2.3.93 Problems 9201 to 9300

Table 2.729: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9201

23533

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

0.609

9202

25834

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

0.609

9203

1031

\begin{align*} x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3} \\ x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3} \\ x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3} \\ \end{align*}

0.610

9204

6430

\begin{align*} y y^{\prime \prime }&={\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2} \\ \end{align*}

0.610

9205

10011

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

0.610

9206

10446

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\ \end{align*}

0.610

9207

10517

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

0.610

9208

14182

\begin{align*} 6 y+18 y^{\prime } x +9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

0.610

9209

18192

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

0.610

9210

19699

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

0.610

9211

22706

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

0.610

9212

23495

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

0.610

9213

24763

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

0.610

9214

25969

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

0.610

9215

2617

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

0.611

9216

7095

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

0.611

9217

8007

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

0.611

9218

9479

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

0.611

9219

10352

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

0.611

9220

16169

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

0.611

9221

17402

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

0.611

9222

2055

\begin{align*} 9 \left (x +3\right ) x^{2} y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.612

9223

2060

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

0.612

9224

2382

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

0.612

9225

2405

\begin{align*} 3 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (t \right ) {\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.612

9226

3748

\begin{align*} y^{\prime \prime }-4 y&=\frac {8}{{\mathrm e}^{2 x}+1} \\ \end{align*}

0.612

9227

3910

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

0.612

9228

14332

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

0.612

9229

15579

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

0.612

9230

16644

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

0.612

9231

16849

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

0.612

9232

23043

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

0.612

9233

23456

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

0.612

9234

23791

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

0.612

9235

3181

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

0.613

9236

8619

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

0.613

9237

9263

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

0.613

9238

12538

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

0.613

9239

22764

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=1 \\ \end{align*}

0.613

9240

23848

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

0.613

9241

23928

\begin{align*} 6 y^{\prime \prime }+11 y^{\prime }+4 y&=2 \\ \end{align*}

0.613

9242

3239

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

0.614

9243

3355

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

0.614

9244

4016

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

0.614

9245

7795

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

0.614

9246

8086

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

0.614

9247

9583

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

0.614

9248

16105

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

0.614

9249

19266

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

0.614

9250

23454

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

0.614

9251

73

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

0.615

9252

2276

\begin{align*} y_{1}^{\prime }&=5 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }&=-y_{1}+9 y_{2}-3 y_{3} \\ y_{3}^{\prime }&=-2 y_{1}+2 y_{2}+4 y_{3} \\ \end{align*}

0.615

9253

3328

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

0.615

9254

3899

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

0.615

9255

9472

\begin{align*} x^{\prime }&=3 x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}

0.615

9256

9514

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

0.615

9257

12880

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

0.615

9258

14387

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

0.615

9259

14431

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

0.615

9260

18856

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (6 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.615

9261

19261

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

0.615

9262

20351

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

0.615

9263

23788

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

0.615

9264

2037

\begin{align*} 4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.616

9265

3916

\begin{align*} x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t} \\ \end{align*}

0.616

9266

4556

\begin{align*} x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\ y^{\prime }-2 y-4 z&=4 \,{\mathrm e}^{2 t} \\ x-z^{\prime }-z&=0 \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 9 \\ y \left (0\right ) &= 3 \\ z \left (0\right ) &= 1 \\ \end{align*}

0.616

9267

7379

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

0.616

9268

7828

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.616

9269

8523

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

0.616

9270

9424

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

0.616

9271

10485

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

0.616

9272

12667

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

0.616

9273

16089

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

0.616

9274

16192

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

0.616

9275

12

\begin{align*} x^{\prime \prime }&=-20 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= -15 \\ \end{align*}

0.617

9276

2040

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.617

9277

3353

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

0.617

9278

7601

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

0.617

9279

9070

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

0.617

9280

14992

\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.617

9281

15231

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}
Using Laplace transform method.

0.617

9282

15993

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

0.617

9283

16842

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

0.617

9284

16990

\begin{align*} y^{\prime }&=\frac {1}{x^{2}-16} \\ \end{align*}

0.617

9285

17507

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

0.617

9286

18154

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

0.617

9287

21271

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

0.617

9288

1353

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

0.618

9289

3885

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=x_{2}-8 x_{3} \\ x_{3}^{\prime }&=2 x_{2}-7 x_{3} \\ \end{align*}

0.618

9290

4841

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

0.618

9291

8587

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

0.618

9292

8621

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

0.618

9293

8946

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

0.618

9294

10137

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

0.618

9295

10342

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

0.618

9296

10425

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

0.618

9297

13073

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

0.618

9298

16093

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.618

9299

22222

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

0.618

9300

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 \(t=0\).

0.619