6.193 Problems 19201 to 19300

Table 6.385: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

19201

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

19202

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

19203

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

19204

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

19205

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

19206

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

19207

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

19208

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

19209

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

19210

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

19211

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

19212

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

19213

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

19214

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

19215

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

19216

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

19217

\[ {} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0 \]

19218

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

19219

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

19220

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

19221

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

19222

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

19223

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

19224

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

19225

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

19226

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

19227

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

19228

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

19229

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

19230

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

19231

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

19232

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

19233

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

19234

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

19235

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

19236

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

19237

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

19238

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

19239

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

19240

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

19241

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

19242

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

19243

\[ {} y^{\prime } = \sqrt {y} \]

19244

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

19245

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

19246

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

19247

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

19248

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

19249

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

19250

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

19251

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

19252

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

19253

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

19254

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

19255

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

19256

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

19257

\[ {} y^{\prime \prime } = \frac {1}{\sqrt {y}} \]

19258

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

19259

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

19260

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

19261

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

19262

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

19263

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

19264

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

19265

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

19266

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

19267

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

19268

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

19269

\[ {} x \left (2 x y+x^{2} y^{\prime }\right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 y y^{\prime } x +4 y^{2}-1 = 0 \]

19270

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

19271

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

19272

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

19273

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

19274

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

19275

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

19276

\[ {} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )} = 0 \]

19277

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

19278

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

19279

\[ {} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 x y^{\prime }-12 y = 0 \]

19280

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

19281

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

19282

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

19283

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

19284

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

19285

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

19286

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

19287

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

19288

\[ {} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1 \]

19289

\[ {} -2 x y+y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime } = x^{4}+12 \]

19290

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

19291

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

19292

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

19293

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

19294

\[ {} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0 \]

19295

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

19296

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

19297

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

19298

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

19299

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

19300

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