2.72 Problems 7101 to 7200

Table 2.143: Main lookup table

#

ODE

Mathematica result

Maple result

7101

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

7102

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

7103

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

7104

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

7105

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

7106

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

7107

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

7108

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

7109

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

7110

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

7111

\[ {}3 y y^{\prime \prime }+y = 5 \]

7112

\[ {}a y y^{\prime \prime }+b y = c \]

7113

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

7114

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

7115

\[ {}[x^{\prime }\left (t \right ) = 9 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )] \]

7116

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

7117

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

7118

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

7119

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

7120

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

7121

\[ {}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{\frac {3}{4}}-3 k x \]

7122

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

7123

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

7124

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

7125

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

7126

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

7127

\[ {}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \]

7128

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

7129

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

7130

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

7131

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

7132

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

7133

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

7134

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

7135

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

7136

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

7137

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

7138

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

7139

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

7140

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

7141

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

7142

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0 \]

7143

\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \]

7144

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

7145

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

7146

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

7147

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

7148

\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0 \]

7149

\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0 \]

7150

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

7151

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

7152

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

7153

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

7154

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

7155

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

7156

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

7157

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

7158

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

7159

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

7160

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

7161

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

7162

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

7163

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

7164

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

7165

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

7166

\[ {}y^{\prime \prime }-x y-x^{6}+64 = 0 \]

7167

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

7168

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

7169

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

7170

\[ {}y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0 \]

7171

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

7172

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

7173

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

7174

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

7175

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

7176

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

7177

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

7178

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

7179

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

7180

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

7181

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

7182

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

7183

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

7184

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

7185

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

7186

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0 \]

7187

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

7188

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

7189

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

7190

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

7191

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

7192

\[ {}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \]

7193

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

7194

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

7195

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

7196

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

7197

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

7198

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

7199

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

7200

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