6.43 Problems 4201 to 4300

Table 6.85: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

4201

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

4202

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

4203

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

4204

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

4205

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

4206

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

4207

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

4208

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

4209

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

4210

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

4211

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

4212

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

4213

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

4214

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

4215

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

4216

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

4217

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

4218

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

4219

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

4220

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

4221

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

4222

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

4223

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

4224

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

4225

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

4226

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

4227

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

4228

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

4229

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

4230

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

4231

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

4232

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

4233

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

4234

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

4235

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

4236

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

4237

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

4238

\[ {} x y y^{\prime } = \sqrt {y^{2}-9} \]

4239

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

4240

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

4241

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

4242

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

4243

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

4244

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

4245

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

4246

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

4247

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

4248

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

4249

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

4250

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

4251

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

4252

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

4253

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

4254

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

4255

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

4256

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

4257

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

4258

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

4259

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

4260

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

4261

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

4262

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

4263

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

4264

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

4265

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

4266

\[ {} x y^{\prime } = x^{5}+x^{3} y^{2}+y \]

4267

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

4268

\[ {} x y^{\prime } = y+x^{2}+9 y^{2} \]

4269

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

4270

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

4271

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

4272

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

4273

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

4274

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

4275

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

4276

\[ {} 2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \]

4277

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

4278

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

4279

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

4280

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

4281

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

4282

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

4283

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

4284

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

4285

\[ {} 6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0 \]

4286

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

4287

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

4288

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

4289

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

4290

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

4291

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

4292

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

4293

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

4294

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

4295

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

4296

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

4297

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

4298

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

4299

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

4300

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