6.132 Problems 13101 to 13200

Table 6.263: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

13101

\[ {} x^{\prime \prime \prime }-x^{\prime }-8 x = 0 \]

13102

\[ {} x^{\prime \prime \prime }+x^{\prime \prime } = 2 \,{\mathrm e}^{t}+3 t^{2} \]

13103

\[ {} x^{\prime \prime \prime }-8 x = 0 \]

13104

\[ {} x^{\prime \prime \prime }+x^{\prime \prime }-x^{\prime }-4 x = 0 \]

13105

\[ {} x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right ) \]

13106

\[ {} x^{\prime }+x = \sin \left (2 t \right ) \]

13107

\[ {} x^{\prime \prime }-x^{\prime }-6 x = 0 \]

13108

\[ {} x^{\prime \prime }-2 x^{\prime }+2 x = 0 \]

13109

\[ {} x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t} \]

13110

\[ {} x^{\prime \prime }-x^{\prime } = 0 \]

13111

\[ {} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right ) \]

13112

\[ {} x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]

13113

\[ {} x^{\prime \prime }-2 x = 1 \]

13114

\[ {} x^{\prime } = 2 x+\operatorname {Heaviside}\left (t -1\right ) \]

13115

\[ {} x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \]

13116

\[ {} x^{\prime } = x-2 \operatorname {Heaviside}\left (t -1\right ) \]

13117

\[ {} x^{\prime } = -x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \]

13118

\[ {} x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \]

13119

\[ {} x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right ) \]

13120

\[ {} x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t} \]

13121

\[ {} x^{\prime }+3 x = \delta \left (t -1\right )+\operatorname {Heaviside}\left (t -4\right ) \]

13122

\[ {} x^{\prime \prime }-x = \delta \left (t -5\right ) \]

13123

\[ {} x^{\prime \prime }+x = \delta \left (t -2\right ) \]

13124

\[ {} x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \]

13125

\[ {} x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right ) \]

13126

\[ {} y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right ) \]

13127

\[ {} x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \]

13128

\[ {} [x^{\prime }\left (t \right ) = -3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )] \]

13129

\[ {} [x^{\prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )] \]

13130

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )] \]

13131

\[ {} [x^{\prime }\left (t \right ) = 4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )] \]

13132

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )] \]

13133

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )] \]

13134

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )] \]

13135

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )] \]

13136

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )] \]

13137

\[ {} [x^{\prime }\left (t \right ) = -3 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )] \]

13138

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )] \]

13139

\[ {} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -4 y \left (t \right )] \]

13140

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+4 y \left (t \right )] \]

13141

\[ {} [x^{\prime }\left (t \right ) = -6 y \left (t \right ), y^{\prime }\left (t \right ) = 6 y \left (t \right )] \]

13142

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-14] \]

13143

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-1] \]

13144

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )] \]

13145

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )] \]

13146

\[ {} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )] \]

13147

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+3 y \left (t \right )] \]

13148

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )] \]

13149

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )] \]

13150

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )] \]

13151

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )] \]

13152

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )] \]

13153

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )] \]

13154

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )] \]

13155

\[ {} [x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-10 y \left (t \right )] \]

13156

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )] \]

13157

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )] \]

13158

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )] \]

13159

\[ {} [x^{\prime }\left (t \right ) = 9 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )] \]

13160

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )] \]

13161

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+4 y \left (t \right )] \]

13162

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )+1, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+2] \]

13163

\[ {} [x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-10 y \left (t \right )] \]

13164

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\cos \left (w t \right )] \]

13165

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+3, y^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )+2 t] \]

13166

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+7 y \left (t \right )] \]

13167

\[ {} y^{\prime }+y = 1+x \]

13168

\[ {} y^{\prime \prime }-7 y^{\prime }+12 y = 0 \]

13169

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2} \]

13170

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

13171

\[ {} 2 x y y^{\prime }+x^{2}+y^{2} = 0 \]

13172

\[ {} x y^{\prime }+y = x^{3} y^{3} \]

13173

\[ {} y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x} \]

13174

\[ {} y^{\prime }+4 x y = 8 x \]

13175

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

13176

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0 \]

13177

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

13178

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

13179

\[ {} y^{\prime }+2 y = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x} \]

13180

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right ) \]

13181

\[ {} {y^{\prime }}^{2}-4 y = 0 \]

13182

\[ {} y^{\prime \prime }+y^{\prime }-6 y = 0 \]

13183

\[ {} y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \]

13184

\[ {} y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \]

13185

\[ {} y^{\prime \prime }-y^{\prime }-12 y = 0 \]

13186

\[ {} y^{\prime \prime }+y = 0 \]

13187

\[ {} y^{\prime \prime }+y = 0 \]

13188

\[ {} y^{\prime \prime }+y = 0 \]

13189

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]

13190

\[ {} y^{\prime } = x^{2} \sin \left (y\right ) \]

13191

\[ {} y^{\prime } = \frac {y^{2}}{x -2} \]

13192

\[ {} y^{\prime } = y^{{1}/{3}} \]

13193

\[ {} 3 x +2 y+\left (y+2 x \right ) y^{\prime } = 0 \]

13194

\[ {} y^{2}+3+\left (2 x y-4\right ) y^{\prime } = 0 \]

13195

\[ {} 2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0 \]

13196

\[ {} 3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0 \]

13197

\[ {} 6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0 \]

13198

\[ {} y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime } = 0 \]

13199

\[ {} \frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime } = 0 \]

13200

\[ {} \frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0 \]