4.62 Problems 6101 to 6200

Table 4.123: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

6101

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

6102

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 6 y_{1} \left (x \right )+y_{2} \left (x \right )] \]

6103

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+{\mathrm e}^{3 x}] \]

6104

\[ {}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+x y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 x y_{2} \left (x \right )-y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right )] \]

6105

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

6106

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

6107

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

6108

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

6109

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

6110

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

6111

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

6112

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

6113

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

6114

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

6115

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

6116

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

6117

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

6118

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

6119

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

6120

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

6121

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

6122

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

6123

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

6124

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

6125

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

6126

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

6127

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

6128

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

6129

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

6130

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

6131

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

6132

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

6133

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

6134

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

6135

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

6136

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

6137

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

6138

\[ {}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0 \]

6139

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

6140

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

6141

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

6142

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

6143

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

6144

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

6145

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

6146

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

6147

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

6148

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

6149

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

6150

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

6151

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

6152

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

6153

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

6154

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

6155

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

6156

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

6157

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

6158

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

6159

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

6160

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

6161

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

6162

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

6163

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

6164

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

6165

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

6166

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

6167

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

6168

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

6169

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

6170

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

6171

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

6172

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

6173

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

6174

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

6175

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

6176

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

6177

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

6178

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

6179

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

6180

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

6181

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

6182

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

6183

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

6184

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

6185

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

6186

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

6187

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

6188

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

6189

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

6190

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

6191

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

6192

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

6193

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

6194

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

6195

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

6196

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

6197

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

6198

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

6199

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

6200

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