2.3.221 Problems 22001 to 22100

Table 2.985: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22001

12009

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

9.007

22002

6898

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

9.012

22003

14445

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

9.012

22004

20688

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

9.015

22005

2846

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

9.023

22006

5344

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

9.023

22007

1351

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

9.032

22008

12246

\begin{align*} y^{\prime }&=-\frac {1296 y}{216-570 y^{8}+216 x^{2}+216 x^{3}-1296 y+594 x y^{6}-846 y^{7}-612 y^{5}-1728 y^{3}+1080 x y^{3}+1080 x y^{5}-2376 y^{2}-432 y x +72 y^{8} x +216 y^{7} x -882 y^{6}-1944 y^{4}-216 x^{2} y^{4}-648 y^{2} x^{2}+1152 y^{4} x +216 x y^{2}-648 x^{2} y-324 x^{2} y^{3}-315 y^{9}-126 y^{10}-8 y^{12}-36 y^{11}} \\ \end{align*}

9.034

22009

734

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

9.036

22010

17090

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

9.038

22011

21988

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

9.043

22012

17904

\begin{align*} x^{3} y^{\prime }-\sin \left (y\right )&=1 \\ y \left (\infty \right ) &= 5 \pi \\ \end{align*}

9.048

22013

23205

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

9.056

22014

11947

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

9.057

22015

20682

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

9.057

22016

4954

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

9.060

22017

22869

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

9.063

22018

13758

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

9.065

22019

25013

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

9.073

22020

6965

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

9.075

22021

19969

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

9.083

22022

14545

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

9.089

22023

22953

\begin{align*} \frac {\tan \left (y\right )}{\cos \left (x \right )}&=\cos \left (x \right ) y^{\prime } \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{2} \\ \end{align*}

9.093

22024

11940

\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y} \\ \end{align*}

9.100

22025

15840

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

9.105

22026

22414

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

9.107

22027

6980

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

9.114

22028

24205

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

9.117

22029

20830

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

9.121

22030

22541

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

9.121

22031

20250

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

9.123

22032

11932

\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y} \\ \end{align*}

9.129

22033

21965

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

9.130

22034

22380

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

9.130

22035

5831

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

9.135

22036

14889

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

9.137

22037

22460

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

9.137

22038

9082

\begin{align*} x^{5} y^{\prime }+y^{5}&=0 \\ \end{align*}

9.142

22039

23174

\begin{align*} \left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \\ y \left (-1\right ) &= 16 \\ \end{align*}

9.143

22040

5846

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

9.144

22041

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*}

9.145

22042

11625

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

9.149

22043

2479

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

9.151

22044

5657

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

9.151

22045

11864

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

9.155

22046

13391

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

9.155

22047

19930

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

9.155

22048

20818

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

9.161

22049

8225

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

9.167

22050

11641

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

9.177

22051

11865

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

9.177

22052

26250

\begin{align*} x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {5 \pi }{4} \\ \end{align*}

9.183

22053

11943

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

9.184

22054

18846

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

9.184

22055

16331

\begin{align*} 6+12 y^{2} x^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}

9.189

22056

4987

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

9.194

22057

9798

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

9.194

22058

23969

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

9.200

22059

14884

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

9.210

22060

22560

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

9.210

22061

11944

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

9.220

22062

24384

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

9.220

22063

21805

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

9.221

22064

2852

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

9.224

22065

14226

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

9.226

22066

3225

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

9.234

22067

22017

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

9.234

22068

5024

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

9.237

22069

23268

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

9.238

22070

5455

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

9.239

22071

11630

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

9.239

22072

17842

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

9.242

22073

14527

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

9.244

22074

5824

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

9.250

22075

21452

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

9.254

22076

24150

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

9.256

22077

5819

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

9.259

22078

1734

\begin{align*} 12 y x +6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

9.260

22079

11444

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

9.260

22080

11933

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

9.263

22081

15024

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

9.264

22082

22948

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

9.264

22083

13266

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

9.267

22084

25662

\begin{align*} y^{\prime }&=25+y^{2} \\ \end{align*}

9.267

22085

13327

\begin{align*} y^{\prime }&=\alpha y^{2}+\beta +\gamma \cosh \left (x \right ) \\ \end{align*}

9.268

22086

25275

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

9.274

22087

17883

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

9.277

22088

4970

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

9.287

22089

20254

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

9.287

22090

11424

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

9.290

22091

14266

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

9.312

22092

14230

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

9.313

22093

20813

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

9.313

22094

11971

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

9.314

22095

12227

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

9.316

22096

20713

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

9.316

22097

5949

\begin{align*} \left (b x +a \right ) y+8 y^{\prime }+16 y^{\prime \prime } x&=0 \\ \end{align*}

9.319

22098

11538

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

9.320

22099

11849

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

9.326

22100

22564

\begin{align*} s^{\prime }&=\frac {1}{s+t +1} \\ \end{align*}

9.326