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2.2.272 Problems 27101 to 27200

Table 2.561: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

27101

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

Eigenvectors

✓

N/A

N/A

N/A

3.733

27102

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

Eigenvectors

✓

N/A

N/A

N/A

4.555

27103

\(\left [\begin {array}{cccc} 5 & 1 & 0 & 9 \\ 0 & 1 & 0 & 9 \\ 0 & 0 & 0 & 9 \\ 0 & 0 & 0 & 0 \end {array}\right ]\)

Eigenvectors

✓

N/A

N/A

N/A

2.570

27104

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

Eigenvectors

✓

N/A

N/A

N/A

2.493

27105

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

Eigenvectors

✓

N/A

N/A

N/A

2.619

27106

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

Eigenvectors

✓

N/A

N/A

N/A

2.480

27107

\(\left [\begin {array}{cc} -13 & 1 \\ 1 & 4 \end {array}\right ]\)

Eigenvectors

✓

N/A

N/A

N/A

2.618

27108

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

Eigenvectors

✓

N/A

N/A

N/A

3.170

27109

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

Eigenvectors

✓

N/A

N/A

N/A

3.601

27110

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

Eigenvectors

✓

N/A

N/A

N/A

2.625

27111

\(\left [\begin {array}{cc} 5 & 3 \\ 1 & 3 \end {array}\right ]\)

Eigenvectors

✓

N/A

N/A

N/A

2.114

27112

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

Eigenvectors

✓

N/A

N/A

N/A

0.970

27113

\(\left [\begin {array}{cc} -5 & 3 \\ 0 & 9 \end {array}\right ]\)

Eigenvectors

✓

N/A

N/A

N/A

1.786

27114

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

Eigenvectors

✓

N/A

N/A

N/A

2.718

27115

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

Eigenvectors

✓

N/A

N/A

N/A

3.141

27116

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

Eigenvectors

✓

N/A

N/A

N/A

1.861

27117

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

Eigenvectors

✓

N/A

N/A

N/A

2.711

27118

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

Eigenvectors

✓

N/A

N/A

N/A

4.050

27119

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

Eigenvectors

✓

N/A

N/A

N/A

1.149

27120

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

Eigenvectors

✓

N/A

N/A

N/A

2.460

27121

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

Eigenvectors

✓

N/A

N/A

N/A

2.500

27122

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

Eigenvectors

✓

N/A

N/A

N/A

2.490

27123

\(\left [\begin {array}{cc} -13 & 1 \\ 1 & 4 \end {array}\right ]\)

Eigenvectors

✓

N/A

N/A

N/A

2.500

27124

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

Eigenvectors

✓

N/A

N/A

N/A

3.075

27125

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

Eigenvectors

✓

N/A

N/A

N/A

3.517

27126

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

Eigenvectors

✓

N/A

N/A

N/A

3.270

27127

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

Eigenvectors

✓

N/A

N/A

N/A

3.192

27128

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

Eigenvectors

✓

N/A

N/A

N/A

3.161

27129

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

Eigenvectors

✓

N/A

N/A

N/A

3.578

27130

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

Eigenvectors

✓

N/A

N/A

N/A

2.744

27131

\(\left [\begin {array}{cc} 0 & 2 i \\ 2 i & 4 \end {array}\right ]\)

Eigenvectors

✓

N/A

N/A

N/A

1.654

27132

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

Eigenvectors

✓

N/A

N/A

N/A

1.672

27133

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

Eigenvectors

✓

N/A

N/A

N/A

3.582

27134

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

Eigenvectors

✓

N/A

N/A

N/A

3.593

27135

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

Eigenvectors

✓

N/A

N/A

N/A

19.316

27136

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

Eigenvectors

✓

N/A

N/A

N/A

3.309

27137

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

Eigenvectors

✓

N/A

N/A

N/A

18.937

27138

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

Eigenvectors

✓

N/A

N/A

N/A

2.298

27139

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

2.507

27140

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

With initial conditions

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

system_of_ODEs

✓

✓

✓

✓

3.359

27141

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= -2 \\ x_{2} \left (0\right ) &= 7 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

17.385

27142

\begin{align*} x_{1}^{\prime }&=5 x_{1}-4 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=12 x_{1}-11 x_{2}+12 x_{3} \\ x_{3}^{\prime }&=4 x_{1}-4 x_{2}+5 x_{3} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -3 \\ x_{3} \left (0\right ) &= 5 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.330

27143

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

system_of_ODEs

✓

✓

✓

✓

2.954

27144

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

system_of_ODEs

✓

✓

✓

✓

3.174

27145

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

system_of_ODEs

✓

✓

✓

✓

2.562

27146

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

system_of_ODEs

✓

✓

✓

✗

125.091

27147

\begin{align*} x_{1}^{\prime }&=2 x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ x_{3}^{\prime }&=-x_{1}-2 x_{2}-x_{3} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✗

249.535

27148

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 7 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

2.625

27149

\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=-6 x_{1} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -19 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.177

27150

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

With initial conditions

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

system_of_ODEs

✓

✓

✓

✓

3.270

27151

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.509

27152

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 7 \\ x_{3} \left (0\right ) &= 3 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

4.167

27153

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

system_of_ODEs

✓

✓

✓

✓

3.299

27154

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

system_of_ODEs

✓

✓

✓

✓

3.671

27155

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

system_of_ODEs

✓

✓

✓

✓

3.486

27156

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

system_of_ODEs

✓

✓

✓

✓

3.425

27157

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

system_of_ODEs

✓

✓

✓

✓

4.707

27158

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

system_of_ODEs

✓

✓

✓

✓

1.754

27159

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

system_of_ODEs

✓

✓

✓

✓

1.706

27160

\begin{align*} x_{1}^{\prime }&=x_{1}+5 x_{2} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=4 x_{1}+8 x_{2}+x_{3} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

2.295

27161

\begin{align*} x_{1}^{\prime }&=2 x_{1}+5 x_{2}+6 x_{3} \\ x_{2}^{\prime }&=8 x_{2}+9 x_{3} \\ x_{3}^{\prime }&=x_{2}-2 x_{3} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

5.466

27162

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

system_of_ODEs

✓

✓

✓

✗

128.678

27163

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

system_of_ODEs

✓

✓

✓

✓

5.418

27164

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

system_of_ODEs

✓

✓

✓

✓

3.221

27165

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

system_of_ODEs

✓

✓

✓

✓

3.297

27166

\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{2}+2 \,{\mathrm e}^{6 t} \\ x_{2}^{\prime }&=x_{1}+5 x_{2}+6 t \,{\mathrm e}^{6 t} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.194

27167

\begin{align*} x_{1}^{\prime }&=2 x_{1}+{\mathrm e}^{2 t} \cos \left (3 t \right ) \\ x_{2}^{\prime }&=6 x_{2}-4 x_{3}-2 \\ x_{3}^{\prime }&=4 x_{2}-2 x_{3}-2 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

4.148

27168

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2}-2 \,{\mathrm e}^{t} \\ x_{3}^{\prime }&=3 x_{3} \\ x_{4}^{\prime }&=-x_{1}+2 x_{2}+9 x_{3}+x_{4}+{\mathrm e}^{t} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

5.346

27169

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

With initial conditions

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

system_of_ODEs

✓

✓

✓

✓

2.023

27170

\begin{align*} x_{1}^{\prime }&=5 x_{1}-4 x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=4 x_{1}-3 x_{2}+2 \,{\mathrm e}^{t} \\ \end{align*}

With initial conditions

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

system_of_ODEs

✓

✓

✓

✗

2.514

27171

\begin{align*} x_{1}^{\prime }&=2 x_{1}-3 x_{2}+x_{3}+10 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{2}+4 x_{3}+6 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }&=x_{3}-{\mathrm e}^{2 t} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= 11 \\ x_{3} \left (0\right ) &= -2 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.773

27172

\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2}+t \,{\mathrm e}^{-2 t} \\ x_{2}^{\prime }&=3 x_{1}-5 x_{2}+t \,{\mathrm e}^{-2 t} \\ x_{3}^{\prime }&=4 x_{1}+7 x_{2}-2 x_{3}+t^{2} {\mathrm e}^{-2 t} \\ \end{align*}

With initial conditions

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

system_of_ODEs

✓

✓

✓

✓

3.434

27173

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2}+10 \cos \left (t \right ) \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.964

27174

\begin{align*} x_{1}^{\prime }&=3 x_{1}+3 x_{2}+8 \\ x_{2}^{\prime }&=x_{1}+5 x_{2}+4 \,{\mathrm e}^{3 t} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

4.072

27175

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=x_{1}+x_{2}+4 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.408

27176

\begin{align*} x_{1}^{\prime }&=6 x_{1}+5 x_{2}-4 \cos \left (3 t \right ) \\ x_{2}^{\prime }&=x_{1}+2 x_{2}+8 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

4.845

27177

\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2}+3 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=9 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

4.458

27178

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+6 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{2 t} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 6 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.074

27179

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 13 \\ x_{2} \left (0\right ) &= 12 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.473

27180

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}+5 \sin \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 10 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

4.478

27181

\begin{align*} x_{1}^{\prime }&=5 x_{1}-4 x_{2}+3 x_{3}-3 \,{\mathrm e}^{-3 t} \\ x_{2}^{\prime }&=12 x_{1}-11 x_{2}+12 x_{3}+t \\ x_{3}^{\prime }&=4 x_{1}-4 x_{2}+5 x_{3} \\ \end{align*}

With initial conditions

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

system_of_ODEs

✓

✓

✓

✓

5.739

27182

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

With initial conditions

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

system_of_ODEs

✓

✓

✓

✓

3.585

27183

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

system_of_ODEs

✓

✓

✓

✓

3.454

27184

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

system_of_ODEs

✓

✓

✓

✓

3.007

27185

\begin{align*} x_{1}^{\prime }&=5 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+8 x_{2} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

17.514

27186

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

system_of_ODEs

✓

✓

✓

✓

3.806

27187

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

system_of_ODEs

✓

✓

✓

✓

5.127

27188

\begin{align*} x_{1}^{\prime }&=3 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=5 x_{1}-7 x_{2} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

2.300

27189

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

system_of_ODEs

✓

✓

✓

✓

3.081

27190

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

system_of_ODEs

✓

✓

✓

✓

3.423

27191

\begin{align*} x_{1}^{\prime }&=9 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-4 x_{2} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.105

27192

\begin{align*} x_{1}^{\prime }&=7 x_{1}-17 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.740

27193

\begin{align*} x_{1}^{\prime }&=2 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=5 x_{1}-10 x_{2} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

3.128

27194

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

system_of_ODEs

✓

✓

✓

✓

2.182

27195

\begin{align*} x_{1}^{\prime }&=3 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=8 x_{1}-3 x_{2} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

16.967

27196

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

system_of_ODEs

✓

✓

✓

✓

3.589

27197

\begin{align*} x_{1}^{\prime }&=-6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=7 x_{1}-20 x_{2} \\ \end{align*}

system_of_ODEs

✓

✓

✓

✓

2.323

27198

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

system_of_ODEs

✗

✓

✓

✗

0.336

27199

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

[[_linear, ‘class A‘]]

✓

✓

✓

✓

27.187

27200

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

[[_linear, ‘class A‘]]

✓

✓

✓

✓

34.119

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