2.3.233 Problems 23201 to 23300

Table 2.997: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23201

11673

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

8.846

23202

20693

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

8.851

23203

13053

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

8.852

23204

13452

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

8.852

23205

12271

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

8.858

23206

19743

\begin{align*} \sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \\ \end{align*}

8.866

23207

24316

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

8.875

23208

19329

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

8.879

23209

14476

\begin{align*} 3 x^{2}+9 y x +5 y^{2}-\left (6 x^{2}+4 y x \right ) y^{\prime }&=0 \\ y \left (2\right ) &= -6 \\ \end{align*}

8.901

23210

2520

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

8.908

23211

24175

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

8.912

23212

17954

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

8.913

23213

20766

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

8.924

23214

21344

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

8.927

23215

1200

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

8.928

23216

19949

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

8.928

23217

21355

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

8.936

23218

24330

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

8.950

23219

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*}

8.951

23220

11930

\begin{align*} y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y} \\ \end{align*}

8.954

23221

21085

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

8.955

23222

21417

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

8.963

23223

24298

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

8.968

23224

12220

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

8.978

23225

6045

\begin{align*} \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+\operatorname {c1} \,x^{2 k}\right ) y+x \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

8.985

23226

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*}

8.989

23227

12000

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

8.999

23228

11607

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

9.005

23229

12207

\begin{align*} y^{\prime }&=-\frac {x \left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y-2 \,{\mathrm e}^{-2 x^{2}} x^{4}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}-8 y^{2}-8 \,{\mathrm e}^{-x^{2}}-8\right )}{8} \\ \end{align*}

9.009

23230

11954

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

9.010

23231

6805

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

9.012

23232

12109

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

9.014

23233

23874

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

9.015

23234

2929

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

9.021

23235

19249

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

9.033

23236

17912

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

9.040

23237

20576

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

9.059

23238

20258

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

9.068

23239

12181

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

9.073

23240

19412

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

9.085

23241

24183

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

9.092

23242

18722

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

9.093

23243

2985

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

9.098

23244

24312

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

9.106

23245

7146

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

9.111

23246

18338

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

9.113

23247

9158

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

9.116

23248

20972

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

9.120

23249

20232

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

9.128

23250

22392

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

9.132

23251

12089

\begin{align*} y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\ \end{align*}

9.136

23252

12218

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

9.148

23253

21795

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

9.153

23254

18573

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

9.161

23255

11875

\begin{align*} y^{\prime }&=\frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x} \\ \end{align*}

9.167

23256

5320

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

9.170

23257

6453

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

9.172

23258

8328

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

9.172

23259

4703

\begin{align*} y^{\prime }&=a \,x^{\frac {n}{1-n}}+b y^{n} \\ \end{align*}

9.194

23260

15637

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

9.195

23261

4688

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

9.201

23262

17957

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

9.202

23263

25800

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

9.207

23264

9148

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

9.211

23265

19400

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

9.212

23266

11575

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

9.218

23267

18483

\begin{align*} y^{\prime }&=4 \sqrt {y x} \\ \end{align*}

9.221

23268

22393

\begin{align*} y^{\prime }&=\frac {6 x^{2}-5 y x -2 y^{2}}{6 x^{2}-8 y x +y^{2}} \\ \end{align*}

9.227

23269

14231

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

9.231

23270

11960

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

9.237

23271

13369

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

9.251

23272

12045

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

9.266

23273

19899

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

9.266

23274

11635

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

9.269

23275

12191

\begin{align*} y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\cos \left (x \right ) \ln \left (y\right )}{\sin \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\ \end{align*}

9.270

23276

11609

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

9.279

23277

19278

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

9.281

23278

10126

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

9.288

23279

5007

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

9.289

23280

12225

\begin{align*} y^{\prime }&=\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 a x y^{2}+12 x^{4} y+48 y a \,x^{3}+48 y a^{2} x^{2}+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \\ \end{align*}

9.295

23281

12127

\begin{align*} y^{\prime }&=\frac {1}{-x +\left (\frac {1}{y}+1\right ) x +\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )} \\ \end{align*}

9.303

23282

13363

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

9.308

23283

21399

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

9.313

23284

12033

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

9.316

23285

12142

\begin{align*} y^{\prime }&=-\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \\ \end{align*}

9.334

23286

2892

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

9.340

23287

17958

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

9.340

23288

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 x^{4} y^{2}+x^{6}\right ) x}{y} \\ \end{align*}

9.345

23289

19337

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

9.345

23290

24150

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

9.345

23291

15898

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

9.348

23292

19925

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

9.352

23293

11985

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

9.355

23294

19417

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

9.356

23295

5305

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

9.360

23296

3036

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

9.382

23297

13920

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

9.385

23298

20400

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

9.392

23299

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*}

9.395

23300

12178

\begin{align*} y^{\prime }&=\frac {32 x^{5} y+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \\ \end{align*}

9.395