2.63 Problems 6201 to 6300

Table 2.125: Main lookup table

#

ODE

Mathematica result

Maple result

6201

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

6202

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

6203

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

6204

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

6205

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

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

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

6211

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

6212

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

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

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

6219

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

6220

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

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

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

6237

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

6238

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

6239

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

6240

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

6241

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

6242

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

6243

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

6244

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

6245

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

6246

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

6247

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

6248

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

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

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

6254

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

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

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

6262

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

6263

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

6264

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

6265

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

6266

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

6267

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

6268

\[ {}x y^{\prime \prime }-3 y^{\prime } = 5 x \]

6269

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

6270

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

6271

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

6272

\[ {}2 y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

6273

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

6274

\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 0 \]

6275

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

6276

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

6277

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

6278

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

6279

\[ {}4 y^{\prime \prime }+20 y^{\prime }+25 y = 0 \]

6280

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

6281

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

6282

\[ {}4 y^{\prime \prime }-8 y^{\prime }+7 y = 0 \]

6283

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

6284

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

6285

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

6286

\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 0 \]

6287

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

6288

\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 0 \]

6289

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

6290

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

6291

\[ {}y^{\prime \prime }+4 y^{\prime }+2 y = 0 \]

6292

\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \]

6293

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \]

6294

\[ {}2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \]

6295

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

6296

\[ {}4 x^{2} y^{\prime \prime }-3 y = 0 \]

6297

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

6298

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

6299

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

6300

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