4.20.30 Problems 2901 to 3000

Table 4.1257: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

16790

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

16791

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

16801

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

16802

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

16803

\[ {} y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x} \]

16804

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \]

16805

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

16815

\[ {} y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x} \]

16816

\[ {} -4 y^{\prime }+y^{\prime \prime \prime } = 30 \,{\mathrm e}^{3 x} \]

16819

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

16820

\[ {} y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right ) \]

16822

\[ {} y^{\prime \prime }+36 y = 0 \]

16823

\[ {} y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

16825

\[ {} y^{\prime \prime }-36 y = 0 \]

16826

\[ {} y^{\prime \prime }-9 y^{\prime }+14 y = 0 \]

16829

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

16830

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

16831

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

16834

\[ {} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime } = 0 \]

16836

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

16839

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

16841

\[ {} y^{\prime \prime }+y^{\prime }-30 y = 0 \]

16842

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

16844

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8 \]

16847

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

16848

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

16849

\[ {} y^{\prime \prime }+20 y^{\prime }+100 y = 0 \]

16851

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

16852

\[ {} y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2} \]

16853

\[ {} y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right ) \]

16854

\[ {} y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x} \]

16855

\[ {} y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x} \]

16857

\[ {} y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \]

16858

\[ {} y^{\prime \prime }+36 y = 6 \sec \left (6 x \right ) \]

16860

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x} \]

16862

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right ) \]

16866

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}} \]

16867

\[ {} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 \sin \left (3 x \right ) x \]

16868

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

16869

\[ {} y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x} \]

16875

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

16876

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

16877

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

16878

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

16879

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

16880

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t} \]

16881

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 7 \]

16882

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

16883

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

16884

\[ {} y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t} \]

16886

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

16887

\[ {} y^{\prime \prime }+9 y = 27 t^{3} \]

16888

\[ {} y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t} \]

16889

\[ {} y^{\prime \prime }-8 y^{\prime }+17 y = 0 \]

16890

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = t^{2} {\mathrm e}^{3 t} \]

16891

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]

16892

\[ {} y^{\prime \prime }+8 y^{\prime }+17 y = 0 \]

16893

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

16894

\[ {} y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t} \]

16895

\[ {} y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t} \]

16896

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

16897

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

16898

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

16899

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

16900

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

16901

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

16902

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 1 \]

16903

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

16904

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

16905

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

16906

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

16909

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

16910

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

16911

\[ {} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \]

16913

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

16914

\[ {} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

16917

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

16918

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

16920

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

16921

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

16923

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

16924

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

16925

\[ {} y^{\prime \prime }+16 y = \delta \left (t -2\right ) \]

16926

\[ {} y^{\prime \prime }-16 y = \delta \left (t -10\right ) \]

16927

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

16928

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \]

16929

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

16930

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \]

16931

\[ {} y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \]

16932

\[ {} y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right ) \]

16933

\[ {} y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right ) \]

17068

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

17070

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

17080

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

17081

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

17082

\[ {} x^{\prime \prime }+2 x^{\prime }-10 x = 0 \]

17083

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

17084

\[ {} y^{\prime \prime }-12 y^{\prime }+40 y = 0 \]

17085

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

17086

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