| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [y^{\prime }\left (x \right ) = x +2 z \left (x \right ), z^{\prime }\left (x \right ) = 3 x +y \left (x \right )-z \left (x \right )]
\]
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| \[
{} [y^{\prime }\left (x \right ) = x^{2}+6 y \left (x \right )+4 z \left (x \right ), z^{\prime }\left (x \right ) = y \left (x \right )+3 z \left (x \right )]
\]
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| \[
{} [y^{\prime }\left (x \right ) = y \left (x \right )+z \left (x \right )+x, z^{\prime }\left (x \right ) = 1-y \left (x \right )-z \left (x \right )]
\]
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| \[
{} [y^{\prime }\left (x \right ) = f \left (x \right )+a y \left (x \right )+b z \left (x \right ), z^{\prime }\left (x \right ) = g \left (x \right )+c y \left (x \right )+d z \left (x \right )]
\]
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| \[
{} [x y^{\prime }\left (x \right ) = y \left (x \right ), z^{\prime }\left (x \right ) = 3 y \left (x \right )-x]
\]
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| \[
{} [y^{\prime }\left (x \right ) = z \left (x \right ), z^{\prime }\left (x \right ) = w \left (x \right ), w^{\prime }\left (x \right ) = y \left (x \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )-x \left (t \right )-y^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right )+3 x \left (t \right )-2 y \left (t \right ) = 0]
\]
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| \[
{} [x \left (t \right )-y \left (t \right )+z^{\prime }\left (t \right ) = 0, x^{\prime }\left (t \right )-y \left (t \right ) = 1, y^{\prime }\left (t \right )-y \left (t \right )+z \left (t \right ) = 0]
\]
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| \[
{} [v^{\prime }\left (x \right )-2 v \left (x \right )+2 w^{\prime }\left (x \right ) = 2-4 \,{\mathrm e}^{2 x}, 2 v^{\prime }\left (x \right )-3 v \left (x \right )+3 w^{\prime }\left (x \right )-w \left (x \right ) = 0]
\]
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| \[
{} [y^{\prime }\left (x \right )-2 y \left (x \right )-v^{\prime }\left (x \right )-v \left (x \right ) = 6 \,{\mathrm e}^{3 x}, 2 y^{\prime }\left (x \right )-3 y \left (x \right )+v^{\prime }\left (x \right )-3 v \left (x \right ) = 6 \,{\mathrm e}^{3 x}]
\]
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| \[
{} [y^{\prime }\left (x \right )+y \left (x \right )-v^{\prime }\left (x \right )-v \left (x \right ) = 0, y^{\prime }\left (x \right )+v^{\prime }\left (x \right )-v \left (x \right ) = {\mathrm e}^{x}]
\]
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| \[
{} [2 v^{\prime }\left (x \right )+2 v \left (x \right )+w^{\prime }\left (x \right )-w \left (x \right ) = 3 x, v^{\prime }\left (x \right )+v \left (x \right )+w^{\prime }\left (x \right )+w \left (x \right ) = 1]
\]
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| \[
{} [3 v^{\prime }\left (x \right )+2 v \left (x \right )+w^{\prime }\left (x \right )-6 w \left (x \right ) = 5 \,{\mathrm e}^{x}, 4 v^{\prime }\left (x \right )+2 v \left (x \right )+w^{\prime }\left (x \right )-8 w \left (x \right ) = 5 \,{\mathrm e}^{x}+2 x -3]
\]
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| \[
{} [2 y^{\prime }\left (x \right )+2 y \left (x \right )+w^{\prime }\left (x \right )-w \left (x \right ) = 1+x, y^{\prime }\left (x \right )+3 y \left (x \right )+w^{\prime }\left (x \right )+w \left (x \right ) = 4 x +14]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-6 y_{1} \left (t \right ) = -4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-3 y_{1} \left (t \right ) = -4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right )+y_{2} \left (t \right ) = y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-2 y_{1} \left (t \right ) = 2 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+2 y_{2}^{\prime }\left (t \right )+y_{2} \left (t \right ) = -2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )+4 y_{1} \left (t \right ) = 10 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-6 y_{2}^{\prime }\left (t \right )+23 y_{2} \left (t \right ) = 9 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-2 y_{1} \left (t \right ) = -2 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+y_{2}^{\prime }\left (t \right )+6 y_{2} \left (t \right ) = 4 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime \prime }\left (t \right )+2 y_{1}^{\prime }\left (t \right )+6 y_{1} \left (t \right ) = 5 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-2 y_{2}^{\prime }\left (t \right )+6 y_{2} \left (t \right ) = 9 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime \prime }\left (t \right )+2 y_{1} \left (t \right ) = -3 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+2 y_{2}^{\prime }\left (t \right )-9 y_{2} \left (t \right ) = 6 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right )-2 y_{2} \left (t \right ) = y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-y_{1} \left (t \right ) = -2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right )-y_{2} \left (t \right ) = 2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )-2 y_{1} \left (t \right ) = -y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-y_{2}^{\prime }\left (t \right )+y_{2} \left (t \right ) = y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right )+2 y_{1} \left (t \right ) = 5 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )-2 y_{2}^{\prime }\left (t \right )+5 y_{2} \left (t \right ) = 2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime \prime }\left (t \right )+2 y_{1} \left (t \right ) = -3 y_{2} \left (t \right ), y_{2}^{\prime \prime }\left (t \right )+2 y_{2}^{\prime }\left (t \right )-9 y_{2} \left (t \right ) = 6 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right ) y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right )+t^{2}, y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+y_{2} \left (t \right )+1]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = \sin \left (t \right ) y_{1} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+\cos \left (t \right ) y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = t \sin \left (y_{1} \left (t \right )\right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+t \cos \left (y_{2} \left (t \right )\right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{4} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{4} \left (t \right ), y_{4}^{\prime }\left (t \right ) = y_{2} \left (t \right )+2 y_{3} \left (t \right )]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{2}-y_{2} \left (t \right )+5, y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+\frac {y_{2} \left (t \right )}{2}-5\right ]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right )+t, y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-t]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-5 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+3 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )+4 y_{2} \left (t \right )-y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+{\mathrm e}^{t}, y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-2 y_{2} \left (t \right )+{\mathrm e}^{t}]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+2 y_{2} \left (t \right )+5, y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-5 y_{2} \left (t \right )+2 \cos \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )+\cos \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-4 y_{2} \left (t \right )+4, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )+1]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right )+{\mathrm e}^{t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+2 y_{2} \left (t \right )-{\mathrm e}^{t}]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )+2 y_{2} \left (t \right )+t, y_{2}^{\prime }\left (t \right ) = -8 y_{1} \left (t \right )-3 y_{2} \left (t \right )-2 t]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+y_{3} \left (t \right )+{\mathrm e}^{-2 t}, y_{2}^{\prime }\left (t \right ) = -y_{2} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-2 y_{2} \left (t \right )-y_{3} \left (t \right )-{\mathrm e}^{-2 t}]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right )+y_{3} \left (t \right )+{\mathrm e}^{2 t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right )+{\mathrm e}^{2 t}, y_{3}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+y_{2} \left (t \right )+3 y_{3} \left (t \right )-{\mathrm e}^{2 t}]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+3 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-3 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = t y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -t y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = t y_{1} \left (t \right )+t y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -t y_{1} \left (t \right )-t y_{2} \left (t \right )]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+\frac {y_{2} \left (t \right )}{t}\right ]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = \left (2 t +1\right ) y_{1} \left (t \right )+2 t y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 t y_{1} \left (t \right )+\left (1-2 t \right ) y_{2} \left (t \right )]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+\frac {y_{2} \left (t \right )}{t}\right ]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+1, y_{2}^{\prime }\left (t \right ) = \frac {y_{2} \left (t \right )}{t}+t\right ]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = -\frac {y_{2} \left (t \right )}{t}+1, y_{2}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+\frac {2 y_{2} \left (t \right )}{t}-1\right ]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {4 t y_{1} \left (t \right )}{t^{2}+1}+\frac {6 y_{2} \left (t \right ) t}{t^{2}+1}-3 t, y_{2}^{\prime }\left (t \right ) = -\frac {2 t y_{1} \left (t \right )}{t^{2}+1}-\frac {4 y_{2} \left (t \right ) t}{t^{2}+1}+t\right ]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 \sec \left (t \right ) y_{1} \left (t \right )+5 \sec \left (t \right ) y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -\sec \left (t \right ) y_{1} \left (t \right )-3 \sec \left (t \right ) y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = t y_{1} \left (t \right )+t y_{2} \left (t \right )+4 t, y_{2}^{\prime }\left (t \right ) = -t y_{1} \left (t \right )-t y_{2} \left (t \right )+4 t]
\]
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