4.1.76 Problems 7501 to 7600

Table 4.151: First order ode

#

ODE

Mathematica

Maple

Sympy

17272

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

17273

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

17274

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

17275

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

17276

\[ {} t^{3} y^{\prime }+4 t^{2} y = {\mathrm e}^{-t} \]

17277

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

17278

\[ {} y^{\prime }-\frac {y}{3} = 3 \cos \left (t \right ) \]

17279

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

17280

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

17281

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

17282

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

17283

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

17284

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

17285

\[ {} y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4} \]

17286

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

17287

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

17288

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

17289

\[ {} y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t} \]

17290

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

17291

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

17292

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

17293

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

17294

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

17295

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

17296

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

17297

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

17298

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

17299

\[ {} y^{\prime } = \frac {t -y}{2 t +5 y} \]

17300

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

17301

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

17302

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

17303

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

17304

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

17305

\[ {} y^{\prime } = y^{{1}/{3}} \]

17306

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

17307

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

17308

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

17309

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

17310

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

17311

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

17312

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

17313

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

17314

\[ {} y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \]

17315

\[ {} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0 \]

17316

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

17317

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

17318

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

17319

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

17320

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

17321

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

17322

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

17323

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

17324

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

17325

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

17326

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

17327

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

17328

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

17329

\[ {} 9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime } = 0 \]

17330

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

17331

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

17332

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

17333

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

17334

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

17335

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

17336

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

17337

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

17338

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

17339

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

17340

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

17341

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

17342

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

17343

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

17344

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

17345

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

17346

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

17347

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

17348

\[ {} y^{\prime } = \frac {4 y-7 x}{5 x -y} \]

17349

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

17350

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

17351

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

17352

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

17353

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

17354

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

17355

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

17356

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

17357

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

17358

\[ {} 5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right ) \]

17359

\[ {} 3 t y^{\prime }+9 y = 2 t y^{{5}/{3}} \]

17360

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

17361

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

17362

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

17363

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

17364

\[ {} \left (3 x-y \right ) x^{\prime }+9 y -2 x = 0 \]

17365

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

17366

\[ {} y^{\prime }-4 \,{\mathrm e}^{x} y^{2} = y \]

17367

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

17368

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

17369

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

17370

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

17371

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