2.3.242 Problems 24101 to 24200

Table 2.1057: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24101

13016

\begin{align*} 2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right )&=0 \\ \end{align*}

12.056

24102

27343

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

12.061

24103

21930

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

12.069

24104

2498

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

12.073

24105

26277

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

12.074

24106

25277

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

12.079

24107

22460

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

12.086

24108

17881

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

12.096

24109

13693

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

12.106

24110

4313

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

12.109

24111

5707

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

12.109

24112

16682

\begin{align*} 3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y&=4 x^{3} \\ \end{align*}

12.109

24113

2897

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

12.119

24114

4733

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

12.120

24115

17005

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

12.125

24116

6877

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

12.135

24117

9096

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

12.135

24118

12196

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

12.141

24119

11345

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

12.160

24120

11993

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

12.161

24121

12690

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

12.164

24122

1655

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

12.168

24123

15623

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

12.170

24124

27323

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

12.188

24125

25490

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

12.191

24126

4805

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

12.200

24127

1582

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

12.206

24128

12128

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

12.211

24129

2868

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

12.212

24130

4081

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

12.212

24131

4709

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

12.212

24132

13651

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

12.214

24133

17837

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

12.220

24134

5911

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

12.221

24135

12233

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

12.221

24136

5756

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

12.222

24137

24152

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

12.231

24138

8475

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

12.232

24139

4804

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

12.239

24140

13403

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

12.240

24141

6250

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

12.241

24142

4308

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

12.247

24143

25663

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

12.248

24144

24210

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

12.249

24145

13719

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

12.255

24146

24167

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

12.258

24147

7252

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

12.260

24148

11646

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

12.260

24149

13309

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

12.270

24150

20974

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

12.271

24151

5285

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

12.274

24152

8662

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

12.274

24153

27246

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

12.279

24154

18591

\begin{align*} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\ \end{align*}

12.285

24155

17104

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

12.286

24156

12438

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

12.287

24157

24172

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

12.291

24158

1657

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

12.307

24159

5874

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

12.311

24160

6990

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

12.315

24161

13464

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

12.316

24162

20596

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

12.320

24163

5641

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

12.322

24164

8728

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

12.322

24165

15883

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

12.327

24166

18098

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

12.331

24167

7251

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

12.332

24168

5326

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

12.348

24169

19073

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

12.352

24170

21594

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

12.352

24171

6488

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

12.354

24172

11680

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

12.357

24173

1205

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

12.365

24174

7392

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

12.366

24175

751

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

12.372

24176

8256

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

12.375

24177

18039

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

12.375

24178

13427

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

12.383

24179

17128

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

12.388

24180

5318

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

12.391

24181

26898

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

12.391

24182

11529

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

12.393

24183

19311

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

12.393

24184

22560

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

12.393

24185

17969

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

12.395

24186

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*}

12.407

24187

12111

\begin{align*} y^{\prime }&=\frac {1+2 \sqrt {1+4 x^{2} y}\, x^{3}+2 x^{5} \sqrt {1+4 x^{2} y}+2 x^{6} \sqrt {1+4 x^{2} y}}{2 x^{3}} \\ \end{align*}

12.410

24188

23837

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

12.411

24189

16351

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

12.413

24190

13472

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

12.415

24191

14050

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

12.415

24192

14032

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

12.417

24193

7551

\begin{align*} y^{\prime }&=\frac {x -y-1}{x +y+5} \\ \end{align*}

12.425

24194

16962

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

12.425

24195

22381

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

12.427

24196

4312

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

12.429

24197

18490

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

12.430

24198

13975

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

12.432

24199

12440

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

12.440

24200

3466

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

12.445