| # | ODE | Mathematica | Maple | Sympy |
| \[
{} R^{\prime \prime } = -\frac {k}{R^{2}}
\]
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| \[
{} x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0
\]
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| \[
{} y^{\prime \prime }-6 y^{\prime }+13 y = 0
\]
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| \[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
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{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 0
\]
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| \[
{} 2 y^{\prime \prime }+7 y^{\prime }-4 y = 0
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| \[
{} 2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0
\]
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{} y^{\prime \prime }+4 y^{\prime }+6 y = 10
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime } = f \left (x \right )
\]
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| \[
{} x^{\prime \prime }+x = 0
\]
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| \[
{} x^{\prime \prime }+x = 0
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| \[
{} x^{\prime \prime }+x = 0
\]
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| \[
{} x^{\prime \prime }+x = 0
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| \[
{} y^{\prime \prime }-y = 0
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| \[
{} y^{\prime \prime }-y = 0
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| \[
{} y^{\prime \prime }-y = 0
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| \[
{} y^{\prime \prime }-y = 0
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| \[
{} y^{\prime \prime }+4 y = 0
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| \[
{} y^{\prime \prime }+4 y = 0
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| \[
{} y^{\prime \prime }+4 y = 0
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| \[
{} y^{\prime \prime }+4 y = 0
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| \[
{} y^{\prime \prime }+4 y = 0
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| \[
{} y^{\prime \prime }+4 y = 0
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| \[
{} 2 y^{\prime \prime }-3 y^{2} = 0
\]
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| \[
{} y^{\prime \prime }+9 y = 18
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| \[
{} x y^{\prime \prime }-y^{\prime } = 0
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| \[
{} y^{\prime \prime } = y^{\prime }
\]
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| \[
{} y^{\prime \prime }+y = 2 \cos \left (x \right )-2 \sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }+y = \sec \left (\ln \left (x \right )\right )
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+y = {\mathrm e}^{x^{2}}
\]
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| \[
{} y^{\prime \prime } = 2 {y^{\prime }}^{3} y
\]
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| \[
{} y^{\prime \prime }+9 y = 5
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-6 y = 0
\]
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| \[
{} y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }-\frac {y}{4} = 0
\]
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| \[
{} y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t}
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
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| \[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8
\]
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| \[
{} y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 0
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3}
\]
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| \[
{} 9 y^{\prime \prime }-6 y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t}
\]
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| \[
{} y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2}
\]
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| \[
{} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
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| \[
{} y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right )
\]
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| \[
{} y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\]
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{} y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
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| \[
{} 4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right )
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right )
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }-y = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y = 0
\]
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| \[
{} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0
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| \[
{} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0
\]
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{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0
\]
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| \[
{} y+x y^{\prime }+y^{\prime \prime } = 2 x \,{\mathrm e}^{x}-1
\]
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| \[
{} x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\]
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{} -y+x y^{\prime }+x^{3} y^{\prime \prime } = \cos \left (\frac {1}{x}\right )
\]
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| \[
{} x \left (1+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = x +\frac {1}{x}
\]
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| \[
{} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = x^{2}-1
\]
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{} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y = x +\frac {1}{x}
\]
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| \[
{} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = x \left (1-\ln \left (x \right )\right )^{2}
\]
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{} x y^{\prime \prime }+2 y^{\prime }+x y = \sec \left (x \right )
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2}
\]
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| \[
{} \left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )-\sin \left (x \right )\right ) y = \left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x}
\]
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| \[
{} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 y^{\prime } \sin \left (x \right )+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2}
\]
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{} y^{\prime \prime }-2 y^{\prime }-3 y = 0
\]
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| \[
{} s^{\prime \prime }+2 s^{\prime }+s = 0
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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