4.27.27 Problems 2601 to 2697

Table 4.1605: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

24873

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

24874

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

24876

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

24877

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

24878

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

24879

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

24880

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

24881

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

24882

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

25043

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

25044

\[ {} y^{\prime \prime } = 6 \sin \left (3 t \right ) \]

25051

\[ {} y^{\prime \prime } = 6 \sin \left (3 t \right ) \]

25186

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

25187

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

25188

\[ {} y^{\prime \prime }+4 y = 8 \]

25189

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

25190

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{2 t} \]

25191

\[ {} y^{\prime \prime }-4 y^{\prime }-5 y = 150 t \]

25192

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

25193

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

25194

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

25195

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

25196

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 50 \sin \left (t \right ) \]

25197

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

25198

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

25199

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

25200

\[ {} y^{\prime \prime }+9 y = 36 t \sin \left (3 t \right ) \]

25201

\[ {} y^{\prime \prime }-3 y = 4 t^{2} \cos \left (t \right ) \]

25202

\[ {} y^{\prime \prime }+4 y = 32 t \cos \left (2 t \right ) \]

25204

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

25208

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

25210

\[ {} y^{\prime \prime }+8 y = t \]

25211

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

25229

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

25230

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{2 t} \]

25231

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

25232

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

25233

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

25234

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

25235

\[ {} y^{\prime \prime }+4 y = 1+{\mathrm e}^{t} \]

25236

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

25237

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

25238

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

25239

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

25240

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t} \]

25241

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{-3 t} \]

25242

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 t} \cos \left (2 t \right ) \]

25243

\[ {} y^{\prime \prime }-8 y^{\prime }+25 y = 104 \sin \left (3 t \right ) \]

25244

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

25245

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \,{\mathrm e}^{-t} \]

25246

\[ {} y^{\prime \prime }+y = 10 \,{\mathrm e}^{2 t} \]

25247

\[ {} y^{\prime \prime }-4 y = 2-8 t \]

25248

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

25249

\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = 16 \,{\mathrm e}^{t} \]

25250

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

25251

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

25252

\[ {} y^{\prime \prime }+2 y^{\prime }-8 y = 6 \,{\mathrm e}^{-4 t} \]

25253

\[ {} y^{\prime \prime }+3 y^{\prime }-10 y = \sin \left (t \right ) \]

25254

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t} \]

25255

\[ {} y^{\prime \prime }-5 y^{\prime }-6 y = 10 t \,{\mathrm e}^{4 t} \]

25256

\[ {} y^{\prime \prime }-8 y^{\prime }+25 y = 36 t \,{\mathrm e}^{4 t} \sin \left (3 t \right ) \]

25257

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

25258

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

25298

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

25328

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

25382

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

25383

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

25384

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

25385

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

25386

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

25387

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

25388

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

25389

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

25393

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

25397

\[ {} y^{\prime \prime }-y = \frac {1}{1+{\mathrm e}^{-t}} \]

25398

\[ {} y^{\prime \prime }+a^{2} y = f \left (t \right ) \]

25399

\[ {} y^{\prime \prime }-a^{2} y = f \left (t \right ) \]

25400

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

25401

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

25402

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

25403

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

25408

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

25409

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

25417

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

25418

\[ {} y^{\prime \prime }-5 y^{\prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <5 \\ 0 & 5\le t \end {array}\right . \]

25419

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right . \]

25420

\[ {} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \]

25421

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

25422

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

25427

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

25428

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

25429

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

25430

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

25431

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

25432

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 3 \delta \left (t -\pi \right ) \]

25435

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

25436

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = \delta \left (t -3\right ) \]