2.3.244 Problems 24301 to 24400

Table 2.1061: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24301

20405

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

12.833

24302

12206

\begin{align*} y^{\prime }&=\frac {-8 x^{2} y^{3}+16 x y^{2}+16 x y^{3}-8+12 y x -6 x^{2} y^{2}+x^{3} y^{3}}{16 \left (-2+y x -2 y\right ) x} \\ \end{align*}

12.837

24303

4703

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

12.842

24304

21833

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

12.860

24305

24212

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

12.860

24306

20960

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

12.865

24307

4230

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

12.881

24308

22564

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

12.892

24309

24392

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

12.899

24310

4856

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

12.902

24311

5699

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

12.908

24312

13710

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

12.908

24313

27510

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

12.911

24314

22952

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

12.932

24315

20245

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

12.934

24316

4796

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

12.938

24317

2841

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

12.939

24318

5907

\begin{align*} \left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}

12.941

24319

15846

\begin{align*} y^{\prime }&=y^{2}-y^{3} \\ y \left (0\right ) &= {\frac {1}{5}} \\ \end{align*}

12.944

24320

23196

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

12.947

24321

5257

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

12.956

24322

24371

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

12.957

24323

5418

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

12.963

24324

26383

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

12.979

24325

3775

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+5 y&=8 x \ln \left (x \right )^{2} \\ \end{align*}

12.984

24326

15532

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

12.984

24327

27402

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

12.995

24328

15642

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

13.000

24329

12439

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

13.001

24330

25768

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

13.003

24331

24377

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

13.004

24332

5049

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

13.006

24333

12122

\begin{align*} y^{\prime }&=\frac {b \,x^{3}+c^{2} \sqrt {a}-2 c b \,x^{2} \sqrt {a}+2 c y^{2} a^{{3}/{2}}+b^{2} x^{4} \sqrt {a}-2 y^{2} a^{{3}/{2}} b \,x^{2}+a^{{5}/{2}} y^{4}}{a \,x^{2} y} \\ \end{align*}

13.008

24334

22985

\begin{align*} y^{\prime }-\frac {6 y}{x}&=7 x \\ y \left (1\right ) &= 0 \\ \end{align*}

13.011

24335

2329

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

13.012

24336

24160

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

13.015

24337

5589

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

13.021

24338

10038

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

13.026

24339

12138

\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \\ \end{align*}

13.030

24340

27457

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

13.030

24341

12014

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

13.037

24342

5276

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

13.039

24343

13739

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

13.040

24344

2501

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

13.045

24345

13315

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

13.052

24346

2942

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

13.053

24347

4827

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

13.059

24348

9056

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

13.060

24349

2941

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

13.063

24350

13494

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

13.063

24351

24061

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

13.065

24352

4429

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

13.072

24353

5254

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

13.083

24354

21039

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

13.087

24355

23883

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

13.089

24356

13409

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

13.093

24357

4078

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

13.098

24358

6127

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

13.099

24359

22512

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

13.102

24360

14437

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

13.105

24361

6949

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

13.109

24362

19897

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

13.112

24363

20805

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

13.114

24364

24171

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

13.115

24365

17271

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

13.119

24366

9976

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

13.122

24367

26665

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

13.133

24368

14027

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

13.158

24369

25503

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

13.158

24370

13684

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

13.161

24371

7544

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

13.163

24372

12222

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

13.171

24373

17129

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

13.173

24374

24954

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

13.181

24375

18075

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

13.182

24376

12012

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

13.186

24377

2863

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

13.194

24378

16355

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

13.201

24379

14026

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

13.203

24380

8751

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

13.214

24381

18060

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

13.221

24382

27440

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

13.221

24383

10314

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

13.224

24384

21055

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

13.230

24385

12226

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

13.234

24386

9020

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

13.236

24387

23885

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

13.237

24388

18478

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

13.249

24389

22521

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

13.252

24390

5007

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

13.254

24391

17198

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

13.264

24392

5094

\begin{align*} 3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2}&=0 \\ \end{align*}

13.265

24393

13752

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

13.267

24394

15626

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

13.271

24395

17200

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

13.272

24396

22518

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

13.278

24397

9093

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

13.283

24398

17342

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

13.283

24399

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*}

13.288

24400

5065

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

13.302