6.253 Problems 25201 to 25300

Table 6.505: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

25201

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

25202

\[ {} y^{\prime \prime }+4 y = 32 t \cos \left (2 t \right ) \]

25203

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

25204

\[ {} y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{t} \]

25205

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

25206

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

25207

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

25208

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

25209

\[ {} y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

25210

\[ {} y^{\prime \prime }+8 y = t \]

25211

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

25212

\[ {} 2 y^{\prime \prime }-12 y^{\prime }+18 y = 0 \]

25213

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

25214

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

25215

\[ {} y^{\prime \prime }+10 y^{\prime }+24 y = 0 \]

25216

\[ {} y^{\prime \prime }-4 y^{\prime }-12 y = 0 \]

25217

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

25218

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

25219

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

25220

\[ {} 2 y^{\prime \prime }-12 y^{\prime }+18 y = 0 \]

25221

\[ {} y^{\prime \prime }+13 y^{\prime }+36 y = 0 \]

25222

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

25223

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

25224

\[ {} y^{\prime \prime }-4 y^{\prime }-21 y = 0 \]

25225

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

25226

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

25227

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

25228

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]

25229

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

25230

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{2 t} \]

25231

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

25232

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

25233

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

25234

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-3 t} \]

25235

\[ {} y^{\prime \prime }+4 y = 1+{\mathrm e}^{t} \]

25236

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

25237

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{t} \]

25238

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

25239

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

25240

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t} \]

25241

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{-3 t} \]

25242

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 t} \cos \left (2 t \right ) \]

25243

\[ {} y^{\prime \prime }-8 y^{\prime }+25 y = 104 \sin \left (3 t \right ) \]

25244

\[ {} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 t} \]

25245

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \,{\mathrm e}^{-t} \]

25246

\[ {} y^{\prime \prime }+y = 10 \,{\mathrm e}^{2 t} \]

25247

\[ {} y^{\prime \prime }-4 y = 2-8 t \]

25248

\[ {} y^{\prime \prime }-4 y = {\mathrm e}^{-6 t} \]

25249

\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = 16 \,{\mathrm e}^{t} \]

25250

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 t} \]

25251

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

25252

\[ {} y^{\prime \prime }+2 y^{\prime }-8 y = 6 \,{\mathrm e}^{-4 t} \]

25253

\[ {} y^{\prime \prime }+3 y^{\prime }-10 y = \sin \left (t \right ) \]

25254

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t} \]

25255

\[ {} y^{\prime \prime }-5 y^{\prime }-6 y = 10 t \,{\mathrm e}^{4 t} \]

25256

\[ {} y^{\prime \prime }-8 y^{\prime }+25 y = 36 t \,{\mathrm e}^{4 t} \sin \left (3 t \right ) \]

25257

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

25258

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

25259

\[ {} y^{\prime \prime \prime }-3 y^{\prime } = {\mathrm e}^{t} \]

25260

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

25261

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

25262

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

25263

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

25264

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

25265

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

25266

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

25267

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \]

25268

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-25 y^{\prime }+50 y = 0 \]

25269

\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }+25 y^{\prime }+50 y = 0 \]

25270

\[ {} y^{\left (6\right )}+27 y^{\prime \prime \prime \prime }+243 y^{\prime \prime }+729 y = 0 \]

25271

\[ {} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+18 y^{\prime \prime }-27 y = 0 \]

25272

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

25273

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

25274

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

25275

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = {\mathrm e}^{2 t} \]

25276

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

25277

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

25278

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

25279

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

25280

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = {\mathrm e}^{2 t} \]

25281

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

25282

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

25283

\[ {} [y_{1}^{\prime }\left (t \right )-6 y_{1} \left (t \right ) = -4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )] \]

25284

\[ {} [y_{1}^{\prime }\left (t \right )-3 y_{1} \left (t \right ) = -4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right )+y_{2} \left (t \right ) = y_{1} \left (t \right )] \]

25285

\[ {} [y_{1}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )] \]

25286

\[ {} [y_{1}^{\prime }\left (t \right )-2 y_{1} \left (t \right ) = 2 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+2 y_{2}^{\prime }\left (t \right )+y_{2} \left (t \right ) = -2 y_{1} \left (t \right )] \]

25287

\[ {} [y_{1}^{\prime }\left (t \right )+4 y_{1} \left (t \right ) = 10 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-6 y_{2}^{\prime }\left (t \right )+23 y_{2} \left (t \right ) = 9 y_{1} \left (t \right )] \]

25288

\[ {} [y_{1}^{\prime }\left (t \right )-2 y_{1} \left (t \right ) = -2 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+y_{2}^{\prime }\left (t \right )+6 y_{2} \left (t \right ) = 4 y_{1} \left (t \right )] \]

25289

\[ {} [y_{1}^{\prime \prime }\left (t \right )+2 y_{1}^{\prime }\left (t \right )+6 y_{1} \left (t \right ) = 5 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-2 y_{2}^{\prime }\left (t \right )+6 y_{2} \left (t \right ) = 9 y_{1} \left (t \right )] \]

25290

\[ {} [y_{1}^{\prime \prime }\left (t \right )+2 y_{1} \left (t \right ) = -3 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+2 y_{2}^{\prime }\left (t \right )-9 y_{2} \left (t \right ) = 6 y_{1} \left (t \right )] \]

25291

\[ {} [y_{1}^{\prime }\left (t \right ) = -y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right )-2 y_{2} \left (t \right ) = y_{1} \left (t \right )] \]

25292

\[ {} [y_{1}^{\prime }\left (t \right )-y_{1} \left (t \right ) = -2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right )-y_{2} \left (t \right ) = 2 y_{1} \left (t \right )] \]

25293

\[ {} [y_{1}^{\prime }\left (t \right )-2 y_{1} \left (t \right ) = -y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-y_{2}^{\prime }\left (t \right )+y_{2} \left (t \right ) = y_{1} \left (t \right )] \]

25294

\[ {} [y_{1}^{\prime }\left (t \right )+2 y_{1} \left (t \right ) = 5 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-2 y_{2}^{\prime }\left (t \right )+5 y_{2} \left (t \right ) = 2 y_{1} \left (t \right )] \]

25295

\[ {} [y_{1}^{\prime \prime }\left (t \right )+2 y_{1} \left (t \right ) = -3 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+2 y_{2}^{\prime }\left (t \right )-9 y_{2} \left (t \right ) = 6 y_{1} \left (t \right )] \]

25296

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

25297

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

25298

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

25299

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

25300

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