6.53 Problems 5201 to 5300

Table 6.105: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

5201

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

5202

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

5203

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

5204

\[ {} 8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0 \]

5205

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

5206

\[ {} 3 x^{4} y y^{\prime } = 1-2 y^{2} x^{3} \]

5207

\[ {} x^{7} y y^{\prime } = 2 x^{2}+2+5 x^{3} y \]

5208

\[ {} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0 \]

5209

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

5210

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

5211

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

5212

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

5213

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

5214

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

5215

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

5216

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

5217

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

5218

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

5219

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

5220

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

5221

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

5222

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

5223

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

5224

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

5225

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

5226

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

5227

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

5228

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

5229

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

5230

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

5231

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

5232

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

5233

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

5234

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

5235

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

5236

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

5237

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

5238

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

5239

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

5240

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

5241

\[ {} 3 y^{2} y^{\prime } = 1+x +a y^{3} \]

5242

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

5243

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

5244

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

5245

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

5246

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

5247

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

5248

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

5249

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

5250

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

5251

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

5252

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

5253

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

5254

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

5255

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

5256

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

5257

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

5258

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

5259

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

5260

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

5261

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

5262

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

5263

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

5264

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

5265

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

5266

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

5267

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

5268

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

5269

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

5270

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

5271

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

5272

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

5273

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

5274

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

5275

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

5276

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

5277

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

5278

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

5279

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

5280

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

5281

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

5282

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

5283

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

5284

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

5285

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

5286

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

5287

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

5288

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

5289

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

5290

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

5291

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

5292

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

5293

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

5294

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

5295

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

5296

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

5297

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

5298

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

5299

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

5300

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