2.3.246 Problems 24501 to 24600

Table 2.1035: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24501

12862

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

31.650

24502

2896

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

31.692

24503

4250

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

31.743

24504

13238

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

31.760

24505

12483

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

31.777

24506

4330

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

31.793

24507

12316

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

31.793

24508

6023

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

31.824

24509

2669

\begin{align*} t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y&=0 \\ \end{align*}
Series expansion around \(t=0\).

31.826

24510

2880

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

31.872

24511

22288

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

31.884

24512

12345

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

31.888

24513

15480

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

31.896

24514

11994

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

31.900

24515

12383

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

31.915

24516

11534

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

31.928

24517

12082

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

31.966

24518

7408

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

31.998

24519

19720

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

32.002

24520

12329

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

32.010

24521

24331

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

32.038

24522

20246

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

32.050

24523

24202

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

32.056

24524

13241

\begin{align*} y^{\prime } x +a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0}&=0 \\ \end{align*}

32.063

24525

13846

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

32.063

24526

25261

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

32.066

24527

24358

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

32.078

24528

2525

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

32.087

24529

13574

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

32.128

24530

10313

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

32.129

24531

7485

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

32.130

24532

12323

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

32.147

24533

5988

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

32.151

24534

7348

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

32.198

24535

24234

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

32.202

24536

9019

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

32.267

24537

13472

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

32.284

24538

12340

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

32.326

24539

2351

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

32.331

24540

23945

\begin{align*} y^{\prime }&=\frac {1}{x^{5}+y x} \\ \end{align*}

32.361

24541

10311

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

32.365

24542

17891

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

32.373

24543

15940

\begin{align*} y^{\prime }&=-\sin \left (y\right )^{5} \\ \end{align*}

32.380

24544

7475

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

32.416

24545

13564

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

32.429

24546

2327

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

32.434

24547

7008

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

32.454

24548

26154

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

32.455

24549

14271

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

32.470

24550

6025

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

32.496

24551

25016

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

32.503

24552

4252

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

32.527

24553

6590

\begin{align*} 6 y y^{\prime \prime }-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+\left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}&=36 x {y^{\prime }}^{2} \\ \end{align*}

32.533

24554

3461

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

32.540

24555

20718

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

32.543

24556

5055

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

32.548

24557

22415

\begin{align*} r^{\prime }&=\frac {r \sin \left (t \right )}{2 r \cos \left (t \right )-1} \\ \end{align*}

32.559

24558

21816

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

32.572

24559

13486

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

32.608

24560

3307

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

32.611

24561

17285

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

32.631

24562

9782

\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*}

32.634

24563

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*}

32.648

24564

22442

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

32.649

24565

17233

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

32.657

24566

7523

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

32.658

24567

13569

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

32.718

24568

11973

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

32.733

24569

12327

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

32.754

24570

13735

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

32.756

24571

20191

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

32.770

24572

12532

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

32.771

24573

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*}

32.773

24574

22396

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

32.789

24575

4255

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

32.814

24576

12851

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

32.821

24577

18611

\begin{align*} 3 y^{\prime } t +9 y&=2 t y^{{5}/{3}} \\ \end{align*}

32.851

24578

17920

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

32.863

24579

12482

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

32.892

24580

17272

\begin{align*} y^{\prime }&=\frac {t +4 y}{4 t +y} \\ \end{align*}

32.908

24581

12572

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

32.918

24582

4286

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

32.934

24583

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*}

32.935

24584

9134

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

32.974

24585

22411

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

33.040

24586

5379

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

33.053

24587

22420

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

33.068

24588

5003

\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\ \end{align*}

33.129

24589

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*}

33.146

24590

2927

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

33.147

24591

2526

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

33.151

24592

17112

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

33.186

24593

4357

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

33.208

24594

1622

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

33.316

24595

20252

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

33.365

24596

9131

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

33.373

24597

17921

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

33.392

24598

16241

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

33.426

24599

13350

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

33.437

24600

11405

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

33.500