2.52 Problems 5101 to 5200

Table 2.103: Main lookup table

#

ODE

Mathematica result

Maple result

5101

\[ {}y^{\prime }+y \cot \left (x \right ) = 5 \,{\mathrm e}^{\cos \left (x \right )} \]

5102

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

5103

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

5104

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

5105

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

5106

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

5107

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

5108

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

5109

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

5110

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

5111

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

5112

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

5113

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

5114

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

5115

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

5116

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

5117

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

5118

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

5119

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

5120

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

5121

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

5122

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

5123

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

5124

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

5125

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

5126

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

5127

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

5128

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

5129

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

5130

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

5131

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

5132

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

5133

\[ {}\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1 \]

5134

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

5135

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

5136

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 8 \]

5137

\[ {}y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \]

5138

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

5139

\[ {}y^{\prime \prime }+25 y = 5 x^{2}+x \]

5140

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

5141

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \]

5142

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

5143

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \]

5144

\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \]

5145

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \]

5146

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \]

5147

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

5148

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

5149

\[ {}y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \]

5150

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

5151

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

5152

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

5153

\[ {}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right ) \]

5154

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

5155

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \]

5156

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

5157

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

5158

\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

5159

\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]

5160

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

5161

\[ {}\frac {x^{\prime \prime }}{2} = -48 x \]

5162

\[ {}x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \]

5163

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

5164

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

5165

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

5166

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \]

5167

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

5168

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

5169

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

5170

\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \]

5171

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

5172

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

5173

\[ {}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \]

5174

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

5175

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

5176

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

5177

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

5178

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

5179

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

5180

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

5181

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

5182

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

5183

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

5184

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

5185

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = \frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \]

5186

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

5187

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

5188

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

5189

\[ {}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right ) \]

5190

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

5191

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

5192

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

5193

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

5194

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

5195

\[ {}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \]

5196

\[ {}y^{\prime \prime }-7 y^{\prime } = -3 \]

5197

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

5198

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

5199

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

5200

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