2.3.135 Problems 13401 to 13500

Table 2.801: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13401

11835

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

0.845

13402

12633

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

0.845

13403

15885

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

0.845

13404

16675

\begin{align*} y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \\ \end{align*}

0.845

13405

17115

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

0.845

13406

18663

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

0.845

13407

20055

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

0.845

13408

20623

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

0.845

13409

5545

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

0.846

13410

6529

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

0.846

13411

9949

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.846

13412

15801

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

0.846

13413

18149

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

0.846

13414

19013

\begin{align*} x_{1}^{\prime }&=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2} \\ x_{2}^{\prime }&=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2} \\ x_{3}^{\prime }&=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2} \\ \end{align*}

0.846

13415

1825

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

0.847

13416

15279

\begin{align*} x^{\prime }&=-4 x+9 y+12 \,{\mathrm e}^{-t} \\ y^{\prime }&=-5 x+2 y \\ \end{align*}

0.847

13417

22079

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

0.847

13418

23229

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

0.847

13419

23615

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

0.847

13420

25311

\begin{align*} y^{\prime \prime }-y&=\delta \left (-1+t \right )-\delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.847

13421

11758

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

0.848

13422

12618

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

0.848

13423

15033

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

0.848

13424

18436

\begin{align*} x^{\prime }+2 x-y&=-{\mathrm e}^{2 t} \\ y^{\prime }+3 x-2 y&=6 \,{\mathrm e}^{2 t} \\ \end{align*}

0.848

13425

20464

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

0.848

13426

23230

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

0.848

13427

2086

\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.849

13428

3966

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=-10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.849

13429

5048

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

0.849

13430

5887

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

0.849

13431

7040

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

0.849

13432

13850

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

0.849

13433

20767

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

0.849

13434

21944

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

0.849

13435

5765

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

0.850

13436

9053

\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}

0.850

13437

22339

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

0.850

13438

2765

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}+{\mathrm e}^{3 t} \\ \end{align*}

0.851

13439

6183

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

0.851

13440

7670

\begin{align*} x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x&=F \cos \left (\omega t \right ) \\ \end{align*}

0.851

13441

15458

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

0.851

13442

16050

\begin{align*} x^{\prime }&=-10 x+10 y \\ y^{\prime }&=28 x-y \\ z^{\prime }&=-\frac {8 z}{3} \\ \end{align*}

0.851

13443

16485

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

0.851

13444

16570

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

0.851

13445

20551

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

0.851

13446

22350

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

0.851

13447

3358

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

0.852

13448

3363

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

0.852

13449

4598

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

0.852

13450

8252

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

0.852

13451

8772

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

0.852

13452

9550

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

0.852

13453

10266

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

0.852

13454

12982

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

0.852

13455

13826

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

0.852

13456

15232

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.852

13457

17711

\begin{align*} 9 y^{\prime \prime } x +14 y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.852

13458

20458

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

0.852

13459

3263

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

0.853

13460

19519

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

0.853

13461

2437

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

0.854

13462

20087

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

0.854

13463

25418

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

0.854

13464

5430

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

0.855

13465

8770

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

0.855

13466

9904

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

0.855

13467

10395

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

0.855

13468

15329

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

0.855

13469

19702

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

0.855

13470

6878

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

0.856

13471

8414

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \\ y \left (0\right ) &= 2 \\ \end{align*}

0.856

13472

9037

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

0.856

13473

9680

\begin{align*} x^{\prime }&=-x-y \\ y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\ \end{align*}

0.856

13474

15251

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.856

13475

15726

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \delta \left (x -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.856

13476

17531

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

0.856

13477

18365

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

0.856

13478

20801

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

0.856

13479

23329

\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}

0.856

13480

24830

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

0.856

13481

25299

\begin{align*} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.856

13482

7309

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

0.857

13483

25043

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

0.857

13484

1823

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=8 x^{{5}/{2}} \\ \end{align*}

0.858

13485

2465

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

0.858

13486

3971

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

0.858

13487

16714

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

0.858

13488

16922

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

0.858

13489

18178

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

0.858

13490

18450

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

0.858

13491

22743

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

0.858

13492

5875

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

0.859

13493

7261

\begin{align*} y^{\prime \prime }+9 y^{\prime }&=0 \\ \end{align*}

0.859

13494

9905

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

0.859

13495

10273

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

0.859

13496

14706

\begin{align*} 9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}

0.859

13497

16482

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

0.859

13498

20441

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

0.859

13499

22767

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

0.859

13500

2528

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

0.860