2.3.256 Problems 25501 to 25600

Table 2.1085: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25501

27255

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

23.783

25502

6299

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

23.791

25503

15345

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

23.822

25504

11904

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

23.837

25505

20021

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

23.838

25506

4252

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

23.849

25507

13761

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

23.855

25508

6414

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

23.861

25509

15832

\begin{align*} \theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\ \end{align*}

23.875

25510

1666

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

23.878

25511

18288

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}

23.891

25512

13281

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

23.894

25513

11543

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

23.895

25514

11755

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

23.902

25515

26327

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

23.904

25516

15850

\begin{align*} \theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\ \theta \left (0\right ) &= 1 \\ \end{align*}

23.905

25517

11679

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

23.918

25518

17112

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

23.931

25519

17966

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

23.944

25520

9196

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

23.948

25521

4665

\begin{align*} y^{\prime }&=\left (1+4 x +9 y\right )^{2} \\ \end{align*}

23.953

25522

23191

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

23.953

25523

5241

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

23.954

25524

26607

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

23.957

25525

25506

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

23.996

25526

19810

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

23.999

25527

27697

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

24.019

25528

22406

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

24.027

25529

5057

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

24.034

25530

18067

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

24.056

25531

39

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

24.063

25532

18057

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

24.073

25533

15045

\begin{align*} x^{\prime }+5 x&=10 t +2 \\ x \left (1\right ) &= 2 \\ \end{align*}

24.079

25534

21087

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

24.088

25535

14479

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

24.094

25536

18284

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

24.101

25537

17921

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

24.181

25538

26199

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

24.191

25539

24345

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

24.196

25540

15017

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

24.208

25541

24233

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

24.211

25542

14548

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

24.212

25543

10071

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

24.213

25544

11540

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

24.213

25545

11633

\begin{align*} \left (\frac {\operatorname {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right )&=0 \\ \end{align*}

24.221

25546

11369

\begin{align*} y^{\prime }-\sqrt {\frac {y^{4} a +b y^{2}+1}{a \,x^{4}+b \,x^{2}+1}}&=0 \\ \end{align*}

24.225

25547

14526

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

24.229

25548

17276

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

24.272

25549

17979

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

24.286

25550

7501

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

24.296

25551

13383

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

24.298

25552

22025

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

24.299

25553

11695

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

24.312

25554

25666

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

24.324

25555

17914

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

24.330

25556

20178

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \\ \end{align*}

24.334

25557

4400

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

24.336

25558

1718

\begin{align*} 6 x y^{2}+2 y+\left (12 x^{2} y+6 x +3\right ) y^{\prime }&=0 \\ \end{align*}

24.337

25559

5309

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

24.353

25560

10044

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

24.362

25561

23864

\begin{align*} x \left (6 x^{2}+14 y^{2}\right )+y \left (13 x^{2}+30 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

24.363

25562

21430

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

24.365

25563

13430

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

24.370

25564

20439

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

24.375

25565

12408

\begin{align*} 5 \left (a x +b \right ) y^{\prime \prime }+8 a y^{\prime }+c \left (a x +b \right )^{{1}/{5}} y&=0 \\ \end{align*}

24.414

25566

11541

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

24.423

25567

2956

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

24.454

25568

22358

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

24.460

25569

21366

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

24.475

25570

7545

\begin{align*} 2 x -2 y-8+\left (x -3 y-6\right ) y^{\prime }&=0 \\ \end{align*}

24.506

25571

20281

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

24.520

25572

20594

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

24.520

25573

6357

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

24.566

25574

19144

\begin{align*} a^{3} y^{\prime \prime \prime } y^{\prime \prime }&=\sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \\ \end{align*}

24.574

25575

7713

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

24.576

25576

5108

\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\ \end{align*}

24.580

25577

16153

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

24.619

25578

18626

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

24.655

25579

5708

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

24.658

25580

5593

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

24.661

25581

12106

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

24.663

25582

24166

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

24.667

25583

22348

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

24.682

25584

22385

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

24.693

25585

25880

\begin{align*} y^{\prime }&=\frac {6 x^{2}-7 y^{2}}{14 y x} \\ \end{align*}

24.695

25586

22540

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

24.705

25587

5331

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

24.711

25588

5080

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

24.723

25589

12411

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

24.736

25590

11657

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

24.756

25591

22958

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

24.758

25592

2979

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

24.763

25593

9149

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

24.771

25594

24409

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

24.778

25595

5869

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

24.802

25596

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*}

24.812

25597

25705

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

24.825

25598

5073

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

24.890

25599

12572

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

24.910

25600

20263

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

24.910