2.3.221 Problems 22001 to 22100

Table 2.973: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22001

16757

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

17.729

22002

15822

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

17.738

22003

13979

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

17.776

22004

22141

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

17.782

22005

22792

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

17.810

22006

12864

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

17.812

22007

21117

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

17.819

22008

6289

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

17.835

22009

20047

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

17.847

22010

12164

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

17.862

22011

8157

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

17.866

22012

1301

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

17.871

22013

12484

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

17.876

22014

19508

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

17.882

22015

17225

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

17.887

22016

11673

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

17.900

22017

9059

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

17.905

22018

11646

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

17.915

22019

13482

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

17.924

22020

11977

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

17.932

22021

21122

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

17.945

22022

1605

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

17.968

22023

6097

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

17.973

22024

12595

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

18.006

22025

16962

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

18.047

22026

11918

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

18.048

22027

4944

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

18.049

22028

17204

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

18.052

22029

12158

\begin{align*} y^{\prime }&=\frac {1+y^{4}-8 a x y^{2}+16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y} \\ \end{align*}

18.059

22030

14021

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

18.077

22031

18347

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

18.078

22032

20621

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

18.078

22033

353

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

18.091

22034

25740

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

18.105

22035

9802

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

18.117

22036

5337

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

18.121

22037

17261

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

18.129

22038

5926

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

18.136

22039

11966

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

18.140

22040

7938

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

18.145

22041

11498

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

18.160

22042

17966

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

18.198

22043

12481

\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2 n}+\operatorname {b1} \,x^{n}+\operatorname {c1} \right ) y&=0 \\ \end{align*}

18.207

22044

24395

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

18.217

22045

12488

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

18.224

22046

10025

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

18.227

22047

14692

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

18.251

22048

6144

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

18.256

22049

8824

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

18.270

22050

17037

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

18.277

22051

20855

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

18.286

22052

19696

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

18.292

22053

12766

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

18.293

22054

14973

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

18.293

22055

9218

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

18.295

22056

6096

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

18.308

22057

7298

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=12 x \,{\mathrm e}^{3 x} \\ \end{align*}

18.313

22058

16476

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

18.316

22059

14155

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

18.319

22060

11914

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

18.325

22061

3034

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

18.341

22062

12929

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

18.354

22063

11535

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

18.367

22064

5429

\begin{align*} {y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\ \end{align*}

18.371

22065

1665

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

18.378

22066

12200

\begin{align*} y^{\prime }&=\frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 x y^{5}+y^{5}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\ \end{align*}

18.384

22067

13591

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

18.384

22068

11647

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

18.393

22069

3471

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

18.398

22070

5265

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

18.406

22071

6922

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

18.414

22072

17346

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

18.441

22073

11574

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

18.448

22074

11579

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

18.464

22075

5895

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

18.469

22076

21826

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

18.475

22077

7112

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

18.482

22078

3666

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

18.487

22079

11538

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

18.490

22080

13523

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

18.494

22081

387

\begin{align*} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

18.516

22082

13750

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

18.516

22083

7740

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

18.521

22084

22391

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

18.531

22085

11337

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

18.536

22086

25134

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

18.539

22087

325

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

18.587

22088

18098

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

18.588

22089

6191

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

18.591

22090

1666

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

18.609

22091

24604

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

18.614

22092

10322

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

18.621

22093

23244

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

18.631

22094

17235

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

18.660

22095

15821

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

18.673

22096

13345

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

18.677

22097

20480

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

18.679

22098

7757

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

18.703

22099

1663

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

18.708

22100

4891

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

18.727