3.9.29 Problems 2801 to 2900

Table 3.563: First order ode linear in derivative

#

ODE

Mathematica

Maple

6149

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

6150

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

6151

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

6152

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

6153

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

6154

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

6157

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

6158

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

6159

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

6160

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

6161

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

6162

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

6163

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

6164

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

6165

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

6166

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

6167

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

6168

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

6169

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

6170

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

6171

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

6172

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

6173

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

6174

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

6175

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

6176

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

6177

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

6178

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

6179

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

6180

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

6181

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

6182

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

6183

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

6184

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

6185

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

6186

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

6187

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

6188

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

6189

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

6190

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

6191

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

6192

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

6193

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

6194

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

6195

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

6196

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

6197

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

6198

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

6199

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

6200

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

6201

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

6202

\[ {}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0 \]

6203

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

6204

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

6205

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

6206

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

6207

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

6208

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

6209

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

6210

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

6211

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

6212

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

6213

\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \]

6214

\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \]

6215

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

6216

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

6217

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

6218

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

6219

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

6220

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

6221

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

6222

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

6223

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

6224

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

6225

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

6226

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

6227

\[ {}x y^{\prime }+y+3 x^{3} y^{4} y^{\prime } = 0 \]

6228

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

6229

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

6230

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

6231

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

6232

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

6233

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

6234

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

6235

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

6236

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

6249

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

6250

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

6251

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

6252

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

6253

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

6254

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

6255

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

6256

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

6257

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

6258

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

6259

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

6260

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

6261

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

6262

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