3.1.16 Problems 1501 to 1600

Table 3.31: First order ode

#

ODE

Mathematica

Maple

3379

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

3380

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

3381

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

3382

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

3383

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

3384

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

3385

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

3386

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

3387

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

3388

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

3389

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

3390

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

3391

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

3392

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

3393

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

3394

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

3395

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

3396

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

3397

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

3398

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

3399

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

3400

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

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

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

3428

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

3429

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

3430

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

3431

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

3432

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

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

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

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

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

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

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

3451

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

3452

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

3453

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

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

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

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

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

3478

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