4.3.47 Problems 4601 to 4700

Table 4.377: Second order ode

#

ODE

Mathematica

Maple

Sympy

14843

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

14844

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

14845

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

14846

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

14847

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

14848

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

14849

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

14850

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

14851

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

14852

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

14853

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

14854

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

14855

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

14856

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

14857

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

14858

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

14859

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

14860

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

14861

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

14862

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

14863

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

14864

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

14865

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

14866

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

14867

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

14868

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

14869

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

14870

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

14871

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

14872

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

14873

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

14874

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

14875

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

14876

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

14877

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

14878

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

14879

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

14880

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

14881

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

14882

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

14883

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

14884

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

14885

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

14886

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

14887

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

14888

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

14889

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

14890

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

14891

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

14892

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

14893

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

14894

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

14895

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

14896

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

14897

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

14898

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

14899

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

14900

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

14901

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

14902

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

14903

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

14904

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

14905

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

14906

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

14907

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

14913

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

14914

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

14915

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

14916

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

14917

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

14927

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

14928

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

14936

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

15138

\[ {} x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

15139

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

15140

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

15141

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

15142

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

15143

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

15144

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

15145

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

15146

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

15147

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

15148

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

15149

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

15150

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

15151

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

15152

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

15157

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

15158

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

15159

\[ {} \sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2} = 0 \]

15160

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

15161

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

15162

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

15163

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

15164

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

15165

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

15166

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

15167

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

15168

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