2.3.32 Problems 3101 to 3200

Table 2.595: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

3101

18882

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

0.237

3102

18901

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

0.237

3103

21713

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

0.237

3104

404

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

0.238

3105

1071

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.238

3106

4514

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*}
Using Laplace transform method.

0.238

3107

16170

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

0.238

3108

17659

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

0.238

3109

18460

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

0.238

3110

20124

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

0.238

3111

24012

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

0.238

3112

24503

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

0.238

3113

542

\begin{align*} x^{\prime \prime }-6 x^{\prime }+8 x&=2 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.239

3114

556

\begin{align*} t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x&=0 \\ x \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.239

3115

2417

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

0.239

3116

3730

\begin{align*} y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime }&=5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \\ \end{align*}

0.239

3117

9487

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

0.239

3118

10935

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

0.239

3119

12839

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

0.239

3120

17631

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\ \end{align*}

0.239

3121

24008

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

0.239

3122

24621

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \\ \end{align*}

0.239

3123

1397

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

0.240

3124

2256

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

0.240

3125

8068

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

0.240

3126

9177

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

0.240

3127

10462

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

0.240

3128

14076

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

0.240

3129

14402

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

0.240

3130

14716

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

0.240

3131

15012

\begin{align*} x^{\prime }&=13 x \\ y^{\prime }&=13 y \\ \end{align*}

0.240

3132

15475

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

0.240

3133

20007

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

0.240

3134

21221

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

0.240

3135

21537

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

0.240

3136

21710

\begin{align*} y^{\prime }+b y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.240

3137

23632

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}
Using Laplace transform method.

0.240

3138

24034

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

0.240

3139

24532

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime }&=12 \\ \end{align*}

0.240

3140

6309

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

0.241

3141

8985

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.241

3142

10857

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

0.241

3143

11170

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

0.241

3144

21711

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

0.241

3145

22234

\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.241

3146

23062

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

0.241

3147

23635

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

0.241

3148

537

\begin{align*} x^{\prime \prime }+9 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.242

3149

543

\begin{align*} x^{\prime \prime }-4 x&=3 t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.242

3150

2413

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

0.242

3151

5387

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

0.242

3152

5474

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

0.242

3153

5479

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

0.242

3154

5553

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

0.242

3155

10727

\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*}

0.242

3156

16184

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

0.242

3157

17626

\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 y^{\prime } x +100 y&=0 \\ \end{align*}

0.242

3158

17658

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 y^{\prime } x&=0 \\ \end{align*}

0.242

3159

24502

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

0.242

3160

1486

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

0.243

3161

2213

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}

0.243

3162

2230

\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \left (x +1\right ) \\ y \left (-1\right ) &= -6 \\ y^{\prime }\left (-1\right ) &= {\frac {43}{6}} \\ y^{\prime \prime }\left (-1\right ) &= -{\frac {5}{2}} \\ \end{align*}

0.243

3163

2415

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

0.243

3164

2424

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

0.243

3165

9715

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

0.243

3166

10775

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

0.243

3167

11182

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

0.243

3168

11237

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

0.243

3169

12840

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

0.243

3170

15040

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

0.243

3171

15250

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.243

3172

18457

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

0.243

3173

20396

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

0.243

3174

22253

\begin{align*} y^{\prime \prime \prime }-y&=5 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.243

3175

23258

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

0.243

3176

24663

\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }-8 y^{\prime \prime }&=48 \,{\mathrm e}^{2 x} \\ \end{align*}

0.243

3177

25639

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

0.243

3178

1452

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

0.244

3179

7729

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

0.244

3180

8102

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

0.244

3181

10619

\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}

0.244

3182

10881

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

0.244

3183

14355

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

0.244

3184

16053

\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.244

3185

18329

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

0.244

3186

18625

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

0.244

3187

24617

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=6 x \,{\mathrm e}^{2 x} \\ \end{align*}

0.244

3188

24622

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

0.244

3189

25640

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

0.244

3190

2176

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&={\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (1+6 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}

0.245

3191

2235

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

0.245

3192

3623

\begin{align*} y^{\prime }+\frac {m y}{x}&=\ln \left (x \right ) \\ \end{align*}

0.245

3193

5018

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

0.245

3194

6301

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

0.245

3195

6847

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

0.245

3196

9535

\begin{align*} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.245

3197

10928

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

0.245

3198

10983

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

0.245

3199

14999

\(\left [\begin {array}{cc} -7 & 6 \\ 12 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.245

3200

16196

\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

0.245