2.3.93 Problems 9201 to 9300

Table 2.717: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9201

21648

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

0.464

9202

1884

\begin{align*} \left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.465

9203

2054

\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.465

9204

3850

\begin{align*} x_{1}^{\prime }&=-x_{1}-6 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+5 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.465

9205

3909

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

0.465

9206

5557

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

0.465

9207

10198

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

0.465

9208

10447

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

0.465

9209

13733

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

0.465

9210

15179

\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime }&=\left (25-6 x \right ) y \\ \end{align*}

0.465

9211

19465

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

0.465

9212

19563

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

0.465

9213

20791

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \\ \end{align*}

0.465

9214

20911

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

0.465

9215

21514

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

0.465

9216

23606

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

0.465

9217

25127

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.465

9218

25270

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

0.465

9219

25422

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

0.465

9220

25702

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

0.465

9221

3839

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

0.466

9222

8538

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

0.466

9223

8939

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

0.466

9224

9371

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

0.466

9225

9983

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

0.466

9226

14876

\begin{align*} x^{\prime }&=\sec \left (t \right )^{2} \\ x \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

0.466

9227

15299

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

0.466

9228

15996

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

0.466

9229

16610

\begin{align*} y^{\prime \prime }+9 y&=10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \\ \end{align*}

0.466

9230

17688

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

0.466

9231

20703

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

0.466

9232

22084

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

0.466

9233

24013

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

0.466

9234

25334

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

0.466

9235

353

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

0.467

9236

635

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

0.467

9237

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 \(t=0\).

0.467

9238

3754

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

0.467

9239

3899

\begin{align*} x_{1}^{\prime }&=-3 x_{1}-10 x_{2} \\ x_{2}^{\prime }&=5 x_{1}+11 x_{2} \\ \end{align*}

0.467

9240

4052

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

0.467

9241

5504

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

0.467

9242

6135

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

0.467

9243

7963

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

0.467

9244

8277

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

0.467

9245

9333

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

0.467

9246

10037

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

0.467

9247

10140

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

0.467

9248

10949

\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}

0.467

9249

14069

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

0.467

9250

15983

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

0.467

9251

16103

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

0.467

9252

17003

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

0.467

9253

23493

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

0.467

9254

23531

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

0.467

9255

23964

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

0.467

9256

1388

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y x&=0 \\ \end{align*}
Series expansion around \(x=4\).

0.468

9257

1841

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

0.468

9258

1914

\begin{align*} \left (7+x \right ) y^{\prime \prime }+\left (8+2 x \right ) y^{\prime }+\left (x +5\right ) y&=0 \\ y \left (-4\right ) &= 1 \\ y^{\prime }\left (-4\right ) &= 2 \\ \end{align*}
Series expansion around \(x=-4\).

0.468

9259

2375

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

0.468

9260

2403

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

0.468

9261

2750

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

0.468

9262

4178

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

0.468

9263

6528

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

0.468

9264

7312

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

0.468

9265

10519

\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}

0.468

9266

10954

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

0.468

9267

14734

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

0.468

9268

16585

\begin{align*} 4 y+y^{\prime \prime }&=24 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.468

9269

17772

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=\frac {{\mathrm e}^{4 t}}{t^{3}} \\ \end{align*}

0.468

9270

21519

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=2 x^{3}+5 x^{2}-7 x +2 \\ \end{align*}

0.468

9271

22140

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

0.468

9272

22901

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

0.468

9273

23613

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

0.468

9274

5410

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

0.469

9275

9845

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

0.469

9276

11438

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

0.469

9277

14335

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

0.469

9278

16119

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

0.469

9279

19248

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

0.469

9280

19695

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

0.469

9281

22113

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

0.469

9282

152

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

0.470

9283

1904

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

0.470

9284

2058

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

0.470

9285

2380

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

0.470

9286

3630

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=9 x \\ \end{align*}

0.470

9287

3808

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

0.470

9288

3907

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

0.470

9289

7079

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

0.470

9290

9208

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

0.470

9291

9900

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

0.470

9292

9952

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

0.470

9293

10135

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

0.470

9294

13061

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

0.470

9295

14107

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

0.470

9296

14127

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

0.470

9297

15269

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

0.470

9298

16080

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.470

9299

16597

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \\ \end{align*}

0.470

9300

17771

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

0.470