4.1.31 Problems 3001 to 3100

Table 4.61: First order ode

#

ODE

Mathematica

Maple

Sympy

7025

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

7026

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

7027

\[ {} x y^{\prime }+a y+b \,x^{n} = 0 \]

7028

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

7029

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

7030

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

7031

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

7032

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

7033

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

7034

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

7035

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

7036

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

7037

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

7038

\[ {} y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \]

7039

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

7040

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

7041

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

7042

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

7043

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

7044

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

7045

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

7046

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

7047

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

7048

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

7049

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

7050

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

7154

\[ {} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0 \]

7155

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

7156

\[ {} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0 \]

7157

\[ {} y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {f \left (x \right ) a +b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0 \]

7158

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

7159

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

7160

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

7162

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

7163

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

7164

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

7166

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

7167

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

7168

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

7169

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

7170

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

7171

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

7172

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

7173

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

7174

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

7210

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

7227

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

7228

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

7229

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

7230

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

7231

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

7232

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

7233

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

7234

\[ {} y y^{\prime }+x y^{2}-8 x = 0 \]

7235

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

7236

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

7237

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

7238

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

7239

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

7240

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

7241

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

7242

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

7243

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

7244

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

7245

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

7246

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

7247

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

7248

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

7249

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

7250

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

7251

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

7252

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

7253

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

7254

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

7255

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

7256

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

7257

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

7258

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

7259

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

7260

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

7261

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

7262

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

7263

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

7264

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

7265

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

7266

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

7267

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

7268

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

7269

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

7343

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

7344

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

7347

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

7349

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

7351

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

7352

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

7353

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

7359

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

7360

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

7361

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

7363

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