4.23.6 Problems 501 to 600

Table 4.1347: Higher order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

19953

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

19954

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

19958

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

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

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

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

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

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

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

20173

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

20174

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

20181

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

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

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

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

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

20197

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

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

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

20204

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

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

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

20255

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

20280

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

20286

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

20468

\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-12 y = \cos \left (4 x \right ) \]

20471

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 = 0 \]

20472

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

20473

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime } = x^{2}+1 \]

20474

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

20475

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

20479

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

20480

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

20483

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

20484

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

20488

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

20489

\[ {} y^{\left (6\right )}-2 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }+y = \sin \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{x} \]

20490

\[ {} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = 16 x^{2}+256 \]

20492

\[ {} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = 96 \sin \left (2 x \right ) \cos \left (x \right ) \]

20495

\[ {} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 24 x \cos \left (x \right ) \]

20649

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

20695

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

20709

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

20816

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

20818

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

20820

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

20821

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

20823

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

20886

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

20922

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} \]

21313

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

21314

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

21315

\[ {} x^{\prime \prime \prime }-x^{\prime \prime } = 1 \]

21316

\[ {} x^{\prime \prime \prime }-x^{\prime } = t \]

21317

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

21649

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

21650

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

21651

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

21652

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

21653

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

21666

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

21667

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

21668

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

21690

\[ {} y^{\left (6\right )}+8 y^{\prime \prime \prime } = a \,{\mathrm e}^{x} \]

21692

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

21694

\[ {} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+16 y^{\prime \prime } = 96 \,{\mathrm e}^{-4 x} \]

21698

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

21699

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y = {\mathrm e}^{3 x} \]

21703

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

21705

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

21706

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

21837

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

21838

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y = 10 \cos \left (t \right ) \]

21998

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 2 x^{2}-3 x -17 \]

22004

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

22006

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

22008

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

22055

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

22057

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

22064

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime } = 6 \]

22076

\[ {} b^{\left (7\right )} = 3 p \]

22199

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

22248

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

22262

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

22263

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

22267

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

22273

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

22354

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

22369

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

22436

\[ {} y^{\prime \prime \prime } = -24 \cos \left (\frac {\pi x}{2}\right ) \]

22594

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