2.3.123 Problems 12201 to 12300

Table 2.777: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12201

18019

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

0.692

12202

19029

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

0.692

12203

21293

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

0.692

12204

22896

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

0.692

12205

25359

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

0.692

12206

4382

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

0.693

12207

9038

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

0.693

12208

9404

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

0.693

12209

9752

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

0.693

12210

9982

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

0.693

12211

14754

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

0.693

12212

228

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\ y \left (2\right ) &= 10 \\ y^{\prime }\left (2\right ) &= 15 \\ \end{align*}

0.694

12213

825

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

0.694

12214

2463

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

0.694

12215

3983

\begin{align*} y^{\prime \prime }+16 y&=4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.694

12216

6042

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

0.694

12217

9406

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

0.694

12218

9579

\begin{align*} 9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y&=0 \\ \end{align*}

0.694

12219

12510

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

0.694

12220

15302

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

0.694

12221

15888

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

0.694

12222

17729

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

0.694

12223

18257

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

0.694

12224

18871

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

0.694

12225

20729

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

0.694

12226

20752

\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 x +\frac {10}{x} \\ \end{align*}

0.694

12227

22104

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

0.694

12228

22519

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

0.694

12229

4019

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

0.695

12230

8078

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

0.695

12231

18386

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

0.695

12232

20236

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

0.695

12233

21970

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

0.695

12234

23244

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

0.695

12235

24921

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

0.695

12236

10113

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

0.696

12237

10208

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

0.696

12238

1492

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.697

12239

2762

\begin{align*} x_{1}^{\prime }&=x_{2}+f_{1} \left (t \right ) \\ x_{2}^{\prime }&=-x_{1}+f_{2} \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

0.697

12240

2807

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

0.697

12241

5878

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

0.697

12242

6161

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

0.697

12243

8582

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

0.697

12244

9902

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

0.697

12245

10115

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

0.697

12246

10178

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

0.697

12247

10209

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

0.697

12248

12519

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

0.697

12249

12562

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

0.697

12250

13853

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

0.697

12251

16657

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=x^{3} \sin \left (4 x \right ) \\ \end{align*}

0.697

12252

20006

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

0.697

12253

20165

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

0.697

12254

21245

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

0.697

12255

23676

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

0.697

12256

25315

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=3 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.697

12257

985

\begin{align*} x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\ \end{align*}

0.698

12258

4548

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

0.698

12259

5968

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

0.698

12260

8648

\begin{align*} y^{\prime \prime }+16 y&=4 \delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.698

12261

9963

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

0.698

12262

10085

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x^{5}+24&=0 \\ \end{align*}

0.698

12263

14174

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

0.698

12264

18294

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

0.698

12265

19135

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

0.698

12266

20494

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

0.698

12267

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*}

0.698

12268

2654

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

0.699

12269

3563

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

0.699

12270

10206

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

0.699

12271

14364

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

0.699

12272

22268

\begin{align*} x^{\prime }&=y \\ y^{\prime }&=8 x-2 y+{\mathrm e}^{t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -4 \\ \end{align*}

0.699

12273

150

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

0.700

12274

236

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

0.700

12275

2455

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

0.700

12276

3218

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

0.700

12277

4464

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

0.700

12278

6054

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

0.700

12279

8976

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

0.700

12280

9278

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

0.700

12281

14510

\begin{align*} \left (2+x \right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \\ y \left (0\right ) &= 4 \\ \end{align*}

0.700

12282

16696

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

0.700

12283

19259

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

0.700

12284

21943

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.700

12285

23820

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

0.700

12286

2264

\begin{align*} y_{1}^{\prime }&=6 y_{1}-5 y_{2}+3 y_{3} \\ y_{2}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\ y_{3}^{\prime }&=2 y_{1}+y_{2}+y_{3} \\ \end{align*}

0.701

12287

2587

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

0.701

12288

3141

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

0.701

12289

8511

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

0.701

12290

14651

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.701

12291

18237

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

0.701

12292

18295

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

0.701

12293

19764

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

0.701

12294

20182

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

0.701

12295

20370

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right ) \\ \end{align*}

0.701

12296

21575

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=16 x^{3} {\mathrm e}^{3 x} \\ \end{align*}

0.701

12297

24717

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

0.701

12298

25681

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

0.701

12299

2686

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right . \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}
Using Laplace transform method.

0.702

12300

9518

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

0.702