6.153 Problems 15201 to 15300

Table 6.305: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

15201

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

15202

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

15203

\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \]

15204

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

15205

\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \]

15206

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

15207

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

15208

\[ {}x^{2} y^{\prime }+3 x y = 6 \,{\mathrm e}^{-x^{2}} \]

15209

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

15210

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

15211

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

15212

\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \]

15213

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

15214

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

15215

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

15216

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

15217

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

15218

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

15219

\[ {}x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5} \]

15220

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

15221

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

15222

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

15223

\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \]

15224

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

15225

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

15226

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

15227

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

15228

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

15229

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

15230

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

15231

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

15232

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

15233

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

15234

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

15235

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

15236

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

15237

\[ {}x y^{\prime \prime }-y^{\prime } = 6 x^{5} \]

15238

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

15239

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

15240

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

15241

\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \]

15242

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

15243

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

15244

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

15245

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

15246

\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \]

15247

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

15248

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

15249

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

15250

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

15251

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

15252

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

15253

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

15254

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

15255

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

15256

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

15257

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

15258

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

15259

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

15260

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

15261

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

15262

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

15263

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

15264

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

15265

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

15266

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

15267

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

15268

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

15269

\[ {}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \]

15270

\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25 = 0 \]

15271

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

15272

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

15273

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

15274

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

15275

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

15276

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

15277

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

15278

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

15279

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

15280

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

15281

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

15282

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

15283

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

15284

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

15285

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

15286

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 \,{\mathrm e}^{2 x} \]

15287

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{4 x} \]

15288

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

15289

\[ {}x^{2} y^{\prime \prime }-20 y = 27 x^{5} \]

15290

\[ {}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \]

15291

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

15292

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = 0 \]

15293

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = {\mathrm e}^{3 x} \sin \left (x \right ) \]

15294

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y = 0 \]

15295

\[ {}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0 \]

15296

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

15297

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

15298

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

15299

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

15300

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