6.55 Problems 5401 to 5500

Table 6.109: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

5401

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

5402

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

5403

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

5404

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

5405

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

5406

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

5407

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

5408

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

5409

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

5410

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

5411

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

5412

\[ {} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \]

5413

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

5414

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

5415

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

5416

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

5417

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

5418

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

5419

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

5420

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

5421

\[ {} {y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y = 0 \]

5422

\[ {} {y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right ) = 0 \]

5423

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

5424

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

5425

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

5426

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

5427

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

5428

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

5429

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

5430

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

5431

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

5432

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

5433

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

5434

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

5435

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

5436

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

5437

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

5438

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

5439

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

5440

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

5441

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

5442

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

5443

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

5444

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

5445

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

5446

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

5447

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

5448

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

5449

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

5450

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

5451

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

5452

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

5453

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

5454

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

5455

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

5456

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

5457

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

5458

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

5459

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

5460

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

5461

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

5462

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

5463

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

5464

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

5465

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

5466

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

5467

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

5468

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

5469

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

5470

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

5471

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

5472

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

5473

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

5474

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

5475

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

5476

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

5477

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

5478

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

5479

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

5480

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

5481

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

5482

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

5483

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

5484

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

5485

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

5486

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

5487

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

5488

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

5489

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

5490

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

5491

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

5492

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

5493

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

5494

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

5495

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

5496

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

5497

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

5498

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

5499

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

5500

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