4.2.66 Problems 6501 to 6600

Table 4.337: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

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

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

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

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

21391

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

21392

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

21393

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

21394

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

21395

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

21398

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

21399

\[ {} x^{\prime \prime }-4 x^{\prime }+3 x = 1 \]

21404

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

21405

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

21414

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

21415

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

21416

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

21575

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

21576

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

21590

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

21591

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

21593

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

21594

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

21595

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

21596

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

21597

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

21598

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

21599

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

21600

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

21601

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

21602

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

21603

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

21604

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

21605

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

21606

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

21607

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

21608

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

21609

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

21610

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

21611

\[ {} y^{\prime \prime }-2 y^{\prime }+10 y = 0 \]

21612

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

21613

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

21614

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

21615

\[ {} y^{\prime \prime }-\frac {6 y^{\prime }}{5}+\frac {9 y}{25} = 0 \]

21630

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

21631

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

21632

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

21633

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

21634

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = x^{3}+3 \]

21635

\[ {} y^{\prime \prime }+y^{\prime }-6 y = 2 x^{3}+5 x^{2}-7 x +2 \]

21636

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

21637

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

21638

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

21639

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

21640

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (x +\frac {\pi }{4}\right ) \]

21641

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

21642

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

21643

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

21644

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

21645

\[ {} y^{\prime \prime }+y^{\prime }+8 y = \left (10 x^{2}+21 x +9\right ) \sin \left (3 x \right )+x \cos \left (3 x \right ) \]

21646

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