2.3.233 Problems 23201 to 23300

Table 2.1039: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23201

26342

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

9.014

23202

17910

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

9.022

23203

18029

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

9.023

23204

7502

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

9.026

23205

5043

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

9.037

23206

14980

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

Series expansion around \(x=0\).

9.038

23207

10285

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

9.043

23208

4895

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

9.046

23209

23835

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

9.046

23210

18076

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

9.050

23211

19943

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

9.050

23212

4860

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

9.051

23213

13659

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

9.052

23214

15478

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

9.056

23215

12383

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

9.059

23216

4899

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

9.062

23217

18087

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

9.069

23218

768

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

9.076

23219

6882

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

9.085

23220

7504

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

9.086

23221

17222

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

9.089

23222

20474

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

9.090

23223

27398

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

9.090

23224

22090

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

9.093

23225

13810

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

9.099

23226

22986

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

9.102

23227

27470

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

9.102

23228

26363

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

9.106

23229

15347

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

9.107

23230

4680

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

9.109

23231

6158

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

9.124

23232

13462

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

9.124

23233

16975

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

9.132

23234

17850

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

9.140

23235

15898

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

9.151

23236

23842

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

9.151

23237

18628

\begin{align*} y^{\prime }+y-y^{{1}/{4}}&=0 \\ \end{align*}

9.157

23238

24896

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

9.160

23239

17857

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

9.165

23240

12064

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

9.166

23241

11877

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

9.171

23242

1803

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

9.172

23243

5547

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

9.172

23244

9144

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

9.172

23245

2866

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

9.173

23246

13460

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

9.173

23247

4701

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

9.174

23248

13969

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

9.174

23249

26250

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

9.174

23250

26471

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

9.175

23251

18590

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

9.180

23252

8244

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

9.181

23253

12184

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

9.181

23254

26249

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

9.183

23255

19722

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

9.184

23256

26865

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

9.193

23257

15512

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

9.199

23258

682

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

9.203

23259

18556

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

9.205

23260

25851

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

9.210

23261

12246

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

9.214

23262

21473

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

9.217

23263

4830

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

9.219

23264

17885

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

9.227

23265

5164

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

9.233

23266

11576

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

9.238

23267

4898

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

9.242

23268

17892

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

9.249

23269

8825

\begin{align*} \phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right )&=0 \\ \end{align*}

9.250

23270

8671

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

9.253

23271

19383

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

9.253

23272

24207

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

9.253

23273

19930

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

9.259

23274

22464

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

9.264

23275

7490

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

9.270

23276

7254

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

9.272

23277

17875

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

9.273

23278

11595

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

9.274

23279

16333

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

9.275

23280

23170

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

9.275

23281

11496

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

9.279

23282

8698

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

9.282

23283

15826

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

9.285

23284

14231

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

9.295

23285

11977

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

9.301

23286

7892

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

9.303

23287

11372

\begin{align*} y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}}&=0 \\ \end{align*}

9.310

23288

779

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

9.314

23289

5545

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

9.316

23290

6828

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

9.326

23291

20829

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

9.329

23292

16224

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

9.335

23293

27411

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

9.337

23294

16290

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

9.340

23295

20318

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

9.343

23296

15342

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

9.344

23297

19977

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

9.349

23298

17982

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

9.351

23299

12183

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

9.352

23300

23192

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

9.352