2.3.246 Problems 24501 to 24600

Table 2.1023: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24501

11931

\begin{align*} y^{\prime }&=-\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\ \end{align*}

25.451

24502

11843

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

25.505

24503

20239

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

25.508

24504

7545

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

25.513

24505

11484

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

25.520

24506

19402

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

25.569

24507

20696

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

25.577

24508

6106

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

25.581

24509

13454

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

25.589

24510

24354

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

25.605

24511

24380

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

25.697

24512

6400

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

25.708

24513

19924

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

25.785

24514

8870

\begin{align*} y^{\prime }+3 y&={\mathrm e}^{i x} \\ \end{align*}

25.819

24515

3322

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

25.825

24516

15568

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

25.853

24517

19304

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

25.913

24518

19767

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

25.940

24519

11608

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

25.954

24520

8159

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

25.964

24521

11744

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

25.982

24522

18535

\begin{align*} y \cos \left (t \right )+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\ y \left (1\right ) &= a \\ \end{align*}

26.003

24523

23215

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

26.021

24524

21062

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

26.037

24525

13532

\begin{align*} y^{\prime } y-y&=A \,x^{2}-\frac {9}{625 A} \\ \end{align*}

26.084

24526

19721

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

26.090

24527

19913

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

26.100

24528

21834

\begin{align*} 2+3 x -5 y+7 y^{\prime }&=0 \\ \end{align*}

26.126

24529

12403

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

26.161

24530

22433

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

26.165

24531

24358

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

26.188

24532

21842

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

26.202

24533

3682

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

26.218

24534

15644

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

26.237

24535

14275

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

26.258

24536

15869

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

26.294

24537

15850

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

26.312

24538

16153

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

26.329

24539

6829

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

26.371

24540

19215

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

26.372

24541

2335

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

26.373

24542

13372

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

26.421

24543

5546

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

26.464

24544

24363

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

26.469

24545

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*}

26.478

24546

17967

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

26.503

24547

12930

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

26.522

24548

15134

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

26.590

24549

11774

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

26.592

24550

21005

\begin{align*} x^{\prime }+\frac {\left (2 t^{3}+\sin \left (t \right )+5\right ) x}{t^{12}+5}&=0 \\ x \left (0\right ) &= 0 \\ \end{align*}

26.614

24551

9828

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

26.625

24552

21377

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

26.637

24553

11993

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

26.657

24554

4111

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

26.700

24555

1147

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

26.733

24556

24322

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

26.752

24557

24404

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

26.756

24558

17275

\begin{align*} 2 t^{2}-7 t y+5 y^{2}+t y y^{\prime }&=0 \\ \end{align*}

26.759

24559

19306

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

26.764

24560

11534

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

26.767

24561

1123

\begin{align*} y \cos \left (t \right )+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\ y \left (1\right ) &= a \\ \end{align*}

26.772

24562

21422

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

26.784

24563

21033

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

26.794

24564

21922

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

26.830

24565

21796

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

26.850

24566

2905

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

26.858

24567

23207

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

26.858

24568

24408

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

26.865

24569

793

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

26.871

24570

11366

\begin{align*} y^{\prime }-\sqrt {\frac {y^{3}+1}{x^{3}+1}}&=0 \\ \end{align*}

26.889

24571

3289

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

26.915

24572

5110

\begin{align*} \left (5-x +6 y\right ) y^{\prime }&=3-x +4 y \\ \end{align*}

26.954

24573

5205

\begin{align*} x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\ \end{align*}

26.961

24574

20821

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

26.973

24575

3478

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

26.985

24576

2525

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

26.987

24577

13485

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

27.010

24578

13803

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

27.056

24579

5090

\begin{align*} \left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\ \end{align*}

27.111

24580

24406

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

27.115

24581

19962

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

27.120

24582

15256

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

27.226

24583

17086

\begin{align*} x^{\prime }&=\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \\ \end{align*}

27.240

24584

4961

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

27.248

24585

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*}

27.299

24586

2526

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

27.308

24587

16231

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

27.312

24588

11645

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

27.323

24589

4311

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

27.336

24590

20870

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

27.446

24591

8702

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

27.450

24592

5166

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

27.512

24593

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*}

27.518

24594

6145

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

27.532

24595

21262

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

27.558

24596

21074

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

27.622

24597

17765

\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

27.691

24598

21087

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

27.693

24599

6564

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

27.697

24600

24387

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

27.732