2.3.276 Problems 27501 to 27600

Table 2.1125: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

27501

6364

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

239.244

27502

13568

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

239.288

27503

6454

\begin{align*} y y^{\prime \prime }&=\operatorname {a2} y^{2}+\operatorname {a3} y^{1+a}+\operatorname {a1} y y^{\prime }+a {y^{\prime }}^{2} \\ \end{align*}

239.460

27504

19707

\begin{align*} v^{\prime \prime }&=\left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \\ \end{align*}

239.754

27505

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*}

241.415

27506

26309

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

241.758

27507

9659

\begin{align*} x^{\prime }&=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right ) \\ y^{\prime }&=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ z^{\prime }&=y+6 z-{\mathrm e}^{-t} \\ \end{align*}

241.984

27508

13627

\begin{align*} \left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta \\ \end{align*}

242.013

27509

13539

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

242.517

27510

27258

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

243.407

27511

27513

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

244.022

27512

27464

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

244.315

27513

14522

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

244.321

27514

12942

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

244.749

27515

13545

\begin{align*} y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\ \end{align*}

245.751

27516

26059

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

246.151

27517

21449

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

246.556

27518

16198

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

246.785

27519

26258

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

247.782

27520

27147

\begin{align*} x_{1}^{\prime }&=2 x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ x_{3}^{\prime }&=-x_{1}-2 x_{2}-x_{3} \\ \end{align*}

249.535

27521

27237

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

250.362

27522

13852

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

251.337

27523

26165

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

251.501

27524

18719

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

252.049

27525

23863

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

252.559

27526

5565

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

252.651

27527

13841

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

253.360

27528

26913

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

253.767

27529

24270

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

254.129

27530

21851

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

255.710

27531

13572

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

256.303

27532

26663

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

256.622

27533

27456

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

256.652

27534

5672

\begin{align*} {y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 y^{2} y^{\prime } x -16 y^{3}&=0 \\ \end{align*}

257.557

27535

24348

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

258.007

27536

14247

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

258.017

27537

13583

\begin{align*} y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}}&=\frac {a^{2} \left (-1+x \right ) \left (3 x +5\right )}{4 x^{{5}/{2}}} \\ \end{align*}

258.118

27538

6235

\begin{align*} \left (\operatorname {b1} \,x^{2}+\operatorname {b0} \right ) y+\left (\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0} \right ) y^{\prime }+4 \left (1-x \right ) x \left (-a x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}

258.122

27539

18352

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

258.214

27540

13609

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

258.804

27541

13861

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

259.320

27542

24180

\begin{align*} 16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}

260.835

27543

13857

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

261.685

27544

24155

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

262.205

27545

7552

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

262.773

27546

23860

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

263.238

27547

24887

\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*}

263.700

27548

27236

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

263.822

27549

11420

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

265.181

27550

19215

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

265.252

27551

26313

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

265.334

27552

23218

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

266.353

27553

9662

\begin{align*} x^{\prime }&=x-y+2 z+{\mathrm e}^{-t}-3 t \\ y^{\prime }&=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t \\ z^{\prime }&=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t \\ \end{align*}

266.773

27554

21823

\begin{align*} 3 y+2 y^{\prime } x +4 x y^{2}+3 x^{2} y y^{\prime }&=0 \\ \end{align*}

267.508

27555

22447

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

267.509

27556

18349

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

268.386

27557

13615

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

268.474

27558

27343

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

268.586

27559

12665

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

268.921

27560

15633

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

269.750

27561

26394

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

270.552

27562

12863

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

271.012

27563

25890

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

271.408

27564

13607

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

271.728

27565

13619

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

272.214

27566

27368

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

273.059

27567

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*}

273.195

27568

19290

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

274.006

27569

17049

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (-4\right ) &= 3 \\ \end{align*}

274.286

27570

26607

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

274.464

27571

13602

\begin{align*} y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (-1+x \right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\ \end{align*}

274.557

27572

26865

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

275.089

27573

26382

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

275.585

27574

25492

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

275.803

27575

25496

\begin{align*} y^{\prime }&=\frac {c t -a y}{A t +b y} \\ \end{align*}

276.683

27576

21466

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

276.846

27577

15631

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

277.006

27578

27427

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

277.040

27579

25009

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

277.501

27580

27397

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

277.552

27581

26329

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

278.223

27582

24324

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

279.332

27583

27327

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

280.107

27584

25037

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

280.133

27585

26259

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

281.368

27586

4820

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

283.430

27587

27467

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

285.496

27588

26207

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

285.706

27589

14068

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

286.203

27590

15167

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

286.692

27591

26277

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

286.885

27592

25732

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

287.003

27593

26263

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

289.253

27594

20476

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

289.888

27595

26276

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

290.239

27596

13524

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

292.074

27597

27523

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

292.425

27598

27259

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

293.241

27599

24386

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

293.402

27600

25891

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

294.976