302

24633

25040

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

26.322

24634

4083

\begin{align*} 6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\ y \left (\frac {1}{2}\right ) &= 3 \\ \end{align*}

26.325

24635

9156

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

26.325

24636

11544

\begin{align*} \left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3&=0 \\ \end{align*}

26.402

24637

13624

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

26.493

24638

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*}

26.548

24639

20984

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

26.575

24640

9128

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

26.578

24641

20021

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

26.589

24642

7532

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

26.593

24643

7148

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

26.621

24644

7714

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

26.647

24645

5298

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

26.683

24646

23887

\begin{align*} \frac {1-6 x^{2} y}{x}+\frac {\left (2+5 y-3 x^{2} y\right ) y^{\prime }}{y}&=0 \\ \end{align*}

26.703

24647

18575

\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*}

26.735

24648

11520

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

26.763

24649

21067

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

26.768

24650

1666

\begin{align*} y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \\ \end{align*}

26.793

24651

5476

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

26.795

24652

13807

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

26.813

24653

19922

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

26.830

24654

19402

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

26.831

24655

12251

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

26.835

24656

1123

\begin{align*} y \cos \left (t \right )+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\ y \left (1\right ) &= a \\ \end{align*}

26.871

24657

13269

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

26.872

24658

25833

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

26.876

24659

8731

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

26.877

24660

26178

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

26.884

24661

17065

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

26.895

24662

19278

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

26.905

24663

25750

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

26.952

24664

1677

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

26.953

24665

5085

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

26.981

24666

15151

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

27.014

24667

17086

\begin{align*} x^{\prime }&=\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \\ \end{align*}

27.049

24668

15356

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

27.052

24669

7493

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

27.069

24670

10316

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

27.069

24671

25748

\begin{align*} y^{\prime }&=6 \sqrt {y}+5 x^{3} \\ y \left (-1\right ) &= 4 \\ \end{align*}

27.074

24672

7544

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

27.092

24673

25788

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

27.096

24674

9059

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

27.112

24675

15869

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

27.134

24676

26275

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

27.137

24677

24294

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

27.152

24678

8684

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

27.156

24679

26081

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

27.168

24680

13295

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

27.215

24681

22556

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

27.223

24682

15036

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

27.235

24683

9167

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

27.241

24684

4238

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

27.270

24685

13267

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

27.293

24686

13256

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

27.312

24687

17652

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

27.377

24688

11642

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

27.400

24689

12929

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

27.408

24690

23219

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

27.415

24691

6296

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

27.418

24692

12245

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

27.447

24693

21814

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

27.451

24694

6400

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

27.472

24695

3666

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

27.503

24696

25050

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

27.507

24697

18553

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

27.565

24698

20718

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

27.581

24699

26321

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

27.589

24700

21816

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

27.606