| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-k^{2} y = f \left (x \right )
\]
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{} -y+y^{\prime \prime } = {\mathrm e}^{-x}
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{} y^{\prime \prime }-4 y = {\mathrm e}^{2 x}
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 0
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
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| \[
{} y^{\prime \prime }-y = t \,{\mathrm e}^{2 t}
\]
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{} y^{\prime \prime }-3 y^{\prime }-4 y = t^{2}
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{} y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{t}
\]
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{} y^{\prime \prime }+4 y = \delta \left (t -1\right )
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{} y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -1\right )
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| \[
{} y^{\prime \prime }+6 y^{\prime }+18 y = 2 \operatorname {Heaviside}\left (\pi -t \right )
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{} y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x}
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{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x}
\]
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| \[
{} u^{\prime \prime }+2 a u^{\prime }+\omega ^{2} u = c \cos \left (\omega t \right )
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| \[
{} x^{\prime \prime }+x = 0
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{} x^{\prime \prime }+4 x = 0
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{} 2 x^{\prime \prime }+x^{\prime }-x = 0
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{} x^{\prime \prime }+2 x^{\prime }+2 x = 0
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| \[
{} x^{\prime \prime }+8 x^{\prime }+16 x = 0
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{} x^{\prime \prime }+2 x^{\prime }-15 x = 0
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{} x^{\prime \prime }-3 x^{\prime }+2 x = 0
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{} 4 x^{\prime }+2 x^{\prime \prime } = -5 x
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{} x^{\prime \prime }-6 x^{\prime }+9 x = 0
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{} x^{\prime \prime }+x^{\prime }-\beta x = 0
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{} x^{\prime \prime }+4 x^{\prime }+k x = 0
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| \[
{} x^{\prime \prime }+b x^{\prime }+c x = 0
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{} x^{\prime \prime }+5 x^{\prime }+6 x = 0
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| \[
{} x^{\prime \prime }+p x^{\prime } = 0
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{} x^{\prime \prime }+x^{\prime }-2 x = 0
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| \[
{} x^{\prime \prime }-2 x^{\prime }+2 x = 0
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| \[
{} x^{\prime \prime }-2 a x^{\prime }+b x = 0
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| \[
{} x^{\prime \prime }+\lambda ^{2} 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^{\prime }-2 x = 0
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| \[
{} x^{\prime \prime }-2 x^{\prime }+5 x = 0
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| \[
{} x^{\prime \prime }-2 x^{\prime }+5 x = 0
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| \[
{} x^{\prime \prime }+2 x^{\prime } = 0
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| \[
{} x^{\prime \prime }-4 x = t
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| \[
{} x^{\prime \prime }-4 x = 4 t^{2}
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| \[
{} x^{\prime \prime }+x = t^{2}-2 t
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{} x^{\prime \prime }+x = 3 t^{2}+t
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{} x^{\prime \prime }-x = {\mathrm e}^{-3 t}
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{} x^{\prime \prime }-x = 3 \,{\mathrm e}^{2 t}
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| \[
{} x^{\prime \prime }-x = t \,{\mathrm e}^{2 t}
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{} x^{\prime \prime }-3 x^{\prime }-x = t^{2}+t
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{} x^{\prime \prime }-4 x^{\prime }+13 x = 20 \,{\mathrm e}^{t}
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{} x^{\prime \prime }-x^{\prime }-2 x = 2 t +{\mathrm e}^{t}
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{} x^{\prime \prime }+4 x = \cos \left (t \right )
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{} x^{\prime \prime }+x = \sin \left (2 t \right )-\cos \left (3 t \right )
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{} x^{\prime \prime }+2 x^{\prime }+2 x = \cos \left (2 t \right )
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{} x^{\prime \prime }+x = t \sin \left (2 t \right )
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| \[
{} x^{\prime \prime }-x^{\prime } = t
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{} x^{\prime \prime }-x = {\mathrm e}^{k t}
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{} x^{\prime \prime }-x^{\prime }-2 x = 3 \,{\mathrm e}^{-t}
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{} x^{\prime \prime }-3 x^{\prime }+2 x = 3 t \,{\mathrm e}^{t}
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{} x^{\prime \prime }-4 x^{\prime }+3 x = 2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t}
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| \[
{} x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
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{} x^{\prime \prime }+4 x = \sin \left (2 t \right )
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{} x^{\prime \prime }+x = 2 \sin \left (t \right )+2 \cos \left (t \right )
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{} x^{\prime \prime }+9 x = \sin \left (t \right )+\sin \left (3 t \right )
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| \[
{} x^{\prime \prime }-x = t
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| \[
{} x^{\prime \prime }+4 x^{\prime }+x = k
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{} x^{\prime \prime }-2 x = 2 \,{\mathrm e}^{t}
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{} x^{\prime \prime }+x^{\prime }+x = 0
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{} 2 x^{\prime \prime \prime } = 0
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| \[
{} x^{\prime \prime \prime }-x^{\prime } = 0
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{} x^{\prime \prime \prime }+5 x^{\prime \prime }-6 x = 0
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{} x^{\prime \prime \prime }-4 x^{\prime \prime }+x^{\prime }-4 x = 0
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{} x^{\prime \prime \prime }-3 x^{\prime \prime }+4 x = 0
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{} x^{\prime \prime \prime }+4 x^{\prime } = 0
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{} x^{\prime \prime \prime }-x^{\prime } = 0
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{} x^{\prime \prime \prime }-x^{\prime } = 0
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{} x^{\prime \prime \prime }+x^{\prime \prime }-2 x = 0
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| \[
{} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x = 0
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{} x^{\prime \prime \prime }-3 x^{\prime }+k x = 0
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{} x^{\prime \prime \prime \prime }-6 x^{\prime \prime }+5 x = 0
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{} x^{\prime \prime \prime \prime }-x = 0
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{} x^{\prime \prime \prime \prime }-x^{\prime \prime } = 0
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{} x^{\prime \prime \prime \prime }-4 x^{\prime \prime }+x = 0
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{} x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x = 0
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{} x^{\prime \prime \prime \prime }+2 x^{\prime \prime }-4 x = 0
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| \[
{} x^{\left (5\right )}-x^{\prime } = 0
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{} x^{\left (5\right )}+x^{\prime \prime \prime \prime }-x^{\prime }-x = 0
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{} x^{\left (5\right )}+x = 0
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| \[
{} x^{\left (6\right )}-x^{\prime \prime } = 0
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{} x^{\left (6\right )}-64 x = 0
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{} x^{\prime \prime \prime \prime }+3 x^{\prime \prime \prime }+2 x^{\prime \prime } = {\mathrm e}^{t}
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{} x^{\prime \prime \prime }+4 x^{\prime } = \sec \left (2 t \right )
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{} x^{\prime \prime \prime }-x^{\prime \prime } = 1
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| \[
{} x^{\prime \prime \prime }-x^{\prime } = t
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{} x^{\prime \prime \prime \prime }+x^{\prime \prime \prime } = t
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{} x^{\prime \prime \prime \prime }-3 x^{\prime \prime \prime }+2 x^{\prime }-5 x = 0
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{} x^{\prime \prime \prime }-2 x^{\prime \prime }+3 x^{\prime }+x = 0
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{} x^{\prime \prime }-2 x^{\prime }+x = 0
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{} x^{\prime \prime }-4 x^{\prime }+3 x = 1
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{} x^{\prime \prime \prime \prime }+x^{\prime \prime } = 0
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{} x^{\prime \prime }+x = g \left (t \right )
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{} x^{\prime \prime } = \delta \left (-t +a \right )
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{} x^{\prime \prime }+2 x^{\prime }-x = 0
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