2.53 Problems 5201 to 5300

Table 2.105: Main lookup table

#

ODE

Mathematica result

Maple result

5201

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

5202

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

5203

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

5204

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

5205

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

5206

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

5207

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

5208

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

5209

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x} \]

5210

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

5211

\[ {}y^{\prime \prime \prime }-y = 5 \]

5212

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

5213

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

5214

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

5215

\[ {}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \]

5216

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

5217

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

5218

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

5219

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

5220

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

5221

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

5222

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

5223

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

5224

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

5225

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

5226

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

5227

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

5228

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

5229

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

5230

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

5231

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

5232

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

5233

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

5234

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

5235

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

5236

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

5237

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

5238

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

5239

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

5240

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

5241

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

5242

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

5243

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

5244

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

5245

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

5246

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

5247

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

5248

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

5249

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

5250

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

5251

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

5252

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

5253

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

5254

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

5255

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

5256

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

5257

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

5258

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

5259

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

5260

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

5261

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

5262

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

5263

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

5264

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

5265

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

5266

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

5267

\[ {}2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime } = 0 \]

5268

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

5269

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

5270

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

5271

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

5272

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

5273

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

5274

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

5275

\[ {}1-\sqrt {a^{2}-x^{2}}\, y^{\prime } = 0 \]

5276

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

5277

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

5278

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

5279

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

5280

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

5281

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

5282

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

5283

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

5284

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

5285

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

5286

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

5287

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

5288

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

5289

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

5290

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

5291

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

5292

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

5293

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

5294

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

5295

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

5296

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

5297

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

5298

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

5299

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

5300

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