4.3.78 Problems 7701 to 7800

Table 4.519: Second order ode

#

ODE

Mathematica

Maple

Sympy

22005

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

22007

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right ) \]

22025

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

22026

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

22027

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

22028

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

22029

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

22030

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

22031

\[ {} y^{\prime \prime }+9 y = 5 \cos \left (2 t \right ) \]

22032

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

22036

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

22037

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

22038

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

22039

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x = 0 \]

22047

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

22048

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

22049

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

22050

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

22051

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

22052

\[ {} x y^{\prime \prime }+y^{\prime } = 16 x^{3} \]

22054

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

22061

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

22062

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

22063

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

22066

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

22067

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

22069

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

22070

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

22072

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

22074

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

22075

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

22078

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

22079

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

22080

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

22083

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

22084

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

22085

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

22086

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

22087

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

22193

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

22195

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

22197

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

22198

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

22202

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

22204

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

22209

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

22210

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

22211

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

22212

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

22213

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

22214

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

22215

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

22216

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

22217

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

22218

\[ {} y^{\prime \prime }-y^{\prime }-30 y = 0 \]

22219

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

22220

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

22221

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

22222

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

22223

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

22224

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

22225

\[ {} y^{\prime \prime }-3 y^{\prime }-5 y = 0 \]

22226

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

22245

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

22246

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

22247

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

22249

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

22254

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

22255

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

22256

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

22257

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

22258

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

22264

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

22265

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

22268

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

22269

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

22270

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

22271

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

22272

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

22274

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

22275

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

22276

\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (x \right ) \]

22278

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

22279

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

22280

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

22281

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

22282

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

22283

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

22284

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

22285

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

22347

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

22348

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

22349

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

22350

\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (t \right ) \]

22351

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

22352

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

22353

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

22360

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

22361

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

22362

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