2.3.133 Problems 13201 to 13300

Table 2.839: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13201

12385

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

0.964

13202

17480

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+37 y&=\cos \left (3 t \right ) \\ y \left (0\right ) &= a \\ y^{\prime }\left (\pi \right ) &= a \\ \end{align*}

0.964

13203

18230

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

0.964

13204

19427

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

0.964

13205

20946

\begin{align*} x^{\prime }&=5 x+3 y+1 \\ y^{\prime }&=-6 x-4 y+{\mathrm e}^{t} \\ \end{align*}

With initial conditions

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

0.964

13206

14661

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} x^{4}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\ \end{align*}

0.965

13207

20584

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

0.965

13208

1429

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

0.966

13209

2189

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y&={\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \\ \end{align*}

0.966

13210

24095

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

Series expansion around \(x=0\).

0.966

13211

1430

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\ \end{align*}

0.967

13212

3293

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

0.967

13213

5413

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

0.967

13214

6160

\begin{align*} 5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}

0.967

13215

6404

\begin{align*} 24+12 y x +x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\ \end{align*}

0.967

13216

16736

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

0.967

13217

18768

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

0.967

13218

19612

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

Series expansion around \(x=0\).

0.967

13219

24799

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

0.967

13220

25584

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

0.967

13221

25932

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

0.967

13222

74

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

0.968

13223

22700

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

0.968

13224

22931

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

0.968

13225

23745

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

Series expansion around \(x=0\).

0.968

13226

12878

\begin{align*} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r}&=0 \\ \end{align*}

0.969

13227

15177

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

0.969

13228

1038

\begin{align*} x_{1}^{\prime }&=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\ x_{2}^{\prime }&=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\ x_{3}^{\prime }&=-10 x_{1}+3 x_{2}-9 x_{4} \\ x_{4}^{\prime }&=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \\ \end{align*}

0.970

13229

4071

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

Series expansion around \(x=0\).

0.970

13230

6540

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

0.970

13231

9255

\begin{align*} y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\ \end{align*}

0.970

13232

14831

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

0.970

13233

15157

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

0.970

13234

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*}

0.970

13235

20999

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

0.970

13236

24908

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

0.970

13237

25316

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

Using Laplace transform method.

0.970

13238

646

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{3} \\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 17 \\ \end{align*}

0.971

13239

1941

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.971

13240

7123

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

0.971

13241

12660

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

0.971

13242

13071

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

0.971

13243

19605

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

Series expansion around \(x=0\).

0.971

13244

23050

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

0.971

13245

24108

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

Series expansion around \(x=0\).

0.971

13246

25464

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

0.971

13247

6478

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

0.972

13248

15439

\begin{align*} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=8 \cos \left (a x \right ) \\ \end{align*}

0.972

13249

16122

\begin{align*} y^{\prime \prime }+6 y^{\prime }+20 y&=-3 \sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.972

13250

4056

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

Series expansion around \(x=0\).

0.973

13251

12326

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

0.973

13252

20073

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

0.973

13253

26024

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

Series expansion around \(x=0\).

0.973

13254

16123

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

0.974

13255

17607

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

0.974

13256

20536

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

0.974

13257

21257

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

0.974

13258

6491

\begin{align*} 5 y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}

0.975

13259

7626

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

Series expansion around \(t=0\).

0.975

13260

12889

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

0.975

13261

16897

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

Series expansion around \(x=0\).

0.975

13262

20186

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

0.975

13263

5622

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

0.976

13264

6334

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

0.976

13265

6422

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

0.976

13266

9959

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

Series expansion around \(x=0\).

0.976

13267

12388

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

0.976

13268

12646

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

0.976

13269

21766

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

0.976

13270

22182

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

Series expansion around \(x=2\).

0.976

13271

2103

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.977

13272

9546

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

Series expansion around \(x=0\).

0.977

13273

13738

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

0.977

13274

15654

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

0.977

13275

17506

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

0.977

13276

20604

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

0.977

13277

20752

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

0.977

13278

25341

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

Series expansion around \(t=0\).

0.977

13279

16869

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

Series expansion around \(x=0\).

0.978

13280

1007

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

0.979

13281

6286

\begin{align*} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}

0.979

13282

9905

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

Series expansion around \(x=0\).

0.979

13283

16646

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

0.979

13284

26981

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

0.979

13285

3512

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

Series expansion around \(z=0\).

0.980

13286

5802

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \\ \end{align*}

0.980

13287

16900

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

Series expansion around \(x=0\).

0.980

13288

20397

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

0.980

13289

22743

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

0.980

13290

26026

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

Series expansion around \(x=0\).

0.980

13291

23081

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

0.981

13292

5410

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

0.982

13293

16870

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

Series expansion around \(x=0\).

0.982

13294

20518

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

0.982

13295

12293

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

0.983

13296

12460

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

0.983

13297

21949

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime } x&={\mathrm e}^{x}+1 \\ \end{align*}

0.983

13298

1824

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=x^{{7}/{2}} \\ \end{align*}

0.984

13299

5594

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

0.984

13300

6485

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

0.984