4.3.28 Problems 2701 to 2800

Table 4.419: Second order ode

#

ODE

Mathematica

Maple

Sympy

9327

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

9328

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

9329

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

9330

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

9331

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

9332

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

9333

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

9334

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

9335

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

9336

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

9337

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

9338

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

9339

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

9340

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

9341

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 2 x -1 \]

9342

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

9343

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

9344

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

9345

\[ {} y^{\prime \prime }+9 y = \sec \left (2 x \right ) \]

9346

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

9347

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

9348

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

9349

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

9350

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

9351

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

9352

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

9353

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

9354

\[ {} y^{\prime \prime }+9 y = -3 \cos \left (2 x \right ) \]

9356

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

9357

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

9453

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

9454

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

9455

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

9459

\[ {} y^{\prime \prime }+3 y^{\prime }-5 y = 1 \]

9460

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

9461

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

9462

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

9463

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

9464

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

9465

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

9466

\[ {} y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \]

9467

\[ {} i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]

9505

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

9507

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

9509

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

9511

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

9573

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \]

9574

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

9575

\[ {} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]

9576

\[ {} 16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \]

9577

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

9578

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

9579

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \]

9580

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

9581

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \]

9582

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]

9583

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

9584

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

9585

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

9586

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

9587

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

9588

\[ {} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \]

9589

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

9590

\[ {} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \]

9591

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

9592

\[ {} x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \]

9593

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

9594

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

9595

\[ {} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

9596

\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y = 0 \]

9614

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

9615

\[ {} y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \]

9616

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

9617

\[ {} y^{\prime \prime }+9 y = {\mathrm e}^{t} \]

9621

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

9624

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

9625

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

9626

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

9627

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

9628

\[ {} y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

9629

\[ {} 2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]

9630

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

9631

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \]

9632

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

9633

\[ {} y^{\prime \prime }+8 y^{\prime }+20 y = 0 \]

9637

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

9638

\[ {} y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \]

9639

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right ) \]

9640

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

9641

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \]

9644

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

9645

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

9646

\[ {} y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

9647

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \]

9648

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

9649

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

9650

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

9653

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

9654

\[ {} y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right ) \]

9655

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