2.3.45 Problems 4401 to 4500

Table 2.621: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

4401

20592

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

0.240

4402

22189

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

0.240

4403

829

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

0.241

4404

1277

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}

0.241

4405

2674

\begin{align*} y^{\prime \prime }+3 y^{\prime }+7 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.241

4406

3066

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

0.241

4407

3197

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

0.241

4408

3789

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

0.241

4409

7335

\begin{align*} r^{\prime \prime }-6 r^{\prime }+9 r&=0 \\ \end{align*}

0.241

4410

7593

\begin{align*} 3 y^{\prime \prime }+11 y^{\prime }-7 y&=0 \\ \end{align*}

0.241

4411

7730

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

0.241

4412

7882

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

0.241

4413

9882

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

0.241

4414

10875

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

0.241

4415

11062

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}

0.241

4416

11295

\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 \left (x -1\right ) x}\right ) y \\ \end{align*}

0.241

4417

12724

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

0.241

4418

13138

\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 1 \end {array}\right ]\)

N/A

N/A

N/A

0.241

4419

18767

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

0.241

4420

20112

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

0.241

4421

20465

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

0.241

4422

20540

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

0.241

4423

22805

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

0.241

4424

22823

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

0.241

4425

23026

\begin{align*} y^{\prime \prime }-5 y^{\prime }+8 y&=0 \\ \end{align*}

0.241

4426

23431

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

0.241

4427

24660

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=20 \,{\mathrm e}^{-4 x} \\ \end{align*}

0.241

4428

24693

\begin{align*} 4 y+y^{\prime \prime }&=8 x^{5} \\ \end{align*}

0.241

4429

25103

\begin{align*} 2 y^{\prime \prime }-12 y^{\prime }+18 y&=0 \\ \end{align*}

0.241

4430

25240

\begin{align*} t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\ \end{align*}
Using Laplace transform method.

0.241

4431

25539

\begin{align*} 4 y^{\prime \prime }+B y^{\prime }+16 y&=0 \\ \end{align*}

0.241

4432

782

\begin{align*} 6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

0.242

4433

9820

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

0.242

4434

10488

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

0.242

4435

11010

\begin{align*} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}

0.242

4436

13139

\(\left [\begin {array}{cc} 5 & -6 \\ 3 & -4 \end {array}\right ]\)

N/A

N/A

N/A

0.242

4437

14636

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \\ \end{align*}

0.242

4438

15217

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.242

4439

15414

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

0.242

4440

16395

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

0.242

4441

19548

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

0.242

4442

20028

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

0.242

4443

22840

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

0.242

4444

24700

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=72 x \,{\mathrm e}^{-x} \\ \end{align*}

0.242

4445

24890

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

0.242

4446

853

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}

0.243

4447

1047

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

0.243

4448

1053

\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*}
Series expansion around \(x=0\).

0.243

4449

3996

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.243

4450

6301

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

0.243

4451

7376

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

0.243

4452

8115

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

0.243

4453

8763

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

0.243

4454

9171

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

0.243

4455

9216

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

0.243

4456

9367

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

0.243

4457

10255

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

0.243

4458

10338

\begin{align*} t y^{\prime }+y&=0 \\ y \left (1\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

0.243

4459

10812

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

0.243

4460

10975

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}

0.243

4461

11131

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

0.243

4462

11168

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

0.243

4463

11220

\begin{align*} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\ \end{align*}

0.243

4464

14195

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

0.243

4465

14795

\(\left [\begin {array}{cc} 1 & 2 \\ 3 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.243

4466

16023

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

0.243

4467

16988

\begin{align*} y^{\prime }&=\frac {\sqrt {x^{2}-16}}{x} \\ \end{align*}

0.243

4468

18760

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

0.243

4469

20412

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

0.243

4470

20840

\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ \end{align*}

0.243

4471

22815

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

0.243

4472

23359

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

0.243

4473

23444

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

0.243

4474

431

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.244

4475

1048

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

0.244

4476

6438

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

0.244

4477

7360

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

0.244

4478

7368

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

0.244

4479

8121

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

0.244

4480

8341

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

0.244

4481

8632

\begin{align*} y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4}&=9 t^{3}+64 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {63}{2}} \\ \end{align*}
Using Laplace transform method.

0.244

4482

9027

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

0.244

4483

9032

\begin{align*} 5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime }&=0 \\ \end{align*}

0.244

4484

9064

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

0.244

4485

9168

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

0.244

4486

10478

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

0.244

4487

10502

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

0.244

4488

10632

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*}

0.244

4489

10656

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

0.244

4490

10785

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

0.244

4491

10992

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

0.244

4492

13172

\(\left [\begin {array}{cc} 5 & -4 \\ 2 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.244

4493

13174

\(\left [\begin {array}{cc} 5 & -3 \\ 2 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.244

4494

13175

\(\left [\begin {array}{cc} 5 & -4 \\ 3 & -2 \end {array}\right ]\)

N/A

N/A

N/A

0.244

4495

13843

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

0.244

4496

16021

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

0.244

4497

16367

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

0.244

4498

16728

\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}

0.244

4499

16835

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

0.244

4500

17420

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

0.244