5.1.26 Problems 2501 to 2600

Table 5.51: First order ode

#

ODE

Mathematica

Maple

5416

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

5417

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

5418

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

5419

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

5420

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

5421

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

5422

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

5423

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

5424

\[ {}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0 \]

5425

\[ {}9 {y^{\prime }}^{2}+3 y^{4} y^{\prime } x +y^{5} = 0 \]

5426

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

5427

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

5428

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

5429

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

5430

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

5431

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

5432

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

5433

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

5434

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

5435

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

5436

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

5437

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

5438

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

5439

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

5440

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

5441

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

5442

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

5443

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

5444

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

5445

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

5446

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

5447

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

5448

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

5449

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

5450

\[ {}x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2} = 0 \]

5451

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

5452

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

5453

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

5454

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

5455

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

5456

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

5457

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

5458

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

5459

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

5460

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

5461

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

5462

\[ {}\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0 \]

5463

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

5464

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

5465

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

5466

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

5467

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

5468

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

5469

\[ {}4 \left (2-x \right ) {y^{\prime }}^{2}+1 = 0 \]

5470

\[ {}16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0 \]

5471

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

5472

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

5473

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

5474

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

5475

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

5476

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

5477

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

5478

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

5479

\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2} = 0 \]

5480

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

5481

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

5482

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

5483

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

5484

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

5485

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

5486

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

5487

\[ {}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0 \]

5488

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

5489

\[ {}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0 \]

5490

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

5491

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

5492

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

5493

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

5494

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

5495

\[ {}\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+4 x^{2} = 0 \]

5496

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

5497

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

5498

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

5499

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

5500

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

5501

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

5502

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

5503

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

5504

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

5505

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

5506

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

5507

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

5508

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

5509

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

5510

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

5511

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

5512

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

5513

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

5514

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

5515

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