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

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