2.34 Problems 3301 to 3400

Table 2.34: Main lookup table

#

ODE

Mathematica result

Maple result

3301

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

3302

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

3303

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

3304

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

3305

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

3306

\[ {}x \left (x^{n}+a y\right ) y^{\prime }+\left (b +c y\right ) y^{2} = 0 \]

3307

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

3308

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

3309

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

3310

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

3311

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

3312

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

3313

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

3314

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

3315

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

3316

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

3317

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

3318

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

3319

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

3320

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

3321

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

3322

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

3323

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

3324

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

3325

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

3326

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

3327

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

3328

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

3329

\[ {}8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0 \]

3330

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

3331

\[ {}3 x^{4} y y^{\prime } = 1-2 x^{3} y^{2} \]

3332

\[ {}x^{7} y y^{\prime } = 2 x^{2}+2+5 x^{3} y \]

3333

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

3334

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

3335

\[ {}\left (\mathit {g0} \relax (x )+y \mathit {g1} \relax (x )\right ) y^{\prime } = \mathit {f0} \relax (x )+\mathit {f1} \relax (x ) y+\mathit {f2} \relax (x ) y^{2}+\mathit {f3} \relax (x ) y^{3} \]

3336

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

3337

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

3338

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

3339

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

3340

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

3341

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

3342

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

3343

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

3344

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

3345

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

3346

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

3347

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

3348

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

3349

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

3350

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

3351

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

3352

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

3353

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

3354

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

3355

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

3356

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

3357

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

3358

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

3359

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

3360

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

3361

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

3362

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

3363

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

3364

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

3365

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

3366

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

3367

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

3368

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

3369

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

3370

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

3371

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

3372

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

3373

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

3374

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

3375

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

3376

\[ {}\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 y a x +b y^{2} = 0 \]

3377

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

3378

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

3379

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

3380

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

3381

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

3382

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

3383

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

3384

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

3385

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

3386

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

3387

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

3388

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

3389

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

3390

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

3391

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

3392

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

3393

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

3394

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

3395

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

3396

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

3397

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

3398

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

3399

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

3400

\[ {}x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y = 0 \]