2.3.246 Problems 24501 to 24600

Table 2.1065: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24501

2506

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

11.963

24502

13731

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

11.976

24503

7000

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

11.978

24504

5203

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

11.984

24505

4252

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

11.994

24506

739

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

11.995

24507

20248

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

11.997

24508

27537

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

12.006

24509

26400

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

12.010

24510

5068

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

12.014

24511

13232

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

12.024

24512

27391

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

12.024

24513

15353

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

12.030

24514

4247

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

12.033

24515

7419

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

12.033

24516

24173

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

12.034

24517

1815

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

12.042

24518

11971

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

12.043

24519

11954

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

12.046

24520

1655

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

12.049

24521

1706

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

12.069

24522

11952

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

12.075

24523

19329

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

12.076

24524

7856

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

12.077

24525

21808

\begin{align*} 3 x^{2}+2 y x +4 y^{2}+\left (20 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

12.077

24526

20962

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

12.080

24527

12234

\begin{align*} y^{\prime }&=\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 \sqrt {x}\, y+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 x^{6} y+600 y x^{{7}/{2}}+1500 y x -8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x} \\ \end{align*}

12.083

24528

19315

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

12.085

24529

20688

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

12.085

24530

27304

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

12.095

24531

12200

\begin{align*} y^{\prime }&=\frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 x y^{5}+y^{5}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\ \end{align*}

12.099

24532

5053

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

12.103

24533

13693

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

12.106

24534

8701

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

12.110

24535

20405

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

12.111

24536

17099

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

12.115

24537

21396

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

12.115

24538

7163

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

12.119

24539

11566

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

12.122

24540

14479

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

12.125

24541

17223

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

12.125

24542

27234

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

12.128

24543

6989

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

12.136

24544

12208

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

12.151

24545

23885

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

12.155

24546

21840

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

12.176

24547

20429

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

12.178

24548

14043

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

12.180

24549

2872

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

12.186

24550

5108

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

12.187

24551

1622

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

12.188

24552

24957

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

12.193

24553

6073

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

12.200

24554

14532

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

12.206

24555

15509

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

12.220

24556

25666

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

12.226

24557

11499

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

12.227

24558

19821

\begin{align*} \left (5 x -2 y+7\right ) y^{\prime }&=10 x -4 y+6 \\ \end{align*}

12.227

24559

26867

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

12.227

24560

26391

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

12.248

24561

5319

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

12.249

24562

3681

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

12.254

24563

19820

\begin{align*} \left (x -3 y+4\right ) y^{\prime }&=2 x -6 y+7 \\ \end{align*}

12.254

24564

13719

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

12.255

24565

23945

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

12.260

24566

26335

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

12.266

24567

18591

\begin{align*} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\ \end{align*}

12.285

24568

23119

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

12.287

24569

5925

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

12.290

24570

27398

\begin{align*} y&=3 y^{\prime } x -7 {y^{\prime }}^{3} \\ \end{align*}

12.291

24571

3277

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

12.295

24572

9657

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

12.296

24573

12152

\begin{align*} y^{\prime }&=\frac {-30 x^{3} y+12 x^{6}+70 x^{{7}/{2}}-30 x^{3}-25 \sqrt {x}\, y+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\ \end{align*}

12.299

24574

3471

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

12.303

24575

12061

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

12.306

24576

21260

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

12.310

24577

19236

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

12.313

24578

19822

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

12.319

24579

20960

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

12.322

24580

1657

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

12.329

24581

8378

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

12.332

24582

13012

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

12.332

24583

13490

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

12.335

24584

13234

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

12.336

24585

7254

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

12.342

24586

14270

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

12.347

24587

5975

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

12.349

24588

3482

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

12.355

24589

22738

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

12.362

24590

19712

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

12.363

24591

12166

\begin{align*} y^{\prime }&=\frac {2 x^{2}-4 x^{3} y+1+y^{2} x^{4}+x^{6} y^{3}-3 x^{5} y^{2}+3 x^{4} y-x^{3}}{x^{4}} \\ \end{align*}

12.364

24592

6244

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

12.371

24593

22385

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

12.375

24594

3568

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

12.395

24595

18483

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

12.395

24596

11918

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

12.401

24597

9158

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

12.411

24598

21428

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

12.414

24599

18572

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

12.428

24600

25492

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

12.447