4.1.12 Problems 1101 to 1200

Table 4.23: First order ode

#

ODE

Mathematica

Maple

Sympy

3288

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

3289

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

3290

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

3291

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

3292

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

3293

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

3294

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

3295

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

3296

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

3297

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

3298

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

3299

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

3300

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

3301

\[ {} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2} = 0 \]

3302

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

3303

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

3304

\[ {} 1+8 x = y {y^{\prime }}^{2} \]

3305

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

3306

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

3307

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

3308

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

3309

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

3310

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

3311

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

3312

\[ {} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2} = 0 \]

3313

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

3314

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

3315

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

3316

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

3317

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

3318

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

3319

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

3320

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

3321

\[ {} 3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1 \]

3322

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

3323

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

3324

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

3325

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

3326

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

3327

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

3328

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

3329

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

3330

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

3331

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

3332

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

3333

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

3334

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

3403

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

3404

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

3405

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

3406

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

3407

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

3408

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

3409

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

3410

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

3411

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

3412

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

3413

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

3414

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

3415

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

3416

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

3417

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

3418

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

3419

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

3420

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

3421

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

3422

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

3423

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

3424

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

3425

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

3426

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

3427

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

3428

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

3429

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

3430

\[ {} y^{\prime } = 8 \,{\mathrm e}^{4 t}+t \]

3431

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

3432

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

3433

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

3434

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

3435

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

3436

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

3437

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

3438

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

3439

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

3440

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

3441

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

3442

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

3443

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

3444

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

3445

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

3446

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

3447

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

3448

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

3449

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

3450

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

3451

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

3452

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

3453

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

3454

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

3455

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