4.2.77 Problems 7601 to 7700

Table 4.359: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

24858

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

24859

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

24860

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

24861

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

24862

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

24863

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

24864

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

24865

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

24866

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}} \]

24867

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

24868

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

24869

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

24870

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

24871

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

24872

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

24873

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

24874

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

24876

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

24877

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

24878

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

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

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

24992

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

24993

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

24996

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

24998

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

25005

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

25027

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

25043

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

25044

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

25051

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

25181

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

25182

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

25183

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

25184

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

25185

\[ {} y^{\prime \prime }+8 y^{\prime }+16 y = 0 \]

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

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

25209

\[ {} y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

25210

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

25211

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

25212

\[ {} 2 y^{\prime \prime }-12 y^{\prime }+18 y = 0 \]

25213

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

25214

\[ {} y^{\prime \prime }+y^{\prime }-12 y = 0 \]

25215

\[ {} y^{\prime \prime }+10 y^{\prime }+24 y = 0 \]

25216

\[ {} y^{\prime \prime }-4 y^{\prime }-12 y = 0 \]

25217

\[ {} y^{\prime \prime }+8 y^{\prime }+16 y = 0 \]

25218

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

25219

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

25220

\[ {} 2 y^{\prime \prime }-12 y^{\prime }+18 y = 0 \]

25221

\[ {} y^{\prime \prime }+13 y^{\prime }+36 y = 0 \]

25222

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

25223

\[ {} y^{\prime \prime }+10 y^{\prime }+25 y = 0 \]

25224

\[ {} y^{\prime \prime }-4 y^{\prime }-21 y = 0 \]

25225

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

25226

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

25227

\[ {} y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

25228

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]

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

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