2.3.219 Problems 21801 to 21900

Table 2.969: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

21801

10007

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

16.111

21802

23863

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

16.115

21803

792

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

16.134

21804

17268

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

16.135

21805

11546

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

16.151

21806

4252

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

16.155

21807

11777

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

16.162

21808

24616

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

16.164

21809

23461

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

16.168

21810

4745

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

16.183

21811

5169

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

16.208

21812

5298

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

16.222

21813

5153

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

16.227

21814

14915

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

16.235

21815

22755

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

16.241

21816

3543

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

16.247

21817

21542

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

16.248

21818

12477

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

16.256

21819

18051

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

16.261

21820

11461

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

16.269

21821

5686

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

16.271

21822

5168

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

16.277

21823

21115

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

16.281

21824

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*}

16.283

21825

9935

\begin{align*} 9 x^{2} y^{\prime \prime }-15 y^{\prime } x +7 \left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

16.290

21826

13799

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

16.291

21827

9015

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

16.293

21828

1302

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

16.308

21829

12167

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

16.313

21830

21811

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

16.321

21831

10037

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

16.335

21832

20295

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

16.344

21833

17241

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

16.345

21834

11550

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

16.352

21835

21012

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

16.359

21836

12467

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

16.376

21837

3636

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

16.378

21838

19937

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

16.381

21839

1332

\begin{align*} t^{2} y^{\prime \prime }+5 y^{\prime } t +13 y&=0 \\ \end{align*}

16.382

21840

18826

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

16.385

21841

24690

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}

16.397

21842

11921

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

16.421

21843

11580

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

16.427

21844

21455

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

16.450

21845

20313

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

16.462

21846

20189

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

16.489

21847

1816

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

16.493

21848

14550

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

16.497

21849

17258

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

16.499

21850

19967

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

16.510

21851

12459

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

16.515

21852

8673

\begin{align*} \frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \\ \end{align*}

16.531

21853

12392

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

16.547

21854

17023

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

16.552

21855

903

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

16.559

21856

682

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

16.566

21857

21827

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

16.588

21858

11551

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

16.602

21859

13495

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

16.620

21860

17340

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

16.625

21861

11328

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

16.626

21862

17125

\begin{align*} y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

16.628

21863

13808

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

16.631

21864

24400

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

16.631

21865

23364

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

16.633

21866

14179

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

16.638

21867

17333

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

16.655

21868

9223

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

16.656

21869

10142

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

16.723

21870

11945

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

16.725

21871

761

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

16.737

21872

606

\begin{align*} x^{\prime }&=2 x-3 y \\ y^{\prime }&=x+y+2 z \\ z^{\prime }&=5 y-7 z \\ \end{align*}

16.741

21873

14687

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

16.743

21874

10063

\begin{align*} x^{\prime }&=4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \\ \end{align*}

16.764

21875

8712

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

16.772

21876

13767

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

16.781

21877

1833

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=\left (3 x -1\right )^{2} {\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

16.782

21878

5376

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

16.783

21879

6835

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

16.784

21880

11657

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

16.787

21881

3548

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

16.788

21882

13797

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

16.790

21883

10285

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

16.792

21884

9230

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

16.793

21885

12175

\begin{align*} y^{\prime }&=\frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \\ \end{align*}

16.794

21886

11922

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

16.798

21887

14187

\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}

16.805

21888

5951

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\ \end{align*}

16.807

21889

11959

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

16.809

21890

18807

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

16.819

21891

23074

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

16.828

21892

17211

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

16.829

21893

17099

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

16.830

21894

368

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

16.835

21895

12389

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

16.858

21896

13281

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

16.864

21897

19840

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

16.866

21898

13801

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

16.870

21899

3678

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

16.874

21900

1647

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

16.883