4.1.75 Problems 7401 to 7500

Table 4.149: First order ode

#

ODE

Mathematica

Maple

Sympy

16785

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

16786

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

16787

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

16788

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

16789

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

16790

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

16791

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

16792

\[ {} 5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \]

16793

\[ {} 3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0 \]

16794

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

16795

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

16796

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

16797

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

16798

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

16799

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

16800

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

16801

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

16802

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

16803

\[ {} y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0 \]

16804

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

16805

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

16806

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

16807

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

16808

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

16809

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

16810

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

16811

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

16812

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

16813

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

16814

\[ {} 2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime } = 0 \]

16815

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

16816

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

16817

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

16818

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

16819

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

16820

\[ {} y^{\prime } = \sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \]

16821

\[ {} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \]

16822

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

16823

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

16824

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

16825

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

16826

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

16831

\[ {} {y^{\prime }}^{4} = 1 \]

16846

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

17204

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

17205

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

17206

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

17207

\[ {} 2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t} \]

17208

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

17221

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

17222

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

17223

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

17224

\[ {} y^{\prime } = \frac {7 x^{2}-1}{7+5 y} \]

17225

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

17226

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

17227

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

17228

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

17229

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

17230

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

17231

\[ {} y^{\prime } = 4 \sqrt {x y} \]

17232

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

17233

\[ {} y^{\prime } = \left (1-12 x \right ) y^{2} \]

17234

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

17235

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

17236

\[ {} r^{\prime } = \frac {r^{2}}{\theta } \]

17237

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

17238

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

17239

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

17240

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

17241

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

17242

\[ {} y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6} \]

17243

\[ {} y^{\prime } = \frac {3 x^{2}-{\mathrm e}^{x}}{2 y-11} \]

17244

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

17245

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

17246

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

17247

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

17248

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

17249

\[ {} y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y} \]

17250

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

17251

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

17252

\[ {} y^{\prime } = \frac {6-{\mathrm e}^{x}}{3+2 y} \]

17253

\[ {} y^{\prime } = \frac {2 \cos \left (2 x \right )}{10+2 y} \]

17254

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

17255

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

17256

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

17257

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

17258

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

17259

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

17260

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

17261

\[ {} y^{\prime }+\frac {y}{t} = 5+\cos \left (2 t \right ) \]

17262

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

17263

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

17264

\[ {} y^{\prime }+2 t y = 16 t \,{\mathrm e}^{-t^{2}} \]

17265

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

17266

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

17267

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

17268

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

17269

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

17270

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

17271

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