2.3.132 Problems 13101 to 13200

Table 2.837: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13101

4739

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

1.188

13102

16425

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

1.188

13103

19230

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

1.188

13104

20787

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

1.188

13105

6745

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

1.189

13106

9352

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

1.189

13107

26507

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

1.189

13108

18993

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

1.190

13109

5378

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

1.191

13110

9027

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

1.191

13111

12988

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

1.191

13112

14301

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

1.191

13113

21174

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

1.191

13114

8884

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

1.192

13115

15824

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

1.192

13116

20091

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

1.192

13117

20661

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

1.192

13118

13876

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

1.193

13119

15844

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

1.193

13120

18641

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

1.193

13121

24488

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

1.193

13122

1515

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

Using Laplace transform method.

1.194

13123

8336

\begin{align*} y^{\prime }&=y^{2}-y-6 \\ \end{align*}

1.194

13124

17491

\begin{align*} y^{\prime \prime }-2 y^{\prime }+26 y&={\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \\ \end{align*}

1.194

13125

18334

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

1.194

13126

20086

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

1.194

13127

22704

\begin{align*} i^{\prime \prime }+9 i&=12 \cos \left (3 t \right ) \\ i \left (0\right ) &= 4 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.194

13128

25740

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

1.194

13129

4015

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

Series expansion around \(x=0\).

1.195

13130

4179

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

Series expansion around \(x=0\).

1.195

13131

17790

\begin{align*} 3 x y^{\prime \prime }+11 y^{\prime }-y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.195

13132

8064

\begin{align*} x^{\prime }+x+2 y^{\prime }+7 y&={\mathrm e}^{t}+2 \\ -2 x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\ \end{align*}

1.196

13133

18116

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

1.196

13134

25622

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

1.196

13135

27549

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

1.196

13136

3256

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

1.197

13137

9991

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

1.197

13138

14151

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

1.197

13139

14682

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

1.197

13140

19467

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

1.197

13141

2214

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&={\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \\ \end{align*}

1.198

13142

2272

\begin{align*} y_{1}^{\prime }&=-7 y_{1}-4 y_{2}+4 y_{3} \\ y_{2}^{\prime }&=y_{1}+y_{3} \\ y_{3}^{\prime }&=-9 y_{1}-5 y_{2}+6 y_{3} \\ \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= -6 \\ y_{2} \left (0\right ) &= 9 \\ y_{3} \left (0\right ) &= -1 \\ \end{align*}

1.198

13143

4570

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+26 \sin \left (t \right ) \\ x_{2}^{\prime }&=3 x_{1}+4 x_{2} \\ \end{align*}

1.198

13144

8856

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

1.198

13145

18245

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

1.198

13146

23373

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

1.198

13147

3360

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

Series expansion around \(x=0\).

1.199

13148

17709

\begin{align*} 2 x y^{\prime \prime }-5 y^{\prime }-3 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.199

13149

21004

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

1.199

13150

7988

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

1.200

13151

14327

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

1.201

13152

15579

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

1.201

13153

16623

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

1.201

13154

21225

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

1.201

13155

4600

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

Series expansion around \(x=0\).

1.202

13156

11861

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

1.202

13157

27023

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <4 \\ 12 & 4\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.202

13158

11890

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

1.203

13159

15290

\begin{align*} x^{\prime }&=-7 x+4 y+6 \,{\mathrm e}^{3 t} \\ y^{\prime }&=-5 x+2 y+6 \,{\mathrm e}^{2 t} \\ \end{align*}

With initial conditions

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

1.203

13160

1513

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

Using Laplace transform method.

1.204

13161

3816

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

1.204

13162

6094

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

1.204

13163

9815

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

1.204

13164

21742

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

1.204

13165

23678

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

Series expansion around \(x=0\).

1.204

13166

23966

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

1.204

13167

7428

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

1.205

13168

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 \(x=0\).

1.205

13169

12987

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

1.206

13170

21410

\begin{align*} y^{\prime }-3 y&=6 \\ \end{align*}

1.206

13171

26418

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

1.206

13172

12311

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

1.207

13173

25268

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

1.207

13174

25623

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

1.207

13175

9982

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

1.208

13176

14666

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

1.208

13177

14981

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

Series expansion around \(x=0\).

1.208

13178

18920

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

With initial conditions

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

1.208

13179

19168

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

1.208

13180

13074

\begin{align*} 4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\ \end{align*}

1.209

13181

18103

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

1.209

13182

22212

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

Series expansion around \(x=0\).

1.209

13183

14313

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

1.210

13184

16612

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \\ \end{align*}

1.210

13185

19849

\begin{align*} e y^{\prime \prime }&=-\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \\ \end{align*}

1.210

13186

2627

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

1.211

13187

6029

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

1.211

13188

6397

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

1.211

13189

13687

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

1.211

13190

21685

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

Series expansion around \(x=0\).

1.211

13191

9733

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

1.212

13192

15801

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

1.212

13193

17518

\begin{align*} y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \tan \left (3 t \right ) \\ \end{align*}

1.212

13194

26458

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

1.212

13195

12428

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

1.213

13196

3588

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

1.214

13197

8871

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

1.214

13198

9766

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

1.214

13199

9891

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

Series expansion around \(x=0\).

1.214

13200

18208

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \\ \end{align*}

1.214