| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+2 y^{\prime }+y = t
\]
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{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right .
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right .
\]
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{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right .
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} {y^{\prime \prime }}^{2} x^{2} \left (x^{2}-1\right )-1 = 0
\]
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| \[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
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| \[
{} x^{\prime \prime } = x^{2}-4 x+\lambda
\]
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| \[
{} y^{\prime \prime }+y^{\prime } = 6 y+5 \,{\mathrm e}^{2 x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x = 0
\]
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{} y^{\prime \prime }+4 y = 2 \tan \left (x \right )
\]
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| \[
{} y^{\prime \prime }-y^{\prime } = 6 x^{5} {\mathrm e}^{x}
\]
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| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = x \,{\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }+2 a y^{\prime }+a^{2} y = x^{2} {\mathrm e}^{-a x}
\]
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| \[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }-3 y = 2 \,{\mathrm e}^{-t}
\]
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{} y^{\prime \prime }+9 y = 5 \cos \left (2 t \right )
\]
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{} y^{\prime \prime }+y = \sin \left (2 t \right )
\]
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{} y^{\prime \prime }+4 y = t \sin \left (t \right )
\]
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{} y^{\prime \prime }+4 y = x \sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x = 0
\]
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{} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}}
\]
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| \[
{} y^{\prime \prime }+y^{\prime } = \sin \left (2 x \right )
\]
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| \[
{} x y^{\prime \prime }+y^{\prime } = 16 x^{3}
\]
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| \[
{} y^{\prime \prime }+4 y = 2 t -8
\]
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{} y^{\prime \prime }+y = 2 \cos \left (t \right )
\]
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| \[
{} t y^{\prime \prime }+t^{2} y^{\prime }-\sin \left (t \right ) \sqrt {t} = t^{2}-t +1
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| \[
{} s^{2} t^{\prime \prime }+s t t^{\prime } = s
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| \[
{} y y^{\prime \prime } = 1+y^{2}
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| \[
{} t^{2} s^{\prime \prime }-t s^{\prime } = 1-\sin \left (t \right )
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| \[
{} {y^{\prime \prime }}^{{3}/{2}}+y = x
\]
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| \[
{} y+2 y^{\prime }+y^{\prime \prime } = x
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{} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x}
\]
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| \[
{} y y^{\prime }+y^{\prime \prime } = x^{2}
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2}
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\]
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{} y^{\prime \prime }-y^{\prime }-2 y = \sin \left (2 x \right )
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| \[
{} y^{\prime \prime } = 9 x^{2}+2 x -1
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = x^{2}-1
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 4 \cos \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}}
\]
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| \[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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{} y^{\prime \prime }+4 y = \sin \left (2 x \right )^{2}
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| \[
{} y^{\prime \prime }-\frac {y}{x} = x^{2}
\]
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| \[
{} y^{\prime \prime }+2 x y = x
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{} y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2}
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
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{} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (x \right )
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
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| \[
{} y^{\prime \prime }+y = x
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{} y^{\prime \prime }+4 y = \sin \left (2 x \right )^{2}
\]
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{} y^{\prime \prime }+2 y^{\prime }+2 y = \sin \left (2 x \right )+\cos \left (2 x \right )
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{} y^{\prime \prime }-y^{\prime }-2 y = 4 t^{2}
\]
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{} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (t \right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = f \left (t \right )
\]
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{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-y = \sin \left (t \right )
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{} y^{\prime \prime }-y = {\mathrm e}^{t}
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{} y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 t \right )
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{} y^{\prime \prime }+y = \sin \left (t \right )
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{} y^{\prime \prime }+y^{\prime }+y = \sin \left (t \right )
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 t}
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (t -4\right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }-3 y = 9 x
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| \[
{} y^{\prime \prime }+y = x
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{} y^{\prime \prime }+y = x
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| \[
{} y^{\prime \prime }+y = x
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{} y^{\prime \prime }-4 y^{\prime }-5 y = {\mathrm e}^{3 x}
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{} x^{\prime \prime }-3 x = \sin \left (y \right )
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| \[
{} y^{\prime \prime }-3 y^{\prime }-10 y = 6 \,{\mathrm e}^{x}
\]
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| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 2 x^{2}
\]
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| \[
{} x^{\prime \prime } = t^{2}-4 t +8
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| \[
{} y^{\prime \prime } = 12 x \left (4-x \right )
\]
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{} y^{\prime \prime } = 1-\cos \left (x \right )
\]
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{} y^{\prime \prime } = \sqrt {2 x +1}
\]
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| \[
{} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime } = 0
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| \[
{} -y+y^{\prime \prime } = 4 x
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{} y^{\prime \prime }+y = {\mathrm e}^{-x^{2}}
\]
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| \[
{} y^{\prime \prime }+x {y^{\prime }}^{2} = 1
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| \[
{} x y^{\prime \prime }-3 y^{\prime } = 4 x^{2}
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{} y^{\prime \prime } = 2 x
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| \[
{} i^{\prime \prime } = t^{2}+1
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{} x^{2} y^{\prime \prime } = x^{2}+1
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| \[
{} y^{\prime } y^{\prime \prime } = 1
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
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| \[
{} y^{\prime \prime }+x y^{\prime } = x
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{} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
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| \[
{} y^{\prime \prime } = y^{\prime }+2 x
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| \[
{} x y^{\prime \prime }+y^{\prime } = 1
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