6.142 Problems 14101 to 14200

Table 6.283: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

14101

\[ {} 2 \sqrt {s t}-s+t s^{\prime } = 0 \]

14102

\[ {} t -s+t s^{\prime } = 0 \]

14103

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

14104

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

14105

\[ {} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \]

14106

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

14107

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

14108

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

14109

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

14110

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

14111

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

14112

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

14113

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

14114

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

14115

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

14116

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

14117

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

14118

\[ {} y^{\prime }+\frac {n y}{x} = a \,x^{-n} \]

14119

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

14120

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

14121

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

14122

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

14123

\[ {} 3 y^{2} y^{\prime }-a y^{3}-x -1 = 0 \]

14124

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

14125

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

14126

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

14127

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

14128

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

14129

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

14130

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

14131

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

14132

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

14133

\[ {} \frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}} \]

14134

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

14135

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

14136

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

14137

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

14138

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

14139

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

14140

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

14141

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

14142

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

14143

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

14144

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

14145

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

14146

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

14147

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

14148

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

14149

\[ {} y^{\prime \prime } = a^{2} y \]

14150

\[ {} y^{\prime \prime } = \frac {a}{y^{3}} \]

14151

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

14152

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

14153

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

14154

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

14155

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

14156

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

14157

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

14158

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

14159

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

14160

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

14161

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

14162

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

14163

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]

14164

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

14165

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

14166

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

14167

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \]

14168

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

14169

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

14170

\[ {} y^{\left (5\right )}-4 y^{\prime \prime \prime } = 0 \]

14171

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y = 0 \]

14172

\[ {} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0 \]

14173

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

14174

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

14175

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

14176

\[ {} s^{\prime \prime }-a^{2} s = t +1 \]

14177

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

14178

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

14179

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

14180

\[ {} y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \]

14181

\[ {} y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

14182

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

14183

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

14184

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

14185

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3 \]

14186

\[ {} y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \]

14187

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

14188

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

14189

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

14190

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

14191

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

14192

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

14193

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

14194

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

14195

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

14196

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

14197

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

14198

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

14199

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

14200

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