6.149 Problems 14801 to 14900

Table 6.297: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

14802

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

14804

\[ {} [x^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )] \]

14805

\[ {} \left [x^{\prime }\left (t \right ) = \pi ^{2} x \left (t \right )+\frac {187 y \left (t \right )}{5}, y^{\prime }\left (t \right ) = \sqrt {555}\, x \left (t \right )+\frac {400617 y \left (t \right )}{5000}\right ] \]

14806

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

14807

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

14808

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

14809

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

14810

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

14811

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

14812

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

14813

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

14814

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]

14815

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

14816

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

14817

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

14818

\[ {} y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t} \]

14819

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \]

14820

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

14821

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \]

14822

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

14823

\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

14824

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

14825

\[ {} y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t} \]

14826

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \]

14827

\[ {} y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \]

14828

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

14829

\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

14830

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

14831

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

14832

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

14833

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \]

14834

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \]

14835

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \]

14836

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

14837

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

14838

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

14839

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 10 \]

14840

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

14841

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

14842

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

14843

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

14844

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

14845

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

14846

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

14847

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

14848

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

14849

\[ {} y^{\prime \prime }+4 y^{\prime } = 3 t +2 \]

14850

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

14851

\[ {} y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \]

14852

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

14853

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

14854

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \]

14855

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \]

14856

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

14857

\[ {} y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \]

14858

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

14859

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

14860

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

14861

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

14862

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]

14863

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \]

14864

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \]

14865

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right ) \]

14866

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

14867

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

14868

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \]

14869

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \]

14870

\[ {} y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

14871

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

14872

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

14873

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \]

14874

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \]

14875

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

14876

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

14877

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

14878

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

14879

\[ {} y^{\prime \prime }+9 y = 2 \cos \left (3 t \right ) \]

14880

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

14881

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

14882

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

14883

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right ) \]

14884

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

14885

\[ {} y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \]

14886

\[ {} y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \]

14887

\[ {} y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \]

14888

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

14889

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

14890

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

14891

\[ {} y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (t -4\right ) \]

14892

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

14893

\[ {} y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \]

14894

\[ {} y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \]

14895

\[ {} y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \]

14896

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

14897

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

14898

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

14899

\[ {} y^{\prime \prime }+16 y = t \]

14900

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