4.1.61 Problems 6001 to 6100

Table 4.121: First order ode

#

ODE

Mathematica

Maple

Sympy

14182

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

14183

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

14184

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

14185

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

14186

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

14187

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

14188

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

14189

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

14190

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

14191

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

14192

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

14193

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

14194

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

14195

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

14196

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

14197

\[ {} 8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \]

14198

\[ {} 4 {y^{\prime }}^{2} = 9 x \]

14199

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

14306

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

14307

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

14308

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

14310

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

14311

\[ {} x^{\prime }+2 x = t^{2}+4 t +7 \]

14312

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

14315

\[ {} x^{\prime } = x \left (1-\frac {x}{4}\right ) \]

14316

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

14317

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

14318

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

14320

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

14321

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

14322

\[ {} \sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right ) \]

14323

\[ {} x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}} \]

14325

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

14326

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

14327

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

14328

\[ {} u^{\prime } = \frac {1}{5-2 u} \]

14329

\[ {} x^{\prime } = a x+b \]

14330

\[ {} Q^{\prime } = \frac {Q}{4+Q^{2}} \]

14331

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

14332

\[ {} y^{\prime } = r \left (a -y\right ) \]

14333

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

14334

\[ {} \theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \]

14335

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

14336

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

14337

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

14338

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

14339

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

14340

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

14341

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

14342

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

14343

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

14344

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

14345

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

14346

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

14347

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

14348

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

14349

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

14350

\[ {} x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}} \]

14351

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

14352

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

14354

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

14355

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

14356

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

14357

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

14358

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

14359

\[ {} 7 t^{2} x^{\prime } = 3 x-2 t \]

14360

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

14361

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

14362

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

14363

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

14364

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

14365

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

14366

\[ {} \theta ^{\prime } = -a \theta +{\mathrm e}^{b t} \]

14367

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

14368

\[ {} x^{\prime }+\frac {5 x}{t} = t +1 \]

14369

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

14370

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

14371

\[ {} N^{\prime } = N-9 \,{\mathrm e}^{-t} \]

14372

\[ {} \cos \left (\theta \right ) v^{\prime }+v = 3 \]

14373

\[ {} R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t} \]

14374

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

14375

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

14376

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

14378

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

14379

\[ {} x^{\prime } = a x+b \]

14380

\[ {} x^{\prime }+p \left (t \right ) x = 0 \]

14381

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

14382

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

14383

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

14384

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

14385

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

14386

\[ {} w^{\prime } = t w+t^{3} w^{3} \]

14387

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

14388

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

14389

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

14390

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

14391

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

14392

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

14465

\[ {} x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right ) \]

14466

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