2.35 Problems 3401 to 3500

Table 2.69: Main lookup table

#

ODE

Mathematica result

Maple result

3401

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

3402

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

3403

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

3404

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

3405

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

3406

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

3407

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

3408

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

3409

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

3410

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

3411

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

3412

\[ {}x y^{\prime } = a +b \,x^{n}+c y \]

3413

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

3414

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

3415

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

3416

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

3417

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

3418

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

3419

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

3420

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

3421

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

3422

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

3423

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

3424

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

3425

\[ {}x y^{\prime } = a \,x^{n}+b y+c y^{2} \]

3426

\[ {}x y^{\prime } = k +a \,x^{n}+b y+c y^{2} \]

3427

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

3428

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

3429

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

3430

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

3431

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

3432

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

3433

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

3434

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

3435

\[ {}x y^{\prime }+\operatorname {a0} +\operatorname {a1} x +\left (\operatorname {a2} +\operatorname {a3} x y\right ) y = 0 \]

3436

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

3437

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

3438

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

3439

\[ {}x y^{\prime } = a \,x^{m}-b y-c \,x^{n} y^{2} \]

3440

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

3441

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

3442

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

3443

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

3444

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

3445

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

3446

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

3447

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

3448

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

3449

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

3450

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

3451

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

3452

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

3453

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

3454

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

3455

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

3456

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

3457

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

3458

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

3459

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

3460

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

3461

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

3462

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

3463

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

3464

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

3465

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

3466

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

3467

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

3468

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

3469

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

3470

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

3471

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

3472

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

3473

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

3474

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

3475

\[ {}x y^{\prime }+n y = f \left (x \right ) g \left (x^{n} y\right ) \]

3476

\[ {}x y^{\prime } = y f \left (x^{m} y^{n}\right ) \]

3477

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

3478

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

3479

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

3480

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

3481

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

3482

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

3483

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

3484

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

3485

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

3486

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

3487

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

3488

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

3489

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

3490

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

3491

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

3492

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

3493

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

3494

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

3495

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

3496

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

3497

\[ {}2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0 \]

3498

\[ {}\left (-2 x +1\right ) y^{\prime } = 16+32 x -6 y \]

3499

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

3500

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