| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{\prime \prime }+2 x^{\prime }+x = \delta \left (t \right )-\delta \left (t -2\right )
\]
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| \[
{} x^{\prime \prime }+4 x = f \left (t \right )
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{} x^{\prime \prime }+6 x^{\prime }+9 x = f \left (t \right )
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{} x^{\prime \prime }+6 x^{\prime }+8 x = f \left (t \right )
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{} x^{\prime \prime }+4 x^{\prime }+8 x = f \left (t \right )
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| \[
{} y^{\prime \prime }+y = 3 x
\]
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| \[
{} y^{\prime \prime }-4 y = 12
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{} y^{\prime \prime }-2 y^{\prime }-3 y = 6
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+2 y = 2 x
\]
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| \[
{} y^{\prime \prime }+2 y = 4
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| \[
{} y^{\prime \prime }+2 y = 6 x
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| \[
{} y^{\prime \prime }+2 y = 6 x +4
\]
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| \[
{} y^{\prime \prime }+16 y = {\mathrm e}^{3 x}
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 3 x +4
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right )
\]
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| \[
{} 4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2}
\]
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| \[
{} 2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2}
\]
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{} y^{\prime \prime }-4 y = \sinh \left (x \right )
\]
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{} y^{\prime \prime }-4 y = \cosh \left (2 x \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right )
\]
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| \[
{} y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5
\]
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{} y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\]
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{} y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right )
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right )
\]
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{} y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }+4 y = 2 x
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+9 y = \sin \left (2 x \right )
\]
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{} y^{\prime \prime }+y = \cos \left (x \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+2 y = 1+x
\]
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{} y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right )
\]
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| \[
{} y^{\prime \prime }+9 y = \sin \left (x \right )^{4}
\]
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| \[
{} y^{\prime \prime }+y = x \cos \left (x \right )^{3}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x}
\]
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| \[
{} 4 y-4 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{2 x}
\]
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{} y^{\prime \prime }-4 y = \sinh \left (2 x \right )
\]
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{} y^{\prime \prime }+4 y = \cos \left (3 x \right )
\]
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{} y^{\prime \prime }+9 y = \sin \left (3 x \right )
\]
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{} y^{\prime \prime }+9 y = 2 \sec \left (3 x \right )
\]
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{} y^{\prime \prime }+y = \csc \left (x \right )^{2}
\]
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{} y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\]
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{} y^{\prime \prime }-4 y = x \,{\mathrm e}^{x}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5}
\]
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| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3}
\]
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{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4}
\]
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| \[
{} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}}
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right )
\]
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| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1
\]
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| \[
{} x^{\prime \prime }+9 x = 10 \cos \left (2 t \right )
\]
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{} x^{\prime \prime }+4 x = 5 \sin \left (3 t \right )
\]
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{} x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right )
\]
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{} x^{\prime \prime }+25 x = 90 \cos \left (4 t \right )
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| \[
{} m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right )
\]
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{} x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right )
\]
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| \[
{} x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right )
\]
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{} 2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right )
\]
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{} x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right )
\]
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{} x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right )
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| \[
{} x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right )
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{} x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right )
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| \[
{} x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right )
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{} x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right )
\]
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{} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t}
\]
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{} y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t}
\]
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{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\]
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| \[
{} 4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}}
\]
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{} y^{\prime \prime }+y = \tan \left (t \right )
\]
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{} y^{\prime \prime }+9 y = 9 \sec \left (3 t \right )^{2}
\]
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{} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 t}}{t^{2}}
\]
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{} y^{\prime \prime }+4 y = 3 \csc \left (2 t \right )
\]
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{} y^{\prime \prime }+y = 2 \sec \left (\frac {t}{2}\right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1}
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right )
\]
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{} y^{\prime \prime }+4 y = g \left (t \right )
\]
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{} t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1
\]
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| \[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3}
\]
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| \[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\]
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| \[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \left (x \right )
\]
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{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
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| \[
{} t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2}
\]
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{} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t
\]
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{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\]
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| \[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right ) {\mathrm e}^{-t}
\]
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| \[
{} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right )
\]
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| \[
{} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right )
\]
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{} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (6 t \right )
\]
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{} u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right )
\]
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| \[
{} y^{\prime \prime }+\omega ^{2} y = \cos \left (2 t \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right .
\]
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