5.3.9 Problems 801 to 900

Table 5.51: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

5211

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

5212

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

5213

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

5215

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

5216

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

5218

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

5219

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

5220

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

5221

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

5222

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

5223

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

5228

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

5230

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

5231

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

5232

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

5233

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

5235

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

5239

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

5240

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

5245

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

5246

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

5247

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

5252

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

5261

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

5262

\[ {} x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y = 0 \]

5266

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

5268

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

5269

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

5270

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

5271

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

5273

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

5274

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

5278

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

5279

\[ {} \left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0 \]

5282

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

5283

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

5288

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

5289

\[ {} \left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4} = 0 \]

5290

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

5293

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

5294

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

5298

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

5301

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

5302

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

5303

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

5305

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

5306

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

5307

\[ {} x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3} = 0 \]

5310

\[ {} f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{1+m}+h \left (x \right ) y^{n} = 0 \]

5312

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

5315

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

5320

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

5323

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

5324

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

5325

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

5326

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

5327

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

5328

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

5329

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

5331

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

5336

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

5337

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

5338

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

5339

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

5355

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

5367

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

5375

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

5376

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

5380

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

5381

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

5384

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

5392

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

5394

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

5395

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

5397

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

5398

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

5400

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

5401

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

5403

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

5407

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

5408

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

5412

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

5413

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

5414

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

5416

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

5418

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

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

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

5430

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

5431

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

5432

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

5433

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

5436

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

5437

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

5439

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

5440

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

5442

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