2.3.226 Problems 22501 to 22600

Table 2.1025: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22501

12041

\begin{align*} y^{\prime }&=-\frac {i \left (54 i x^{2}+81 y^{4}+18 y^{2} x^{4}+x^{8}\right ) x}{243 y} \\ \end{align*}

7.391

22502

6993

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

7.392

22503

5008

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

7.394

22504

13305

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

7.394

22505

13780

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

7.394

22506

4310

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

7.395

22507

12177

\begin{align*} y^{\prime }&=\frac {\left (-108 x^{{3}/{2}} y+18 x^{{9}/{2}}-108 x^{{3}/{2}}-216 y^{3}+108 x^{3} y^{2}-18 x^{6} y+x^{9}\right ) \sqrt {x}}{-216 y+36 x^{3}-216} \\ \end{align*}

7.395

22508

12405

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

7.396

22509

9520

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

Series expansion around \(x=1\).

7.398

22510

4211

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

7.401

22511

15530

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

7.401

22512

11970

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

7.402

22513

8343

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

7.404

22514

14258

\begin{align*} \cos \left (\theta \right ) v^{\prime }+v&=3 \\ \end{align*}

7.405

22515

5159

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

7.408

22516

23153

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

7.411

22517

123

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

7.414

22518

11552

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

7.414

22519

22207

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

Series expansion around \(x=0\).

7.414

22520

6812

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

7.415

22521

11632

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

7.416

22522

11697

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

7.416

22523

8322

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

7.417

22524

6553

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

7.421

22525

24840

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

7.421

22526

22223

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

Series expansion around \(x=0\).

7.425

22527

27472

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

7.425

22528

9973

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

7.426

22529

5132

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

7.428

22530

13450

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

7.430

22531

5190

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

7.431

22532

9926

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

Series expansion around \(x=0\).

7.433

22533

14459

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

7.433

22534

19177

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

7.435

22535

19797

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

7.441

22536

8180

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

7.448

22537

5041

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

7.451

22538

26893

\begin{align*} x \cos \left (x -2 y\right )+\sin \left (x -2 y\right )-2 x \cos \left (x -2 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\ \end{align*}

7.454

22539

10416

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

7.464

22540

5370

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

7.469

22541

16296

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

7.469

22542

11947

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

7.472

22543

4109

\begin{align*} 2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right )&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\ \end{align*}

7.473

22544

12701

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

7.473

22545

24968

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

7.473

22546

6125

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

7.474

22547

18034

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

7.474

22548

22440

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

7.474

22549

2336

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

7.477

22550

11347

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

7.477

22551

19939

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

7.480

22552

26082

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

7.483

22553

7147

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

7.488

22554

114

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

7.489

22555

12192

\begin{align*} y^{\prime }&=\frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\ \end{align*}

7.492

22556

20283

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

7.493

22557

18606

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

7.494

22558

8372

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

7.496

22559

22608

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

7.496

22560

9011

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

7.497

22561

11866

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

7.497

22562

22989

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

7.497

22563

5852

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

7.500

22564

8290

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

7.500

22565

22069

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

7.503

22566

1594

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

7.504

22567

12029

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

7.506

22568

14248

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

7.506

22569

15337

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

7.510

22570

18932

\begin{align*} y^{\prime \prime \prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= 7 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ y^{\prime \prime \prime }\left (0\right ) &= -9 \\ \end{align*}

Using Laplace transform method.

7.510

22571

9597

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

Series expansion around \(x=0\).

7.517

22572

24173

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

7.523

22573

25057

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

7.525

22574

1725

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

7.526

22575

21846

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

7.526

22576

3568

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

7.527

22577

1696

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

7.530

22578

18623

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

7.530

22579

11663

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

7.531

22580

27504

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

7.541

22581

8349

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

7.542

22582

11936

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

7.544

22583

12150

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

7.546

22584

17946

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

7.546

22585

8398

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

7.549

22586

17327

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

7.549

22587

14004

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

7.553

22588

4291

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

7.562

22589

4952

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

7.562

22590

13283

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

7.562

22591

22978

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

7.562

22592

22995

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

7.564

22593

1597

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

7.565

22594

8788

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

7.565

22595

4832

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

7.566

22596

6868

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

7.566

22597

6960

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

7.566

22598

19714

\begin{align*} x^{\prime }&=k \left (A -n x\right ) \left (M -m x\right ) \\ \end{align*}

7.576

22599

22036

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

7.576

22600

12223

\begin{align*} y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 x^{2} y^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \\ \end{align*}

7.579