4.9.52 Problems 5101 to 5200

Table 4.941: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

14095

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

14096

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

14097

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

14098

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

14099

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

14100

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

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

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

14166

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

14306

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

14307

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

14308

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

14310

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

14311

\[ {} x^{\prime }+2 x = t^{2}+4 t +7 \]

14312

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

14315

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

14316

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

14317

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

14318

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

14320

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

14321

\[ {} x^{\prime } = \frac {1}{t \ln \left (t \right )} \]

14322

\[ {} \sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right ) \]

14323

\[ {} x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}} \]

14325

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

14326

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

14327

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

14328

\[ {} u^{\prime } = \frac {1}{5-2 u} \]

14329

\[ {} x^{\prime } = a x+b \]

14330

\[ {} Q^{\prime } = \frac {Q}{4+Q^{2}} \]

14331

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

14332

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

14333

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

14334

\[ {} \theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \]

14335

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

14336

\[ {} R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right ) \]

14337

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

14338

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

14339

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

14340

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

14341

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

14342

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

14343

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

14344

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

14345

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

14346

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

14347

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