3.1.61 Problems 6001 to 6100

Table 3.121: First order ode




#

ODE

Mathematica

Maple





13037

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





13038

\[ {}y^{\prime } = 3 y+{\mathrm e}^{7 t} \]





13039

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





13040

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





13041

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





13042

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





13043

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





13044

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





13045

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





13046

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





13047

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





13048

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





13049

\[ {}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t} \]





13050

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





13051

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





13052

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





13053

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





13054

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





13055

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





13056

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





13057

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





13058

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





13059

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





13060

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





13243

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





13244

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





13245

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





13246

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





13247

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





13253

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





13254

\[ {}y^{\prime } = 20 \,{\mathrm e}^{-4 x} \]





13255

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





13256

\[ {}\sqrt {x +4}\, y^{\prime } = 1 \]





13257

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





13258

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





13259

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





13260

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





13261

\[ {}1 = x^{2}-9 y^{\prime } \]





13265

\[ {}y^{\prime } = 40 \,{\mathrm e}^{2 x} x \]





13266

\[ {}\left (x +6\right )^{\frac {1}{3}} y^{\prime } = 1 \]





13267

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





13268

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





13269

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





13270

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





13272

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





13273

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





13274

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





13275

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





13276

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





13277

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





13278

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





13279

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





13280

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





13281

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





13282

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





13283

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





13284

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





13285

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





13286

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





13287

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





13288

\[ {}y^{\prime }+3 x y = 6 x \]





13289

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





13290

\[ {}y^{\prime }-y^{3} = 8 \]





13291

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





13292

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





13293

\[ {}y^{3}-25 y+y^{\prime } = 0 \]





13294

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





13295

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





13296

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





13297

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





13298

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





13299

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





13300

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





13301

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





13302

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





13303

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





13304

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





13305

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





13306

\[ {}y^{\prime } = x y-3 x -2 y+6 \]





13307

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





13308

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





13309

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





13310

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





13311

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





13312

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





13313

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





13314

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





13315

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





13316

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





13317

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





13318

\[ {}y y^{\prime } = 3 \sqrt {x y^{2}+9 x} \]





13319

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





13320

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





13321

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





13322

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





13323

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





13324

\[ {}y^{\prime } = 200 y-2 y^{2} \]





13325

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





13326

\[ {}y^{\prime } = x y-3 x -2 y+6 \]





13327

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