2.3.247 Problems 24601 to 24700

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

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24601

3667

\begin{align*} 2 y^{\prime }+\cot \left (x \right ) y&=\frac {8 \cos \left (x \right )^{3}}{y} \\ \end{align*}

33.504

24602

19309

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

33.530

24603

22416

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

33.576

24604

2913

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

33.598

24605

20314

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

33.669

24606

17991

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

33.678

24607

7248

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

33.688

24608

11900

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

33.689

24609

3579

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

33.694

24610

1233

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

33.695

24611

20274

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

33.743

24612

4297

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

33.760

24613

5420

\begin{align*} {y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right )&=0 \\ \end{align*}

33.763

24614

6362

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

33.767

24615

6585

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

33.777

24616

13732

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

33.796

24617

13762

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

33.835

24618

12986

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

33.888

24619

21929

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

33.900

24620

10316

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

33.902

24621

17291

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

33.944

24622

5706

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

33.961

24623

5530

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

33.987

24624

13362

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

34.048

24625

23192

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

34.082

24626

12384

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

34.122

24627

17276

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

34.132

24628

12929

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

34.158

24629

22983

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

34.161

24630

5176

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

34.188

24631

1754

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

34.219

24632

3653

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

34.224

24633

7462

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

34.286

24634

13347

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

34.328

24635

17253

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

34.338

24636

19303

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

34.345

24637

9140

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

34.346

24638

14866

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

34.396

24639

17254

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

34.400

24640

23874

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

34.435

24641

22982

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

34.469

24642

13280

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

34.473

24643

2955

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

34.513

24644

14548

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

34.531

24645

12305

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

34.534

24646

5148

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

34.536

24647

7715

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

34.542

24648

1723

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

34.547

24649

21360

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

34.556

24650

6902

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

34.564

24651

19458

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

34.577

24652

3012

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

34.619

24653

12145

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

34.624

24654

11551

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

34.787

24655

5678

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

34.794

24656

11363

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

34.823

24657

15291

\begin{align*} x^{\prime }&=-3 x-3 y+z \\ y^{\prime }&=2 y+2 z+29 \,{\mathrm e}^{-t} \\ z^{\prime }&=5 x+y+z+39 \,{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}

34.834

24658

13576

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

34.877

24659

23129

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

34.923

24660

20695

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

34.928

24661

22992

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

34.931

24662

23872

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

34.940

24663

17261

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

34.947

24664

5502

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

34.973

24665

22546

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

34.981

24666

2922

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

35.079

24667

6041

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

35.086

24668

6037

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

35.107

24669

7712

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

35.111

24670

4778

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

35.118

24671

13009

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

35.170

24672

13258

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

35.184

24673

12108

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

35.185

24674

6310

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

35.203

24675

2887

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

35.204

24676

7401

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

35.258

24677

13891

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

35.269

24678

2995

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

35.273

24679

19705

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

35.298

24680

22383

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

35.340

24681

5145

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

35.356

24682

19493

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

35.390

24683

10071

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

35.391

24684

5702

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

35.421

24685

11451

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

35.448

24686

5170

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

35.512

24687

2349

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

35.513

24688

13966

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

35.592

24689

4243

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

35.607

24690

16315

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

35.615

24691

13577

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

35.618

24692

24347

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

35.624

24693

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*}

35.631

24694

7470

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

35.703

24695

22413

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

35.703

24696

24886

\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*}

35.714

24697

4989

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

35.727

24698

13423

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

35.729

24699

4258

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

35.763

24700

3650

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

35.789