4.27.12 Problems 1101 to 1200

Table 4.1575: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

15049

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

15050

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

15051

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

15052

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

15053

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \]

15054

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

15055

\[ {} x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \]

15056

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

15057

\[ {} x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \]

15058

\[ {} x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

15059

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

15060

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

15071

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

15072

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

15073

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

15075

\[ {} x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \]

15181

\[ {} y^{\prime \prime }-6 y^{\prime }+10 y = 100 \]

15182

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

15184

\[ {} y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}} \]

15186

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

15188

\[ {} x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \]

15199

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

15203

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

15204

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

15206

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

15215

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

15216

\[ {} x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \]

15222

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

15254

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

15326

\[ {} y^{\prime \prime }+2 y^{\prime }+3 y = 9 t \]

15327

\[ {} 4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \]

15328

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

15329

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

15330

\[ {} y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \]

15331

\[ {} 2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \]

15332

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

15333

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

15335

\[ {} y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \]

15336

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

15337

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

15339

\[ {} 3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \]

15342

\[ {} y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \]

15343

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

15344

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]

15345

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \]

15346

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \]

15347

\[ {} y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right ) \]

15348

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \]

15349

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

15350

\[ {} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \]

15351

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \]

15352

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \]

15353

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

15354

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \]

15355

\[ {} y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right ) \]

15356

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (t -1\right ) \]

15357

\[ {} y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \]

15358

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (t -1\right ) \]

15359

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

15360

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right ) \]

15373

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

15374

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

15375

\[ {} y^{\prime \prime }-3 y^{\prime }-7 y = 4 \]

15377

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

15413

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

15414

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

15416

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

15435

\[ {} y^{\prime \prime }+9 y = 18 t \]

15436

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

15437

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = \left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \]

15440

\[ {} c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L} = \delta \left (t -1\right )-\delta \left (t \right ) \]

15446

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

15541

\[ {} 12 y-7 y^{\prime }+y^{\prime \prime } = x \]

15542

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

15543

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right ) \]

15544

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

15545

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

15546

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

15547

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

15548

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

15549

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

15550

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

15555

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

15556

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

15557

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

15558

\[ {} y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \]

15565

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

15568

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

15767

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

15780

\[ {} y^{\prime \prime }-4 y = 31 \]

15781

\[ {} y^{\prime \prime }+9 y = 27 x +18 \]

15811

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

15812

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

15813

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

15817

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

15818

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

15819

\[ {} y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right ) \]

15820

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

15824

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

15825

\[ {} y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \]