2.3.103 Problems 10201 to 10300

Table 2.779: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10201

10177

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

Series expansion around \(x=0\).

0.766

10202

10185

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

Series expansion around \(x=0\).

0.766

10203

12997

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

0.766

10204

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.

0.766

10205

16878

\begin{align*} y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.766

10206

17818

\begin{align*} x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.766

10207

25471

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

0.766

10208

493

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

Series expansion around \(x=0\).

0.767

10209

3869

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

With initial conditions

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

0.767

10210

7671

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

0.767

10211

9046

\begin{align*} y_{1}^{\prime }&=y_{1}+y_{2} \\ y_{2}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{3 x} \\ \end{align*}

With initial conditions

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

0.767

10212

12945

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

0.767

10213

14296

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

0.767

10214

16868

\begin{align*} y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\ \end{align*}

Series expansion around \(x=1\).

0.767

10215

21933

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

0.767

10216

25363

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

0.767

10217

2029

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

Series expansion around \(x=0\).

0.768

10218

2466

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

Series expansion around \(t=0\).

0.768

10219

2698

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

0.768

10220

7119

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

0.768

10221

7575

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

0.768

10222

14658

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=x^{3}+x +{\mathrm e}^{-2 x} \\ \end{align*}

0.768

10223

18156

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

0.768

10224

19615

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

Series expansion around \(x=0\).

0.768

10225

25548

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

0.768

10226

2782

\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\ \end{align*}

With initial conditions

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

0.769

10227

3857

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

0.769

10228

4578

\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}+35 \,{\mathrm e}^{t} t^{{3}/{2}} \\ \end{align*}

0.769

10229

7903

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

0.769

10230

12378

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

0.769

10231

14295

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

0.769

10232

14857

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

0.769

10233

16140

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

Using Laplace transform method.

0.769

10234

16199

\begin{align*} y^{\prime }-y^{3}&=8 \\ \end{align*}

0.769

10235

16862

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

Series expansion around \(x=0\).

0.769

10236

17690

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

Series expansion around \(x=0\).

0.769

10237

17795

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

0.769

10238

18889

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&=t^{2}+7 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.769

10239

20559

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

0.769

10240

21690

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

Series expansion around \(x=0\).

0.769

10241

23249

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

0.769

10242

25525

\begin{align*} y^{\prime \prime }+100 y&=\cos \left (\omega t \right )-\sin \left (\omega t \right ) \\ \end{align*}

0.769

10243

26430

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

0.769

10244

26578

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

0.769

10245

148

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

0.770

10246

152

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

0.770

10247

3840

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

0.770

10248

6550

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

0.770

10249

8563

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

Series expansion around \(x=0\).

0.770

10250

9261

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

0.770

10251

15975

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

0.770

10252

16390

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

0.770

10253

18325

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

0.770

10254

19269

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

0.770

10255

20675

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

0.770

10256

20809

\begin{align*} 4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\ \end{align*}

0.770

10257

22201

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

Series expansion around \(x=1\).

0.770

10258

23508

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

0.770

10259

25579

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

0.770

10260

5919

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

0.771

10261

6533

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

0.771

10262

8594

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

Series expansion around \(t=0\).

0.771

10263

14303

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

0.771

10264

22267

\begin{align*} x^{\prime }&=y \\ y^{\prime }&=8 x-2 y \\ \end{align*}

With initial conditions

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

0.771

10265

23053

\begin{align*} s^{\prime \prime }&=5 t^{2}-7 t \\ s \left (0\right ) &= 0 \\ s \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}

0.771

10266

27034

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

Using Laplace transform method.

0.771

10267

27376

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

0.771

10268

3815

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

0.772

10269

7952

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

0.772

10270

8107

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

Series expansion around \(x=0\).

0.772

10271

10166

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

Series expansion around \(x=0\).

0.772

10272

2038

\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.773

10273

3887

\begin{align*} x_{1}^{\prime }&=-8 x_{1}+6 x_{2}-3 x_{3} \\ x_{2}^{\prime }&=-12 x_{1}+10 x_{2}-3 x_{3} \\ x_{3}^{\prime }&=-2 x_{3} \\ \end{align*}

0.773

10274

7474

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

0.773

10275

10228

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

0.773

10276

12332

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

0.773

10277

12388

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

0.773

10278

14375

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

0.773

10279

14623

\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=16 x -12 \,{\mathrm e}^{2 x} \\ \end{align*}

0.773

10280

15249

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

Using Laplace transform method.

0.773

10281

16723

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

0.773

10282

18151

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=\left (1-x \right ) {\mathrm e}^{4 x} \\ \end{align*}

0.773

10283

18264

\begin{align*} y^{\prime \prime }+9 y&=36 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.773

10284

18862

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}

0.773

10285

22648

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

0.773

10286

26587

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime }&={\mathrm e}^{x}+3 \sin \left (2 x \right )+1 \\ \end{align*}

0.773

10287

1631

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

0.774

10288

2429

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

Series expansion around \(t=0\).

0.774

10289

4167

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

0.774

10290

8501

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

Series expansion around \(x=0\).

0.774

10291

14656

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \\ y \left (0\right ) &= {\frac {33}{40}} \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

0.774

10292

18671

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

With initial conditions

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

0.774

10293

18702

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

0.774

10294

19147

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

0.774

10295

21588

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \left (x +1\right ) \\ \end{align*}

0.774

10296

21891

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=2 \,{\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}

0.774

10297

24854

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

0.774

10298

25194

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

0.774

10299

25948

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

0.774

10300

26733

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

0.774