3.9.55 Problems 5401 to 5500

Table 3.615: First order ode linear in derivative

#

ODE

Mathematica

Maple

14079

\[ {}y^{\prime } = \frac {\sqrt {x^{2}-16}}{x} \]

14080

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

14081

\[ {}y^{\prime } = \frac {1}{x^{2}-16} \]

14082

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

14083

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

14084

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

14085

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

14092

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

14093

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

14094

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

14095

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

14096

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

14097

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

14098

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

14101

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

14102

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

14106

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

14107

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

14114

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

14115

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

14116

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

14117

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

14118

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

14119

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

14120

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

14123

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

14124

\[ {}y^{\prime } = \frac {4 x -9}{3 \left (x -3\right )^{\frac {2}{3}}} \]

14125

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

14126

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

14127

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

14128

\[ {}y^{\prime } = y^{\frac {1}{5}} \]

14129

\[ {}\frac {y^{\prime }}{t} = \sqrt {y} \]

14130

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

14131

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

14132

\[ {}y^{\prime } = 6 y^{\frac {2}{3}} \]

14133

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

14134

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

14135

\[ {}y^{\prime } = y \tan \left (t \right ) \]

14136

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

14137

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

14138

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

14139

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

14140

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

14141

\[ {}y^{\prime } = \sqrt {25-y^{2}} \]

14142

\[ {}y^{\prime } = \sqrt {25-y^{2}} \]

14143

\[ {}y^{\prime } = \sqrt {25-y^{2}} \]

14144

\[ {}y^{\prime } = \sqrt {25-y^{2}} \]

14145

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

14146

\[ {}t^{3} y^{\prime }+t^{4} y = 2 t^{3} \]

14147

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

14148

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

14149

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

14150

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

14151

\[ {}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t \]

14152

\[ {}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t \]

14153

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

14154

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

14155

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

14156

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

14157

\[ {}y^{\prime } = -\frac {t}{y} \]

14158

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

14159

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

14160

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

14161

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

14162

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

14163

\[ {}6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime } = 0 \]

14164

\[ {}\frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime } = 0 \]

14165

\[ {}4 \sinh \left (4 y\right ) y^{\prime } = 6 \cosh \left (3 x \right ) \]

14166

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

14167

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

14168

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

14169

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

14170

\[ {}\cos \left (y\right ) y^{\prime } = 8 \sin \left (8 t \right ) \]

14171

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

14172

\[ {}\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right ) = 0 \]

14173

\[ {}\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime } = 0 \]

14174

\[ {}y^{\prime } = {\mathrm e}^{2 y+10 t} \]

14175

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

14176

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

14177

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

14178

\[ {}x^{\prime } = \frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \]

14179

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

14180

\[ {}y^{\prime } = \frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \]

14181

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

14182

\[ {}y^{\prime } = \frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \]

14183

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

14184

\[ {}\frac {-2+x}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \]

14185

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

14186

\[ {}y^{\prime } = \frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \]

14187

\[ {}\frac {\sqrt {\ln \left (x \right )}}{x} = \frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \]

14188

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

14189

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

14190

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

14191

\[ {}4 \left (-1+x \right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0 \]

14192

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

14193

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

14194

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

14195

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

14196

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

14197

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