6.142 Problems 14101 to 14200

Table 6.283: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

14101

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

14102

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

14103

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

14104

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

14105

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

14106

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

14107

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

14108

\[ {} 4 x y^{\prime }+3 y+{\mathrm e}^{x} x^{4} y^{5} = 0 \]

14109

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

14110

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

14111

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

14112

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

14113

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

14114

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

14115

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

14116

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

14117

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

14118

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

14119

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

14120

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

14121

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

14122

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

14123

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

14124

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

14125

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

14126

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

14127

\[ {} x y^{\prime }-a y+b y^{2} = c \,x^{2 a} \]

14128

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

14129

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

14130

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

14131

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

14132

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

14133

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

14134

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

14135

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

14136

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

14137

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

14138

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

14139

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

14140

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

14141

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

14142

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

14143

\[ {} 5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0 \]

14144

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

14145

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

14146

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

14147

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

14148

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

14149

\[ {} 2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0 \]

14150

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

14151

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

14152

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

14153

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

14154

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

14155

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

14156

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

14157

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

14158

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

14159

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

14160

\[ {} \left (2 x y^{\prime }-y\right )^{2} = 8 x^{3} \]

14161

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

14162

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

14163

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

14164

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

14165

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

14166

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

14167

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

14168

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

14169

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

14170

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

14171

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

14172

\[ {} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0 \]

14173

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

14174

\[ {} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0 \]

14175

\[ {} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0 \]

14176

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

14177

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

14178

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

14179

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

14180

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

14181

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

14182

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

14183

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

14184

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

14185

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

14186

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

14187

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

14188

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

14189

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

14190

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

14191

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

14192

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

14193

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

14194

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

14195

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

14196

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

14197

\[ {} 8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \]

14198

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

14199

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

14200

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