2.3.264 Problems 26301 to 26400

Table 2.1101: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

26301

7859

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

37.159

26302

5854

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

37.164

26303

20965

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

37.201

26304

14477

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

37.228

26305

11561

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

37.268

26306

13714

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

37.271

26307

6000

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

37.306

26308

13618

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

37.344

26309

13381

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

37.366

26310

11847

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

37.400

26311

9117

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

37.408

26312

13477

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

37.438

26313

15134

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

37.488

26314

15568

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

37.537

26315

24387

\begin{align*} \left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \\ \end{align*}

37.600

26316

5912

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

37.666

26317

11643

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

37.694

26318

9346

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

37.808

26319

22556

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

37.852

26320

5345

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

37.925

26321

16210

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

37.944

26322

672

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

37.945

26323

6985

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

37.994

26324

22546

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

37.996

26325

15363

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

38.015

26326

26392

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

38.037

26327

5109

\begin{align*} \left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y&=0 \\ \end{align*}

38.056

26328

21433

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

38.070

26329

13478

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

38.082

26330

12651

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

38.092

26331

5147

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

38.129

26332

6486

\begin{align*} 3 y y^{\prime \prime }&=36 y^{2}+2 {y^{\prime }}^{2} \\ \end{align*}

38.148

26333

23893

\begin{align*} 20 y-20 x y^{2}+\left (5 x -8 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

38.162

26334

13330

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

38.192

26335

6842

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

38.214

26336

17974

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

38.215

26337

6919

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

38.230

26338

4319

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

38.327

26339

6337

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

38.327

26340

4375

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

38.342

26341

4350

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

38.349

26342

25089

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

38.428

26343

13362

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

38.474

26344

5173

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

38.523

26345

5994

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

38.556

26346

22019

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

38.560

26347

2945

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

38.592

26348

22387

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

38.598

26349

18593

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

38.631

26350

3653

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

38.632

26351

6943

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

38.673

26352

5993

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

38.697

26353

21275

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

38.700

26354

21033

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

38.750

26355

2955

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

38.757

26356

20313

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

38.772

26357

13647

\begin{align*} y^{\prime }&=a \,x^{n} y^{3}+3 a b \,x^{n +m} y^{2}+c \,x^{k} y-2 a \,b^{3} x^{n +3 m}+b c \,x^{m +k}-b m \,x^{m -1} \\ \end{align*}

38.784

26358

14465

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

38.812

26359

24340

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

38.848

26360

13423

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

38.853

26361

12004

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

38.889

26362

14439

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

38.899

26363

6190

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

38.902

26364

5060

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

38.924

26365

9204

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

38.926

26366

10322

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

38.938

26367

4332

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

38.996

26368

13265

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

39.024

26369

13275

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

39.050

26370

13576

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

39.060

26371

6359

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

39.098

26372

13426

\begin{align*} x y^{\prime }&=\lambda \arcsin \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arcsin \left (x \right )^{n} \\ \end{align*}

39.107

26373

21044

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

39.113

26374

22758

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

39.151

26375

18616

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

39.157

26376

3650

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

39.160

26377

5340

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

39.235

26378

5924

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

39.273

26379

5072

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

39.344

26380

13280

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

39.348

26381

13324

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

39.382

26382

22738

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

39.411

26383

19351

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

39.433

26384

22597

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

39.455

26385

21985

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

39.456

26386

6897

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

39.544

26387

24325

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

39.565

26388

4713

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

39.566

26389

5992

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

39.598

26390

17340

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

39.620

26391

21835

\begin{align*} 4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime }&=0 \\ \end{align*}

39.650

26392

5128

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

39.667

26393

12169

\begin{align*} y^{\prime }&=-\frac {\left (-8-8 y^{3}+24 y^{{3}/{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{{9}/{2}}+36 y^{3} {\mathrm e}^{x}-54 y^{{3}/{2}} {\mathrm e}^{2 x}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \\ \end{align*}

39.689

26394

4509

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

39.734

26395

12622

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

39.792

26396

5951

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\ \end{align*}

39.799

26397

15029

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

39.815

26398

13347

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

39.824

26399

8710

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

39.842

26400

24359

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

39.858