4.20.40 Problems 3901 to 4000

Table 4.1277: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

19953

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

19954

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x \]

19955

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

19956

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

19957

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

19958

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

19959

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

19960

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

19961

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

19962

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

19963

\[ {} e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2} \]

19964

\[ {} e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \]

19965

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

19966

\[ {} e y^{\prime \prime } = -P \left (L -x \right ) \]

19967

\[ {} e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \]

19968

\[ {} e y^{\prime \prime } = P \left (a -y\right ) \]

19983

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

19985

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

19991

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

20011

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

20152

\[ {} y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

20153

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

20154

\[ {} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

20155

\[ {} 9 y^{\prime \prime }+18 y^{\prime }-16 y = 0 \]

20156

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

20157

\[ {} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

20158

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

20159

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

20160

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0 \]

20161

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{4 x} \]

20162

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

20163

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

20164

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y = X \left (x \right ) \]

20165

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

20166

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

20167

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

20168

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

20169

\[ {} y^{\prime \prime \prime }+8 y = x^{4}+2 x +1 \]

20170

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

20171

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

20172

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

20173

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

20174

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

20175

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

20176

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

20177

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

20178

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

20179

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

20180

\[ {} y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0 \]

20181

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

20182

\[ {} y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2} \]

20183

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

20184

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

20185

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-6 y^{\prime }+8 y = x \]

20186

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

20187

\[ {} y^{\prime \prime \prime }-13 y^{\prime }+12 y = x \]

20188

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

20189

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

20190

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

20191

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

20192

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

20193

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

20194

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

20195

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

20196

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

20197

\[ {} y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (1+x \right ) \]

20198

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

20199

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

20200

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

20201

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

20202

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

20203

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = \cos \left (2 x \right ) {\mathrm e}^{x}+\cos \left (3 x \right ) \]

20204

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = {\mathrm e}^{x}+\cos \left (x \right ) \]

20205

\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = 20 x \]

20206

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

20207

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

20239

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

20241

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

20242

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

20254

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

20255

\[ {} y^{\left (5\right )}-m^{2} y^{\prime \prime \prime } = {\mathrm e}^{a x} \]

20271

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

20278

\[ {} y^{\prime \prime } = \frac {a}{x} \]

20280

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

20281

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

20284

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

20286

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

20444

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

20445

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

20446

\[ {} 2 x^{\prime \prime }+5 x^{\prime }-12 x = 0 \]

20447

\[ {} y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

20448

\[ {} 9 x^{\prime \prime }+18 x^{\prime }-16 x = 0 \]

20449

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

20450

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

20451

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

20452

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

20453

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

20454

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

20455

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

20456

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