4.1.61 Problems 6001 to 6100

Table 4.121: First order ode

#

ODE

Mathematica

Maple

Sympy

13258

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

13259

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

13260

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

13261

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

13262

\[ {} y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \]

13263

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

13264

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

13265

\[ {} a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x} \]

13266

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

13267

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

13268

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

13269

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

13270

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

13271

\[ {} y^{\prime } = -8 x y^{2}+4 x \left (4 x +1\right ) y-8 x^{3}-4 x^{2}+1 \]

13272

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

13273

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

13274

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

13275

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

13276

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

13277

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

13278

\[ {} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0 \]

13279

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

13280

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

13281

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

13282

\[ {} y^{\prime } = \frac {2 x -7 y}{3 y-8 x} \]

13283

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

13284

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

13285

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

13286

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

13287

\[ {} 2 y^{2}+8+\left (-x^{2}+1\right ) y y^{\prime } = 0 \]

13288

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

13289

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

13290

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

13291

\[ {} y^{\prime } = \frac {2 x +7 y}{2 x -2 y} \]

13292

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

13293

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

13294

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

13295

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

13296

\[ {} 5 x y+4 y^{2}+1+\left (2 x y+x^{2}\right ) y^{\prime } = 0 \]

13297

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

13298

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

13299

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

13300

\[ {} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \]

13301

\[ {} 8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime } = 0 \]

13302

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

13303

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

13304

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

13305

\[ {} 10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0 \]

13306

\[ {} 6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \]

13307

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

13308

\[ {} 2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \]

13309

\[ {} 4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0 \]

13565

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

13566

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

13625

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

13626

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

13627

\[ {} u^{\prime } = 4 t \ln \left (t \right ) \]

13628

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

13629

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

13630

\[ {} x^{\prime } = \sec \left (t \right )^{2} \]

13631

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

13632

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

13633

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

13634

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

13635

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

13636

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

13637

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

13638

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

13639

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

13640

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

13641

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

13642

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

13643

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

13644

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

13645

\[ {} x^{\prime }+p x = q \]

13646

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

13647

\[ {} i^{\prime } = p \left (t \right ) i \]

13648

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

13649

\[ {} m v^{\prime } = -m g +k v^{2} \]

13650

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

13651

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

13652

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

13653

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

13654

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

13655

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

13656

\[ {} x^{\prime }+x \tanh \left (t \right ) = 3 \]

13657

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

13658

\[ {} x^{\prime }+5 x = t \]

13659

\[ {} x^{\prime }+\left (a +\frac {1}{t}\right ) x = b \]

13660

\[ {} T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \]

13661

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

13662

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

13663

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

13664

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

13665

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

13666

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

13667

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

13668

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

13669

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

13670

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