4.27.23 Problems 2201 to 2300

Table 4.1597: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

22865

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

22866

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

22867

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

22892

\[ {} y^{\prime \prime }+3 y = x^{2}+1 \]

22893

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

22894

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

22896

\[ {} i^{\prime \prime }+2 i^{\prime }+5 i = 34 \cos \left (2 t \right ) \]

22898

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

22902

\[ {} y^{\prime \prime }+4 y = x \left (\cos \left (x \right )+1\right ) \]

22903

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

22905

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

22908

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

22922

\[ {} Q^{\prime \prime }+k Q = e \left (t \right ) \]

22923

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

22924

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

22926

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

22927

\[ {} y^{\prime \prime }+9 y = 20 \,{\mathrm e}^{-t} \]

22928

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

22929

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 100 \]

22935

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

22936

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 6 \delta \left (t -2\right ) \]

23148

\[ {} y^{\prime \prime }-9 y = 5 \]

23149

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

23150

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

23151

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

23152

\[ {} x^{\prime \prime }-6 x^{\prime }-7 x = 4 z -7 \]

23153

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

23154

\[ {} x^{\prime \prime }-2 x^{\prime }+5 x = 3 \cos \left (2 t \right ) \]

23155

\[ {} y^{\prime \prime }+5 y^{\prime }+8 y = 4 \sin \left (5 x \right ) \]

23156

\[ {} x^{\prime \prime }+9 x^{\prime }+8 x = \sin \left (5 t \right ) \]

23157

\[ {} x^{\prime \prime }-9 x^{\prime }-10 x = \cos \left (4 t \right ) \]

23158

\[ {} y^{\prime \prime }-9 y^{\prime }+14 y = {\mathrm e}^{2 x} \]

23159

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

23160

\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = {\mathrm e}^{4 x} \]

23166

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

23167

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

23168

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

23169

\[ {} s^{\prime \prime } = 5 t^{2}-7 t \]

23181

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

23182

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

23183

\[ {} y^{\prime \prime }-5 y^{\prime }+4 y = x^{2} \]

23184

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

23185

\[ {} y^{\prime \prime }-11 y^{\prime }+30 y = {\mathrm e}^{5 x} \]

23186

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

23187

\[ {} 2 y^{\prime \prime }-3 y^{\prime }-5 y = 2 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]

23188

\[ {} y^{\prime \prime }-7 y^{\prime }+2 y = {\mathrm e}^{2 x} \]

23189

\[ {} 2 y^{\prime \prime }-4 y^{\prime }-y = 7 \,{\mathrm e}^{5 x} \]

23190

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

23191

\[ {} y^{\prime \prime }+2 y = 7 \cos \left (3 x \right ) \]

23192

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

23193

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

23194

\[ {} y^{\prime \prime }+y^{\prime }+y = 2 x^{3}+7 x^{2}-x \]

23195

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 5 \sin \left (x \right ) \]

23196

\[ {} x^{\prime \prime }-3 x^{\prime }+2 x = 5 \cos \left (t \right ) \]

23198

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

23199

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 8 \sin \left (2 x \right ) \]

23200

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

23201

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 x} \sin \left (3 x \right ) \]

23202

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

23203

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

23204

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

23205

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

23206

\[ {} 16 y+8 y^{\prime }+y^{\prime \prime } = x \left (12-{\mathrm e}^{-4 x}\right ) \]

23207

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

23224

\[ {} m s^{\prime \prime } = \frac {g \,t^{2}}{2} \]

23227

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

23232

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

23342

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

23377

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

23378

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

23570

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = x^{2}+3 \]

23571

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

23572

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

23573

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

23574

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

23576

\[ {} y^{\prime \prime }-13 y^{\prime }+36 y = x \,{\mathrm e}^{4 x} \]

23578

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

23583

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

23586

\[ {} y^{\prime \prime }+5 y^{\prime } = \sin \left (x \right ) \]

23587

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

23589

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

23591

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

23592

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

23593

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

23594

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

23595

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

23598

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

23599

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

23600

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

23601

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

23604

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

23606

\[ {} y^{\prime \prime }+4 y = 4 x^{3}-8 x^{2}-14 x +7 \]

23608

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

23609

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

23610

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

23611

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

23612

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

23613

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

23614

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

23615

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