2.3.266 Problems 26501 to 26600

Table 2.1105: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

26501

27001

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y&=0 \\ \end{align*}

43.913

26502

10196

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

43.957

26503

20257

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

43.992

26504

25037

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

44.018

26505

6047

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

44.084

26506

21107

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

44.109

26507

6822

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

44.114

26508

21094

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

44.142

26509

25863

\begin{align*} y^{\prime }-2 y x&=6 y \,{\mathrm e}^{y^{2}} \\ \end{align*}

44.191

26510

4807

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

44.266

26511

20568

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

44.277

26512

13493

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

44.309

26513

2514

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

44.401

26514

8730

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

44.425

26515

24283

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

44.437

26516

2889

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

44.542

26517

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*}

44.560

26518

6295

\begin{align*} \left (\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a0} \right ) y+a^{2} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1-a^{2} \cos \left (x \right )^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}

44.580

26519

11620

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

44.650

26520

8702

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

44.678

26521

13424

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

44.690

26522

6814

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

44.753

26523

22411

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

44.822

26524

20874

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

44.911

26525

27444

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

44.915

26526

13439

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

44.935

26527

5337

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

44.964

26528

26617

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y&=0 \\ \end{align*}

44.965

26529

5690

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

44.994

26530

6801

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

45.109

26531

5167

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

45.112

26532

3289

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

45.158

26533

6830

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

45.234

26534

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*}

45.243

26535

9019

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

45.260

26536

15019

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

45.279

26537

5780

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

45.355

26538

6446

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

45.384

26539

5076

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

45.416

26540

6151

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

45.450

26541

12935

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

45.460

26542

20961

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

45.507

26543

22407

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

45.534

26544

5050

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

45.542

26545

20990

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

45.546

26546

16257

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

45.574

26547

7129

\begin{align*} r^{\prime \prime }&=\frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \\ \end{align*}

45.634

26548

4112

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

45.636

26549

2902

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

45.651

26550

13307

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

45.667

26551

9756

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

45.684

26552

13762

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

45.713

26553

5118

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

45.737

26554

13830

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

45.751

26555

6009

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

45.753

26556

5092

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

45.758

26557

18289

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}

45.793

26558

21388

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

45.870

26559

13535

\begin{align*} y y^{\prime }-y&=12 x +\frac {A}{x^{{5}/{2}}} \\ \end{align*}

45.901

26560

22383

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

45.917

26561

3004

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

45.951

26562

24963

\begin{align*} y^{\prime }&=t^{m} y^{n} \\ \end{align*}

45.994

26563

5238

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

46.066

26564

25516

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

46.082

26565

1664

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

46.084

26566

12034

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

46.159

26567

25729

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y^{\prime }\left (\frac {\pi }{3}\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}

46.186

26568

6310

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

46.217

26569

26668

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

46.219

26570

13437

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

46.244

26571

18734

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

46.302

26572

6010

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

46.320

26573

25882

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

46.335

26574

6989

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

46.384

26575

22773

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

46.418

26576

21969

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

46.419

26577

8156

\begin{align*} R^{\prime \prime }&=-\frac {k}{R^{2}} \\ \end{align*}

46.433

26578

5149

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

46.471

26579

1622

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

46.484

26580

6166

\begin{align*} -y-8 x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

46.590

26581

7000

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

46.592

26582

21277

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

46.713

26583

5077

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

46.784

26584

5115

\begin{align*} \left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y&=0 \\ \end{align*}

46.876

26585

15348

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

46.894

26586

10195

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

46.897

26587

24822

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

46.932

26588

13432

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

46.966

26589

15557

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

46.973

26590

6245

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

47.119

26591

13767

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

47.128

26592

5359

\begin{align*} {y^{\prime }}^{2}+3 x^{2}&=8 y \\ \end{align*}

47.168

26593

13390

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

47.328

26594

5489

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

47.369

26595

13968

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

47.372

26596

9661

\begin{align*} x^{\prime }&=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }&=4 x+y+z+2 \,{\mathrm e}^{5 t} \\ z^{\prime }&=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \\ \end{align*}

47.398

26597

22530

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

47.430

26598

13373

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

47.472

26599

13561

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

47.483

26600

12652

\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 )^{2}-4 n^{2} x \right ) y}{4 x^{2} \left (x -1\right )^{2}} \\ \end{align*}

47.519