3.1.65 Problems 6401 to 6500

Table 3.129: First order ode

#

ODE

Mathematica

Maple

14222

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

14223

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

14224

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

14225

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

14226

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

14227

\[ {}y^{\prime } = 16 y-8 y^{2} \]

14228

\[ {}y^{\prime } = 12+4 y-y^{2} \]

14229

\[ {}y^{\prime } = f \left (t \right ) y \]

14230

\[ {}y^{\prime }-y = 10 \]

14231

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

14232

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

14233

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

14234

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

14235

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

14236

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

14237

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

14238

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

14239

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

14240

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

14241

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

14242

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

14243

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

14244

\[ {}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t \]

14245

\[ {}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x \]

14246

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

14247

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

14248

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

14249

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

14250

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

14251

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

14252

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

14253

\[ {}p^{\prime } = t^{3}+\frac {p}{t} \]

14254

\[ {}v^{\prime }+v = {\mathrm e}^{-s} \]

14255

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

14256

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

14257

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

14258

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

14259

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

14260

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

14261

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

14262

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

14263

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

14264

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

14265

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

14267

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \]

14268

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

14269

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

14270

\[ {}y^{\prime }+y = 5 \,{\mathrm e}^{2 t} \]

14271

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

14272

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

14273

\[ {}y^{\prime }-5 y = t \]

14274

\[ {}y^{\prime }+3 y = 27 t^{2}+9 \]

14275

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

14276

\[ {}y^{\prime }+4 y = 8 \cos \left (4 t \right ) \]

14277

\[ {}y^{\prime }+10 y = 2 \,{\mathrm e}^{t} \]

14278

\[ {}y^{\prime }-3 y = 27 t^{2} \]

14279

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

14280

\[ {}y^{\prime }+y = 4+3 \,{\mathrm e}^{t} \]

14281

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

14282

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

14283

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

14284

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

14285

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

14286

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

14287

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

14288

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

14289

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

14290

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

14291

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

14292

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

14293

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

14294

\[ {}t -y \sin \left (t \right )+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0 \]

14295

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

14296

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

14297

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

14298

\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \]

14299

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

14300

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

14301

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

14302

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

14303

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

14304

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

14305

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

14306

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

14307

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

14308

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

14309

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

14310

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

14311

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

14312

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

14313

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

14314

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

14315

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

14316

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

14317

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

14318

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

14319

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

14320

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

14321

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

14322

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