4.3.76 Problems 7501 to 7600

Table 4.515: Second order ode

#

ODE

Mathematica

Maple

Sympy

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

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

21364

\[ {} L x^{\prime \prime }+g \sin \left (x\right ) = 0 \]

21370

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

21371

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

21372

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

21373

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

21374

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

21375

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

21376

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

21377

\[ {} x^{\prime \prime }+x+8 x^{7} = 0 \]

21378

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

21379

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

21380

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

21381

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

21382

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

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

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

21434

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

21435

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

21436

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

21437

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

21438

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

21439

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

21440

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

21441

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

21442

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

21443

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

21444

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

21445

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

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

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

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

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