| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+a^{2} y = \sin \left (b x \right )
\]
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| \[
{} y^{\prime \prime }+x y = 0
\]
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| \[
{} \left (b x +a \right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (x^{2}+a \right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (-x^{2}+a \right ) y+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = \left (x^{2}+a \right ) y
\]
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| \[
{} \left (b^{2} x^{2}+a \right ) y+y^{\prime \prime } = 0
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{} \left (c \,x^{2}+b x +a \right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime } = 0
\]
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| \[
{} a \,x^{k} y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \cos \left (2 x \right )+k \cos \left (4 x \right )\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = 2 \csc \left (x \right )^{2} y
\]
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| \[
{} a \csc \left (x \right )^{2} y+y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a2} \csc \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = \left (a^{2}+\left (-1+p \right ) p \csc \left (x \right )^{2}+\left (-1+q \right ) q \sec \left (x \right )^{2}\right ) y
\]
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{} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = \left (1+2 \tan \left (x \right )^{2}\right ) y
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| \[
{} -\left (a^{2}-b \,{\mathrm e}^{x}\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \,{\mathrm e}^{x}+c \,{\mathrm e}^{2 x}\right ) y+y^{\prime \prime } = 0
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| \[
{} a \,{\mathrm e}^{b x} y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \cosh \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
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| \[
{} \frac {\left (a +b \right ) y}{x^{2}}+y^{\prime \prime } = 0
\]
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| \[
{} x y-y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \left (x -6\right ) x^{2}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \left (3 x^{2}+2 x +1\right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}+x^{2}-\cos \left (x \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = 8 x^{2} {\mathrm e}^{3 x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = 50 \cosh \left (x \right ) \cos \left (x \right )
\]
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| \[
{} 3 y+2 y^{\prime }+y^{\prime \prime } = 0
\]
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{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \cos \left (x \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \sinh \left (x \right )
\]
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| \[
{} \csc \left (a \right )^{2} y-2 \tan \left (a \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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{} \csc \left (a \right )^{2} y-2 \tan \left (a \right ) y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x \tan \left (a \right )} x^{2}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (a x \right )
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}+\sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 2 \,{\mathrm e}^{-x}+x^{2}
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{a x} x
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| \[
{} -4 y-3 y^{\prime }+y^{\prime \prime } = 0
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| \[
{} -4 y-3 y^{\prime }+y^{\prime \prime } = 10 \cos \left (2 x \right )
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x} \cos \left (x \right )^{2}
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = 0
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \sin \left (x \right )
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| \[
{} y^{\prime \prime }-4 y^{\prime }+13 y = 0
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 0
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 4 x^{2} {\mathrm e}^{x}
\]
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{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{a x}
\]
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| \[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 0
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{} y^{\prime \prime }+6 y^{\prime }+9 y = \cosh \left (x \right ) {\mathrm e}^{-3 x}
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| \[
{} 12 y-7 y^{\prime }+y^{\prime \prime } = 0
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| \[
{} 12 y-7 y^{\prime }+y^{\prime \prime } = x
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{} 16 y+8 y^{\prime }+y^{\prime \prime } = 0
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| \[
{} 16 y+8 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x}
\]
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{} 20 y-9 y^{\prime }+y^{\prime \prime } = 0
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{} 20 y-9 y^{\prime }+y^{\prime \prime } = x^{2} {\mathrm e}^{3 x}
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| \[
{} y b^{2}+2 a y^{\prime }+y^{\prime \prime } = 0
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| \[
{} y b^{2}+2 a y^{\prime }+y^{\prime \prime } = c \sin \left (k x \right )
\]
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{} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x}
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{} \left (a^{2}+b^{2}\right )^{2} y-4 a b y^{\prime }+y^{\prime \prime } = 0
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{} b y+a y^{\prime }+y^{\prime \prime } = 0
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| \[
{} b y+a y^{\prime }+y^{\prime \prime } = f \left (x \right )
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| \[
{} \left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime } = 0
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| \[
{} \left (c \,x^{2}+b \right ) y+a y^{\prime }+y^{\prime \prime } = 0
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| \[
{} \left (b +{\mathrm e}^{x} c \right ) y+a y^{\prime }+y^{\prime \prime } = 0
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| \[
{} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime } = 0
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| \[
{} b \,{\mathrm e}^{k x} y+a y^{\prime }+y^{\prime \prime } = 0
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| \[
{} y+x y^{\prime }+y^{\prime \prime } = 0
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| \[
{} -y+x y^{\prime }+y^{\prime \prime } = 0
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| \[
{} 2 y-x y^{\prime }+y^{\prime \prime } = 0
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| \[
{} n y-x y^{\prime }+y^{\prime \prime } = 0
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{} -a y-x y^{\prime }+y^{\prime \prime } = 0
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| \[
{} -\left (1-x \right ) y-x y^{\prime }+y^{\prime \prime } = 0
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| \[
{} 6 y-2 x y^{\prime }+y^{\prime \prime } = 0
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{} -8 y+2 x y^{\prime }+y^{\prime \prime } = 0
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{} 2 n y-2 x y^{\prime }+y^{\prime \prime } = 0
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| \[
{} -\left (-x^{2}-x +1\right ) y-\left (2 x +1\right ) y^{\prime }+y^{\prime \prime } = 0
\]
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{} 2 \left (2 x^{2}+1\right ) y+4 x y^{\prime }+y^{\prime \prime } = 0
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{} -\left (-4 x^{2}+3\right ) y-4 x y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -\left (-4 x^{2}+3\right ) y-4 x y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x^{2}}
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{} a^{2} x^{2} y-2 a x y^{\prime }+y^{\prime \prime } = 0
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| \[
{} b y+a x y^{\prime }+y^{\prime \prime } = 0
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| \[
{} c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime } = 0
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| \[
{} \left (\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -2 a \left (-2 x^{2} a +1\right ) y-4 a x y^{\prime }+y^{\prime \prime } = 0
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| \[
{} x y-x^{2} y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} x y-x^{2} y^{\prime }+y^{\prime \prime } = x
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{} -4 x y+x^{2} y^{\prime }+y^{\prime \prime } = 0
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| \[
{} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} a \left (1+k \right ) x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} a k \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0
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