2.52 Problems 5101 to 5200

Table 2.52: Main lookup table

#

ODE

Mathematica result

Maple result

5101

\[ {}y^{\prime \prime }+y = 4 \sin \relax (x ) \]

5102

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

5103

\[ {}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \relax (x ) \]

5104

\[ {}\sin \relax (x ) u^{\prime \prime }+2 \cos \relax (x ) u^{\prime }+\sin \relax (x ) u = 0 \]

5105

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

5106

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

5107

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

5108

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

5109

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \relax (t )-5 \cos \relax (t ) \]

5110

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = g \relax (t ) \]

5111

\[ {}y^{\relax (5)}-\frac {y^{\prime \prime \prime \prime }}{t} = 0 \]

5112

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

5113

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y = f \relax (x ) \]

5114

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

5115

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x} \]

5116

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x} \]

5117

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

5118

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \]

5119

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

5120

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

5121

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

5122

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

5123

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

5124

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

5125

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

5126

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

5127

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

5128

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

5129

\[ {}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0 \]

5130

\[ {}u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0 \]

5131

\[ {}\left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \left (\sin ^{2}\left (\theta \right )\right )-\phi \sin \left (\theta \right ) \cos \left (\theta \right ) = \frac {\cos \left (2 \theta \right )}{2}+1 \]

5132

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

5133

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

5134

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

5135

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

5136

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

5137

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

5138

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

5139

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

5140

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

5141

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

5142

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

5143

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

5144

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

5145

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-18 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )-9 x_{2}\relax (t )] \]

5146

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )+3 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 5 x_{1}\relax (t )+3 x_{2}\relax (t )] \]

5147

\[ {}[x_{1}^{\prime }\relax (t ) = -x_{1}\relax (t )+3 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = -3 x_{1}\relax (t )+5 x_{2}\relax (t )] \]

5148

\[ {}[x_{1}^{\prime }\relax (t ) = 4 x_{1}\relax (t )-x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 5 x_{1}\relax (t )+2 x_{2}\relax (t )] \]

5149

\[ {}[x_{1}^{\prime }\relax (t ) = -2 x_{1}\relax (t )+x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )-2 x_{2}\relax (t )] \]

5150

\[ {}[x_{1}^{\prime }\relax (t ) = -2 x_{1}\relax (t )+x_{2}\relax (t )+2 \,{\mathrm e}^{-t}, x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )-2 x_{2}\relax (t )+3 t] \]

5151

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 16 x_{1}\relax (t )-5 x_{2}\relax (t )] \]

5152

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )-2 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-4 x_{2}\relax (t )] \]

5153

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-18 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )-9 x_{2}\relax (t )] \]

5154

\[ {}[x_{1}^{\prime }\relax (t ) = -x_{1}\relax (t )+3 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = -3 x_{1}\relax (t )+5 x_{2}\relax (t )] \]

5155

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-18 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )-9 x_{2}\relax (t )] \]

5156

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 4 x_{1}\relax (t )-2 x_{2}\relax (t )] \]

5157

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )+x_{2}\relax (t )-8, x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+x_{2}\relax (t )+3] \]

5158

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )+x_{2}\relax (t )-8, x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+x_{2}\relax (t )+3] \]

5159

\[ {}y^{\prime } = {\mathrm e}^{3 x}+\sin \relax (x ) \]

5160

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

5161

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

5162

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

5163

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

5164

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

5165

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

5166

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

5167

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

5168

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

5169

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

5170

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

5171

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

5172

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

5173

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

5174

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

5175

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

5176

\[ {}L y^{\prime }+R y = E \]

5177

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

5178

\[ {}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x} \]

5179

\[ {}y^{\prime }+a y = b \relax (x ) \]

5180

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

5181

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

5182

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

5183

\[ {}y^{\prime }-y \tan \relax (x ) = {\mathrm e}^{\sin \relax (x )} \]

5184

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

5185

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

5186

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

5187

\[ {}y^{\prime }+2 y = b \relax (x ) \]

5188

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

5189

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

5190

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

5191

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

5192

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

5193

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

5194

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

5195

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

5196

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

5197

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

5198

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

5199

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

5200

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