2.3.73 Problems 7201 to 7300

Table 2.677: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7201

10837

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

0.629

7202

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.

0.629

7203

23626

\begin{align*} x^{\prime }&=7 x+4 y-4 z \\ y^{\prime }&=4 x-8 y-z \\ z^{\prime }&=-4 x-y-8 z \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 5 \\ z \left (0\right ) &= -1 \\ \end{align*}

0.629

7204

25356

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

0.629

7205

3508

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

0.630

7206

3893

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

0.630

7207

7196

\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.630

7208

8392

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

0.630

7209

9174

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

0.630

7210

13105

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

0.630

7211

14666

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \\ \end{align*}

0.630

7212

19439

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

0.630

7213

20808

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

0.630

7214

1900

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

0.631

7215

2025

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.631

7216

4050

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

0.631

7217

5567

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

0.631

7218

8597

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{49}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.631

7219

12885

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

0.631

7220

15845

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

0.631

7221

17592

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

0.631

7222

17696

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

0.631

7223

21752

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

0.631

7224

2739

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

0.632

7225

4072

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

0.632

7226

5216

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

0.632

7227

8129

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

0.632

7228

10964

\begin{align*} 12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align*}

0.632

7229

11096

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

0.632

7230

21753

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

0.632

7231

1909

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

0.633

7232

3505

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

0.633

7233

5622

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

0.633

7234

11077

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

0.633

7235

11114

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}

0.633

7236

19612

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

0.633

7237

643

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

0.634

7238

7193

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

0.634

7239

9421

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

0.634

7240

11290

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

0.634

7241

15239

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.634

7242

17691

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

0.634

7243

19438

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

0.634

7244

19602

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

0.634

7245

997

\begin{align*} x_{1}^{\prime }&=147 x_{1}+23 x_{2}-202 x_{3} \\ x_{2}^{\prime }&=-90 x_{1}-9 x_{2}+129 x_{3} \\ x_{3}^{\prime }&=90 x_{1}+15 x_{2}-123 x_{3} \\ \end{align*}

0.635

7246

2182

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime }&=-{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3 x +3\right ) \sin \left (3 x \right )\right ) \\ \end{align*}

0.635

7247

2649

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

0.635

7248

9169

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

0.635

7249

9372

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

0.635

7250

11004

\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}

0.635

7251

11010

\begin{align*} 9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}

0.635

7252

12028

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

0.635

7253

10669

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

0.636

7254

10720

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

0.636

7255

10721

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

0.636

7256

11084

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

0.636

7257

11120

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

0.636

7258

22279

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{3} \\ x_{3}^{\prime }&=6 t \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 12 \\ \end{align*}

0.636

7259

25380

\begin{align*} y_{1}^{\prime }&=-y_{1}-4 y_{2}+4 \\ y_{2}^{\prime }&=y_{1}-y_{2}+1 \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}

0.636

7260

11209

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

0.637

7261

16065

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

0.637

7262

21095

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

0.637

7263

25308

\begin{align*} y^{\prime }-4 y&=\delta \left (t -4\right ) \\ y \left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.637

7264

6348

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

0.638

7265

8537

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

0.638

7266

8551

\begin{align*} 9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.638

7267

11267

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

0.638

7268

12990

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

0.638

7269

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*}

0.638

7270

22203

\begin{align*} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.638

7271

24806

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

0.638

7272

24944

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

0.638

7273

2005

\begin{align*} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.639

7274

4071

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

0.639

7275

7963

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

0.639

7276

8080

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

0.639

7277

20942

\begin{align*} x^{\prime }&=8 x-5 y \\ y^{\prime }&=16 x+8 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.639

7278

637

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

0.640

7279

7101

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

0.640

7280

8563

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

0.640

7281

8900

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

0.640

7282

9181

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

0.640

7283

9356

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

0.640

7284

9422

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

0.640

7285

19982

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

0.640

7286

1414

\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }&=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }&=\frac {x_{3}}{10} \\ \end{align*}

0.641

7287

2011

\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.641

7288

3999

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

0.641

7289

9464

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

0.641

7290

11139

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

0.641

7291

11207

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

0.641

7292

15578

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

0.641

7293

15977

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

0.641

7294

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*}

0.642

7295

7650

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

0.642

7296

10692

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

0.642

7297

10885

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

0.642

7298

10923

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

0.642

7299

15236

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \\ y \left (0\right ) &= -6 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.642

7300

23611

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

0.642