2.3.43 Problems 4201 to 4300

Table 2.659: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

4201

18759

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

0.530

4202

19690

\begin{align*} x^{\prime \prime }-4 x^{\prime }+5 x&=0 \\ \end{align*}

0.530

4203

1083

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

Series expansion around \(x=1\).

0.531

4204

14748

\begin{align*} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.531

4205

17755

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=3 \,{\mathrm e}^{-2 t} \\ \end{align*}

0.531

4206

18758

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

0.531

4207

25928

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

0.531

4208

615

\begin{align*} x_{1}^{\prime }&=4 x_{1}-3 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-7 x_{2} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 8 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

0.532

4209

16665

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

0.532

4210

18689

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

0.532

4211

23404

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

0.532

4212

660

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

0.533

4213

815

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

0.533

4214

4172

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 3 \\ y_{2} \left (0\right ) &= 7 \\ \end{align*}

0.533

4215

7853

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

0.533

4216

14576

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \\ \end{align*}

0.533

4217

16660

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

0.533

4218

17696

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

Series expansion around \(x=0\).

0.533

4219

17763

\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

0.533

4220

1092

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

Series expansion around \(x=0\).

0.534

4221

1415

\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{2}-\frac {x_{2}}{8} \\ x_{2}^{\prime }&=2 x_{1}-\frac {x_{2}}{2} \\ \end{align*}

0.534

4222

2052

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

Series expansion around \(x=0\).

0.534

4223

10462

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

0.534

4224

20487

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

0.534

4225

20611

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

0.534

4226

2035

\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.535

4227

3423

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

0.535

4228

4169

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

0.535

4229

6551

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

0.535

4230

6701

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

0.535

4231

17689

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

Series expansion around \(x=0\).

0.535

4232

18696

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

With initial conditions

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

0.535

4233

1364

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

Series expansion around \(x=0\).

0.536

4234

2287

\begin{align*} y_{1}^{\prime }&=y_{1}+2 y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+5 y_{2} \\ \end{align*}

0.536

4235

2462

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

Series expansion around \(t=0\).

0.536

4236

2621

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

Series expansion around \(t=0\).

0.536

4237

3148

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

0.536

4238

10674

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

0.536

4239

15496

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}

0.536

4240

17683

\begin{align*} y^{\prime \prime }+3 y^{\prime }-18 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.536

4241

17684

\begin{align*} y^{\prime \prime }-11 y^{\prime }+30 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.536

4242

20553

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

0.536

4243

24607

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

0.536

4244

25896

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

0.536

4245

2161

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }&=-16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \\ \end{align*}

0.537

4246

2179

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y&=8 \cos \left (2 x \right )-16 \sin \left (2 x \right ) \\ \end{align*}

0.537

4247

2390

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

0.537

4248

4127

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.537

4249

5768

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

0.537

4250

5797

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

0.537

4251

5958

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

0.537

4252

7588

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

0.537

4253

8791

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

0.537

4254

17398

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

0.537

4255

17762

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.537

4256

18765

\begin{align*} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\ \end{align*}

0.537

4257

658

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

0.538

4258

1089

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

Series expansion around \(x=0\).

0.539

4259

2057

\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.539

4260

8893

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

0.539

4261

9079

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}

0.539

4262

9212

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

0.539

4263

12763

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+\left (a \,x^{3}-12\right ) y&=0 \\ \end{align*}

0.539

4264

17806

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

0.539

4265

22335

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

0.539

4266

1382

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

Series expansion around \(x=0\).

0.540

4267

2602

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

0.540

4268

2620

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

Series expansion around \(t=0\).

0.540

4269

2743

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.540

4270

18280

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

0.540

4271

18770

\begin{align*} 25 y^{\prime \prime }-20 y^{\prime }+4 y&=0 \\ \end{align*}

0.540

4272

469

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

Series expansion around \(x=0\).

0.541

4273

3710

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=18 \,{\mathrm e}^{5 x} \\ \end{align*}

0.541

4274

5383

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

0.541

4275

8183

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

0.541

4276

659

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

0.542

4277

2036

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

Series expansion around \(x=0\).

0.542

4278

3715

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

0.542

4279

7977

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}

0.542

4280

14795

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

N/A

N/A

N/A

0.542

4281

16995

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

0.542

4282

17426

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

0.542

4283

17695

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

Series expansion around \(x=0\).

0.542

4284

18429

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

0.542

4285

23408

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

0.542

4286

25918

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

0.542

4287

2722

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

0.543

4288

3343

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

Series expansion around \(x=0\).

0.543

4289

3711

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=4 x^{2}+5 \\ \end{align*}

0.543

4290

3811

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

0.543

4291

10942

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\ \end{align*}

0.543

4292

16986

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

0.543

4293

22161

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ y^{\prime \prime }\left (\pi \right ) &= 1 \\ \end{align*}

0.543

4294

23430

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

0.543

4295

591

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

0.544

4296

2285

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

0.544

4297

3930

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

Using Laplace transform method.

0.544

4298

18684

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

0.544

4299

23421

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

0.544

4300

3923

\begin{align*} x_{1}^{\prime }&=7 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ \end{align*}

0.545