2.2.132 Problems 13101 to 13200

Table 2.281: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

13101

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

system_of_ODEs

0.150

13102

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

system_of_ODEs

1.155

13103

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

system_of_ODEs

1.199

13104

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

system_of_ODEs

1.080

13105

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

system_of_ODEs

1.517

13106

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

system_of_ODEs

3.822

13107

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

system_of_ODEs

3.056

13108

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

system_of_ODEs

1.602

13109

\begin{align*} x^{\prime }&=-3 x+48 y-28 z \\ y^{\prime }&=-4 x+40 y-22 z \\ z^{\prime }&=-6 x+57 y-31 z \\ \end{align*}

system_of_ODEs

1.520

13110

\begin{align*} x^{\prime }&=6 x-72 y+44 z \\ y^{\prime }&=4 x-4 y+26 z \\ z^{\prime }&=6 x-63 y+38 z \\ \end{align*}

system_of_ODEs

23.904

13111

\begin{align*} x^{\prime }&=a x+g y+\beta z \\ y^{\prime }&=g x+b y+\alpha z \\ z^{\prime }&=\beta x+\alpha y+c z \\ \end{align*}

system_of_ODEs

311.451

13112

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

system_of_ODEs

0.267

13113

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

system_of_ODEs

0.234

13114

\begin{align*} x_{1}^{\prime }&=a x_{2}+b x_{3} \cos \left (c t \right )+b x_{4} \sin \left (c t \right ) \\ x_{2}^{\prime }&=-a x_{1}+b x_{3} \sin \left (c t \right )-b x_{4} \cos \left (c t \right ) \\ x_{3}^{\prime }&=-b x_{1} \cos \left (c t \right )-b x_{2} \sin \left (c t \right )+a x_{4} \\ x_{4}^{\prime }&=-b x_{1} \sin \left (c t \right )+b x_{2} \cos \left (c t \right )-a x_{3} \\ \end{align*}

system_of_ODEs

0.264

13115

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

system_of_ODEs

0.148

13116

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

system_of_ODEs

0.327

13117

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

system_of_ODEs

0.334

13118

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

system_of_ODEs

0.213

13119

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

system_of_ODEs

0.135

13120

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

system_of_ODEs

0.287

13121

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

system_of_ODEs

0.339

13122

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

system_of_ODEs

0.237

13123

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

system_of_ODEs

0.200

13124

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

system_of_ODEs

0.220

13125

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

system_of_ODEs

0.352

13126

\begin{align*} x&=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right ) \\ y&=y^{\prime } t +g \left (x^{\prime }, y^{\prime }\right ) \\ \end{align*}

system_of_ODEs

0.326

13127

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

system_of_ODEs

0.162

13128

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

system_of_ODEs

0.135

13129

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

system_of_ODEs

0.281

13130

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

system_of_ODEs

0.157

13131

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

system_of_ODEs

0.172

13132

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

system_of_ODEs

0.177

13133

\begin{align*} x^{\prime }&=\frac {x^{2}}{2}-\frac {y}{24} \\ y^{\prime }&=2 x y-3 z \\ z^{\prime }&=3 x z-\frac {y^{2}}{6} \\ \end{align*}

system_of_ODEs

0.243

13134

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

system_of_ODEs

0.162

13135

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

system_of_ODEs

0.275

13136

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

system_of_ODEs

0.190

13137

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

system_of_ODEs

0.200

13138

\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.498

13139

\(\left [\begin {array}{cc} 5 & -6 \\ 3 & -4 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.486

13140

\(\left [\begin {array}{cc} 8 & -6 \\ 3 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.571

13141

\(\left [\begin {array}{cc} 4 & -3 \\ 2 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.644

13142

\(\left [\begin {array}{cc} 10 & -9 \\ 6 & -5 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.614

13143

\(\left [\begin {array}{cc} 6 & -4 \\ 3 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.658

13144

\(\left [\begin {array}{cc} 10 & -8 \\ 6 & -4 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.622

13145

\(\left [\begin {array}{cc} 7 & -6 \\ 12 & -10 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.698

13146

\(\left [\begin {array}{cc} 8 & -10 \\ 2 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.655

13147

\(\left [\begin {array}{cc} 9 & -10 \\ 2 & 0 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.651

13148

\(\left [\begin {array}{cc} 19 & -10 \\ 21 & -10 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.585

13149

\(\left [\begin {array}{cc} 13 & -15 \\ 6 & -6 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.652

13150

\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 2 & -2 & -1 \\ -2 & 6 & 3 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.967

13151

\(\left [\begin {array}{ccc} 5 & 0 & 0 \\ 4 & -4 & -2 \\ -2 & 12 & 6 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.081

13152

\(\left [\begin {array}{ccc} 2 & -2 & 0 \\ 2 & -2 & -1 \\ -2 & 2 & 3 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.930

13153

\(\left [\begin {array}{ccc} 1 & 0 & -1 \\ -2 & 3 & -1 \\ -6 & 6 & 0 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.086

13154

\(\left [\begin {array}{ccc} 3 & 5 & -2 \\ 0 & 2 & 0 \\ 0 & 2 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.848

13155

\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -6 & 8 & 2 \\ 12 & -15 & -3 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.024

13156

\(\left [\begin {array}{ccc} 3 & 6 & -2 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.757

13157

\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -4 & 7 & 2 \\ 10 & -15 & -4 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.786

13158

\(\left [\begin {array}{ccc} 4 & -3 & 1 \\ 2 & -1 & 1 \\ 0 & 0 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.840

13159

\(\left [\begin {array}{ccc} 5 & -6 & 3 \\ 6 & -7 & 3 \\ 6 & -6 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.707

13160

\(\left [\begin {array}{cccc} 1 & 2 & 2 & 2 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 0 & 4 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.467

13161

\(\left [\begin {array}{cccc} 1 & 0 & 4 & 0 \\ 0 & 1 & 4 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.809

13162

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

Eigenvectors

N/A

N/A

N/A

0.881

13163

\(\left [\begin {array}{cccc} 4 & 0 & 0 & -3 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 6 & 0 & 0 & -5 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.385

13164

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

Eigenvectors

N/A

N/A

N/A

0.686

13165

\(\left [\begin {array}{cc} 0 & -6 \\ 6 & 0 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.668

13166

\(\left [\begin {array}{cc} 0 & -3 \\ 12 & 0 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.674

13167

\(\left [\begin {array}{cc} 0 & -12 \\ 12 & 0 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.642

13168

\(\left [\begin {array}{cc} 0 & 24 \\ -6 & 0 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.572

13169

\(\left [\begin {array}{cc} 0 & -4 \\ 36 & 0 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.754

13170

\(\left [\begin {array}{ccc} 32 & -67 & 47 \\ 7 & -14 & 13 \\ -7 & 15 & -6 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.108

13171

\(\left [\begin {array}{cccc} 22 & -9 & -8 & -8 \\ 10 & -7 & -14 & 2 \\ 10 & 0 & 8 & -10 \\ 29 & -9 & -3 & -15 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.813

13172

\(\left [\begin {array}{cc} 5 & -4 \\ 2 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.510

13173

\(\left [\begin {array}{cc} 6 & -6 \\ 4 & -4 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.618

13174

\(\left [\begin {array}{cc} 5 & -3 \\ 2 & 0 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.490

13175

\(\left [\begin {array}{cc} 5 & -4 \\ 3 & -2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.608

13176

\(\left [\begin {array}{cc} 9 & -8 \\ 6 & -5 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.615

13177

\(\left [\begin {array}{cc} 10 & -6 \\ 12 & -7 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.750

13178

\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.527

13179

\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.548

13180

\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.426

13181

\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.312

13182

\(\left [\begin {array}{cc} 5 & 1 \\ -9 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.480

13183

\(\left [\begin {array}{cc} 11 & 9 \\ -16 & -13 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.483

13184

\(\left [\begin {array}{ccc} 1 & 3 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.726

13185

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

Eigenvectors

N/A

N/A

N/A

0.770

13186

\(\left [\begin {array}{ccc} 3 & -3 & 1 \\ 2 & -2 & 1 \\ 0 & 0 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.719

13187

\(\left [\begin {array}{ccc} 3 & -2 & 0 \\ 0 & 1 & 0 \\ -4 & 4 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.697

13188

\(\left [\begin {array}{ccc} 7 & -8 & 3 \\ 6 & -7 & 3 \\ 2 & -2 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.022

13189

\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.022

13190

\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ -2 & 4 & -1 \\ -4 & 4 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.011

13191

\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ -6 & 11 & 2 \\ 6 & -15 & 0 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

1.052

13192

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

Eigenvectors

N/A

N/A

N/A

0.435

13193

\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ -1 & 2 & 0 \\ -5 & 7 & -1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.434

13194

\(\left [\begin {array}{ccc} -2 & 4 & -1 \\ -3 & 5 & -1 \\ -1 & 1 & 1 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.645

13195

\(\left [\begin {array}{ccc} 3 & -2 & 1 \\ 1 & 0 & 1 \\ -1 & 1 & 2 \end {array}\right ]\)

Eigenvectors

N/A

N/A

N/A

0.733

13196

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

Eigenvectors

N/A

N/A

N/A

0.959

13197

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

Eigenvectors

N/A

N/A

N/A

0.905

13198

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

Eigenvectors

N/A

N/A

N/A

0.747

13199

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

Eigenvectors

N/A

N/A

N/A

0.775

13200

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

Eigenvectors

N/A

N/A

N/A

0.828