4.8.14 Problems 1301 to 1400

Table 4.621: Third and higher order ode

#

ODE

Mathematica

Maple

Sympy

18813

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

18814

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

18817

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

18818

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

18823

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

18824

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

18825

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

18829

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

18830

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

18831

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

18832

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

18833

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

18837

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

18838

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

18839

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

18841

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

18843

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

18844

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

18845

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

18848

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

18850

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

18851

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

18854

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

18855

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

18862

\[ {} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1 \]

18864

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0 \]

18866

\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0 \]

18867

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 c +\frac {10}{x} \]

18868

\[ {} 16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 \left (1+x \right ) y^{\prime }+y = x^{2}+4 x +3 \]

18871

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2} \]

18872

\[ {} x^{4} y^{\prime \prime \prime }+2 x^{3} y^{\prime \prime }-y^{\prime } x^{2}+x y = 1 \]

18876

\[ {} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

18883

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

18884

\[ {} x^{2} y^{\prime \prime \prime \prime }+1 = 0 \]

18890

\[ {} x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime } = 4 \]

18893

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

18898

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

18899

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

18900

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

18904

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

18913

\[ {} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (6 x +3\right ) y^{\prime \prime }+6 y = 0 \]

18914

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

18915

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

18917

\[ {} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = \frac {2}{x^{3}} \]

18921

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

18924

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

18926

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

18930

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

18956

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

19089

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

19093

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

19095

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

19096

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

19097

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

19098

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

19099

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

19100

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

19101

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

19112

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

19115

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

19116

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

19117

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

19118

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

19119

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

19123

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

19124

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

19127

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

19128

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

19132

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

19133

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

19134

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

19136

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

19137

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

19139

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

19246

\[ {} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-2 y = 0 \]

19247

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

19248

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = \ln \left (x \right )^{2} \]

19249

\[ {} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1 \]

19250

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

19251

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0 \]

19253

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

19264

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

19265

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 4 x \]

19266

\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

19268

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = x^{2}+\frac {1}{x^{2}} \]

19269

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

19272

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

19273

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2} \]

19279

\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

19280

\[ {} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

19289

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

19290

\[ {} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right ) \]

19291

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

19293

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

19294

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

19298

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

19300

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

19313

\[ {} x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime } = 4 \]

19318

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

19331

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