2.3.237 Problems 23601 to 23700

Table 2.1047: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23601

17050

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}

10.347

23602

16344

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

10.349

23603

13391

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

10.350

23604

4794

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

10.358

23605

13262

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

10.358

23606

5333

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

10.361

23607

15035

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

10.363

23608

13456

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

10.366

23609

2499

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

10.371

23610

20244

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

10.372

23611

12156

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

10.376

23612

25695

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

10.377

23613

5709

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

10.381

23614

25045

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

10.382

23615

13796

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

10.385

23616

17928

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

10.386

23617

25483

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

10.388

23618

9781

\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*}

10.392

23619

19820

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

10.398

23620

19821

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

10.398

23621

16254

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

10.401

23622

17075

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

10.402

23623

17220

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

10.402

23624

25011

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

10.404

23625

5949

\begin{align*} \left (b x +a \right ) y+8 y^{\prime }+16 x y^{\prime \prime }&=0 \\ \end{align*}

10.405

23626

19822

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

10.405

23627

18849

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

10.407

23628

14825

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

10.409

23629

14018

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

10.411

23630

21159

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

10.412

23631

23147

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

10.415

23632

20249

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

10.421

23633

18936

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

10.422

23634

12384

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

10.425

23635

13709

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

10.425

23636

20019

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

10.427

23637

8266

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

10.430

23638

27294

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

10.431

23639

15491

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

10.433

23640

1246

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

10.434

23641

7479

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

10.434

23642

1162

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

10.436

23643

7247

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

10.441

23644

22075

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

10.457

23645

4508

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

10.459

23646

5344

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

10.463

23647

14544

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

10.463

23648

15234

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+5 y&=25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

10.463

23649

5657

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

10.464

23650

13679

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

10.466

23651

17064

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

10.471

23652

11522

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

10.477

23653

5511

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

10.483

23654

20253

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

10.483

23655

18935

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right . \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

10.485

23656

12115

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

10.486

23657

12855

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

10.487

23658

11518

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

10.489

23659

13661

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

10.491

23660

5450

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

10.494

23661

12031

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

10.494

23662

6809

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

10.500

23663

12189

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

10.502

23664

3048

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

10.503

23665

7876

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

10.503

23666

14452

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

10.504

23667

13461

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

10.508

23668

27552

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

10.520

23669

4085

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

10.522

23670

11580

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

10.523

23671

13236

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

10.526

23672

17263

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

10.539

23673

1647

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

10.547

23674

15504

\begin{align*} {y^{\prime }}^{2}-9 y x&=0 \\ \end{align*}

10.547

23675

2854

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

10.553

23676

4801

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

10.555

23677

27236

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

10.556

23678

12007

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

10.558

23679

7873

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

10.563

23680

25497

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

10.564

23681

13729

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

10.578

23682

6046

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

10.596

23683

17877

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

10.597

23684

2852

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

10.598

23685

15378

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

10.599

23686

17923

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

10.606

23687

25491

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

10.610

23688

3230

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

10.615

23689

2289

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

10.616

23690

15402

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

10.617

23691

5548

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

10.619

23692

26903

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

10.622

23693

25802

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

10.624

23694

5187

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

10.626

23695

13629

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

10.636

23696

13681

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

10.639

23697

5908

\begin{align*} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+a y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}

10.646

23698

12109

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

10.651

23699

11523

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

10.654

23700

16294

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

10.657