6.152 Problems 15101 to 15200

Table 6.303: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

15101

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{3 t}, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )] \]

15102

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

15103

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

15104

\[ {} [x^{\prime }\left (t \right ) = 8 x \left (t \right )+14 y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )] \]

15114

\[ {} [x^{\prime }\left (t \right ) = 8 x \left (t \right )+14 y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )] \]

15115

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

15116

\[ {} [x^{\prime }\left (t \right ) = 11 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right )] \]

15117

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+20 y \left (t \right ), y^{\prime }\left (t \right ) = 40 x \left (t \right )-19 y \left (t \right )] \]

15118

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

15119

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

15120

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

15121

\[ {} [x^{\prime }\left (t \right ) = -11 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 13 x \left (t \right )-9 y \left (t \right )] \]

15122

\[ {} [x^{\prime }\left (t \right ) = 7 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 10 x \left (t \right )-3 y \left (t \right )] \]

15123

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

15124

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

15125

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

15126

\[ {} [x^{\prime }\left (t \right ) = 13 x \left (t \right ), y^{\prime }\left (t \right ) = 13 y \left (t \right )] \]

15127

\[ {} [x^{\prime }\left (t \right ) = 7 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )] \]

15128

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

15129

\[ {} \tan \left (y\right )-\cot \left (x \right ) y^{\prime } = 0 \]

15130

\[ {} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \]

15131

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

15132

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

15133

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

15134

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

15135

\[ {} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y = 1 \]

15136

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

15137

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

15138

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

15139

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

15140

\[ {} {y^{\prime }}^{2} = 9 y^{4} \]

15141

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

15142

\[ {} {y^{\prime }}^{2}+x^{2} = 1 \]

15143

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

15144

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

15145

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

15146

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

15147

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

15148

\[ {} y^{\prime } = \frac {2 y-x -4}{2 x -y+5} \]

15149

\[ {} y^{\prime }-\frac {y}{1+x}+y^{2} = 0 \]

15150

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

15151

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

15152

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

15153

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

15154

\[ {} {y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime } = 0 \]

15155

\[ {} y = 5 x y^{\prime }-{y^{\prime }}^{2} \]

15156

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

15157

\[ {} y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2 \]

15158

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

15159

\[ {} x^{\prime }+5 x = 10 t +2 \]

15160

\[ {} x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}} \]

15161

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

15162

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

15163

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

15164

\[ {} x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right ) \]

15165

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

15166

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

15167

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

15168

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

15169

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

15170

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

15171

\[ {} y^{\prime } = \frac {x +y-3}{-x +y+1} \]

15172

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

15173

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

15174

\[ {} \left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1 = 0 \]

15175

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

15176

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

15177

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

15178

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

15179

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

15180

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

15181

\[ {} y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]

15182

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

15183

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

15184

\[ {} y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}} \]

15185

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

15186

\[ {} y^{\prime \prime }+y = \cosh \left (x \right ) \]

15187

\[ {} y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0 \]

15188

\[ {} x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \]

15189

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

15190

\[ {} x^{3} x^{\prime \prime }+1 = 0 \]

15191

\[ {} y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x} \]

15192

\[ {} {y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1 \]

15193

\[ {} x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1 \]

15194

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

15195

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

15196

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0 \]

15197

\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]

15198

\[ {} y^{\prime \prime } = 3 \sqrt {y} \]

15199

\[ {} y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )} \]

15200

\[ {} u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \]