6.193 Problems 19201 to 19300

Table 6.385: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

19201

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

19202

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

19203

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

19204

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

19205

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

19206

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

19207

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

19208

\[ {} 4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0 \]

19209

\[ {} \left (8 {y^{\prime }}^{3}-27\right ) x = \frac {12 {y^{\prime }}^{2}}{x} \]

19210

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

19211

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

19212

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

19213

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

19214

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

19215

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

19216

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

19217

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

19218

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

19219

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

19220

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

19221

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

19222

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

19223

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

19224

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

19225

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

19226

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

19227

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

19228

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

19229

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

19230

\[ {} 8 {y^{\prime }}^{3} x = y \left (12 {y^{\prime }}^{2}-9\right ) \]

19231

\[ {} 4 {y^{\prime }}^{2} x^{2} \left (x -1\right )-4 y^{\prime } x y \left (4 x -3\right )+\left (16 x -9\right ) y^{2} = 0 \]

19232

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

19233

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

19234

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

19235

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

19236

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

19237

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

19238

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

19239

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

19240

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

19241

\[ {} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1 \]

19242

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

19243

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0 \]

19244

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

19245

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

19246

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

19247

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

19248

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

19249

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

19250

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

19251

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

19252

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

19253

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

19254

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

19255

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

19256

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

19257

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 4 x \]

19258

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

19259

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2} \]

19260

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = x^{2}+\frac {1}{x^{2}} \]

19261

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

19262

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

19263

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

19264

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

19265

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2} \]

19266

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

19267

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

19268

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

19269

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

19270

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

19271

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

19272

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

19273

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

19274

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

19275

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

19276

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

19277

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

19278

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

19279

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

19280

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

19281

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

19282

\[ {} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right ) \]

19283

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

19284

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

19285

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

19286

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

19287

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

19288

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

19289

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

19290

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

19291

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

19292

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

19293

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

19294

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

19295

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

19296

\[ {} y^{3} y^{\prime \prime } = a \]

19297

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

19298

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

19299

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

19300

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