6.213 Problems 21201 to 21300

Table 6.425: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

21201

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

21202

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

21203

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

21204

\[ {} x^{\prime } = \frac {x-t +1}{x-t +2} \]

21205

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

21206

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

21207

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

21208

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

21209

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

21210

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

21211

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

21212

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

21213

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

21214

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

21215

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

21216

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

21217

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

21218

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

21219

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

21220

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

21221

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

21222

\[ {} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0 \]

21223

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

21224

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

21225

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

21226

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

21227

\[ {} x^{\prime \prime }+2 x^{\prime }-15 x = 0 \]

21228

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

21229

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

21230

\[ {} x^{\prime \prime }-6 x^{\prime }+9 x = 0 \]

21231

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

21232

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

21233

\[ {} x^{\prime \prime }+b x^{\prime }+c x = 0 \]

21234

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

21235

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

21236

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

21237

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

21238

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

21239

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

21240

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

21241

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

21242

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

21243

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

21244

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

21245

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

21246

\[ {} x^{\prime \prime }-4 x = t \]

21247

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

21248

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

21249

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

21250

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

21251

\[ {} x^{\prime \prime }-x = 3 \,{\mathrm e}^{2 t} \]

21252

\[ {} x^{\prime \prime }-x = t \,{\mathrm e}^{2 t} \]

21253

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

21254

\[ {} x^{\prime \prime }-4 x^{\prime }+13 x = 20 \,{\mathrm e}^{t} \]

21255

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

21256

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

21257

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

21258

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

21259

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

21260

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

21261

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

21262

\[ {} x^{\prime \prime }-x^{\prime }-2 x = 3 \,{\mathrm e}^{-t} \]

21263

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

21264

\[ {} x^{\prime \prime }-4 x^{\prime }+3 x = 2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t} \]

21265

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

21266

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

21267

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

21268

\[ {} x^{\prime \prime }+9 x = \sin \left (t \right )+\sin \left (3 t \right ) \]

21269

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

21270

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

21271

\[ {} x^{\prime \prime }-2 x = 2 \,{\mathrm e}^{t} \]

21272

\[ {} x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5} = 0 \]

21273

\[ {} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x = 0 \]

21274

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

21275

\[ {} x^{\prime \prime }-p \left (t \right ) x = q \left (t \right ) \]

21276

\[ {} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0 \]

21277

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

21278

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

21279

\[ {} x^{\prime \prime }-\frac {x^{\prime }}{t} = 0 \]

21280

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

21281

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

21282

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

21283

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

21284

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

21285

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

21286

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

21287

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

21288

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

21289

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

21290

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

21291

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

21292

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

21293

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

21294

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

21295

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

21296

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

21297

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

21298

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

21299

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

21300

\[ {} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x = 0 \]