2.3.113 Problems 11201 to 11300

Table 2.799: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11201

17379

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

0.872

11202

19359

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

0.872

11203

19363

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

0.872

11204

19886

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

0.872

11205

21149

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

0.872

11206

23282

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

0.872

11207

26358

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

0.872

11208

26574

\begin{align*} 5 y^{\prime \prime }-6 y^{\prime }+5 y&=13 \,{\mathrm e}^{x} \cosh \left (x \right ) \\ \end{align*}

0.872

11209

26992

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

0.872

11210

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 \(x=2\).

0.873

11211

11760

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

0.873

11212

14338

\begin{align*} x^{\prime \prime }-x&=\frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \\ \end{align*}

0.873

11213

2224

\begin{align*} 16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y&=96 x^{{5}/{2}} \\ \end{align*}

0.874

11214

8542

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.874

11215

23144

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

0.874

11216

25756

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

0.874

11217

2649

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

Series expansion around \(t=0\).

0.875

11218

5786

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

0.875

11219

8537

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

Series expansion around \(x=0\).

0.875

11220

12962

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

0.875

11221

14330

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

0.875

11222

16411

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

0.875

11223

18855

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (2 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.875

11224

20895

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

Series expansion around \(x=0\).

0.875

11225

602

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

0.876

11226

1998

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

Series expansion around \(x=0\).

0.876

11227

6216

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

0.876

11228

6459

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

0.876

11229

17589

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

0.876

11230

22813

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=100 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 20 \\ \end{align*}

Using Laplace transform method.

0.876

11231

1963

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

Series expansion around \(x=0\).

0.877

11232

10377

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

0.877

11233

13883

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

0.877

11234

15889

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

0.877

11235

825

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

0.878

11236

1833

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=\left (3 x -1\right )^{2} {\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.878

11237

1988

\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*}

Series expansion around \(x=0\).

0.878

11238

5567

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

0.878

11239

5639

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

0.878

11240

15811

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

0.878

11241

16171

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

0.878

11242

17506

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \\ \end{align*}

0.878

11243

18831

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

0.878

11244

18917

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

With initial conditions

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

0.878

11245

20516

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

0.878

11246

20894

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

Series expansion around \(x=0\).

0.878

11247

23569

\begin{align*} x_{1}^{\prime }&=-10 x_{1}+x_{2}+7 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}+4 x_{2}+5 x_{3} \\ x_{3}^{\prime }&=-17 x_{1}+x_{2}+12 x_{3} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= -2 \\ \end{align*}

0.878

11248

6506

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

0.879

11249

10085

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

0.879

11250

12318

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

0.879

11251

13871

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

0.879

11252

14408

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

With initial conditions

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

0.879

11253

2590

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

0.880

11254

9985

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

0.880

11255

14294

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

0.880

11256

18913

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 5 \\ y_{2} \left (0\right ) &= 4 \\ \end{align*}

0.880

11257

18919

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

With initial conditions

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

0.880

11258

22701

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

0.880

11259

1753

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

0.881

11260

4034

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

Series expansion around \(x=0\).

0.881

11261

9709

\begin{align*} x^{\prime }&=5 x+9 y+2 \\ y^{\prime }&=-x+11 y+6 \\ \end{align*}

0.881

11262

15945

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

0.881

11263

22170

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

Series expansion around \(x=1\).

0.881

11264

25192

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

0.881

11265

7164

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

Series expansion around \(x=0\).

0.882

11266

7310

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

0.882

11267

9371

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

Series expansion around \(x=0\).

0.882

11268

9842

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

Series expansion around \(x=0\).

0.882

11269

15328

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

0.882

11270

18265

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

0.882

11271

26093

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

0.882

11272

5736

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

0.883

11273

8622

\begin{align*} y^{\prime }+\frac {26 y}{5}&=\frac {97 \sin \left (2 t \right )}{5} \\ y \left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.883

11274

26377

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

0.883

11275

1996

\begin{align*} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.884

11276

4564

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

0.884

11277

10392

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

0.884

11278

14106

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

0.884

11279

14875

\begin{align*} T^{\prime }&={\mathrm e}^{-t} \sin \left (2 t \right ) \\ \end{align*}

0.884

11280

15064

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

0.884

11281

22621

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

0.884

11282

27157

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

0.884

11283

4025

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

Series expansion around \(x=0\).

0.885

11284

4066

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

Series expansion around \(x=0\).

0.885

11285

8946

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

0.885

11286

9699

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

0.885

11287

12119

\begin{align*} y^{\prime }&=\frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 x^{3} y-100 y \sqrt {x}+4 x^{6}+40 x^{{7}/{2}}+100 x}{25 x} \\ \end{align*}

0.885

11288

14729

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

Series expansion around \(x=0\).

0.885

11289

15331

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

0.885

11290

18910

\begin{align*} y_{1}^{\prime }&=-5 y_{1}+y_{2} \\ y_{2}^{\prime }&=-9 y_{1}+5 y_{2} \\ \end{align*}

With initial conditions

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

0.885

11291

24889

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

0.885

11292

3383

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

Series expansion around \(x=0\).

0.886

11293

14877

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

0.886

11294

18434

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

0.886

11295

21189

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

0.886

11296

21884

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

0.886

11297

22269

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

With initial conditions

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

0.886

11298

24101

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

Series expansion around \(x=0\).

0.886

11299

27076

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

Series expansion around \(x=0\).

0.886

11300

5482

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

0.887