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# |
ODE |
Mathematica |
Maple |
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\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime } = 0
\] |
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\[
{}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
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\[
{}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
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\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0
\] |
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\[
{}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0
\] |
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\[
{}y^{\prime \prime }+\alpha y = 0
\] |
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\[
{}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime } = 0
\] |
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\[
{}y^{\prime }-i y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3+\cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 \,{\mathrm e}^{x} x^{2}
\] |
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\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right )
\] |
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\[
{}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right )
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0
\] |
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✓ |
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\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = 0
\] |
✓ |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x}
\] |
✓ |
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\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 x +4
\] |
✓ |
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\[
{}y^{\prime }-y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
✓ |
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\[
{}y^{\prime }+2 y = 4
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right )
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2}
\] |
✓ |
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\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{x}
\] |
✓ |
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\[
{}y^{\prime \prime }-9 y = x +2
\] |
✓ |
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\[
{}y^{\prime \prime }+9 y = x +2
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right )
\] |
✓ |
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\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1
\] |
✓ |
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\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x +\cos \left (x \right )
\] |
✓ |
✓ |
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\[
{}y^{\prime }-2 y = 6
\] |
✓ |
✓ |
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\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+9 y = 1
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x}
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right )
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right .
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right .
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right .
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
✓ |
✓ |
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\[
{}y^{\prime }+3 y = \delta \left (x -2\right )
\] |
✓ |
✓ |
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\[
{}y^{\prime }-3 y = \delta \left (x -1\right )+2 \operatorname {Heaviside}\left (x -2\right )
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right )
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (x -1\right )
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right )
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right )
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right )
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+3 y_{2} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+2 y_{2} \left (x \right )+x -1, y_{2}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+2 y_{2} \left (x \right )-5 x -2]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \frac {2 y_{1} \left (x \right )}{x}-\frac {y_{2} \left (x \right )}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}}, y_{2}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+1-6 x\right ]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x\right ]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+y_{2} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ]
\] |
✗ |
✗ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ]
\] |
✗ |
✗ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}}\right ]
\] |
✗ |
✗ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}}\right ]
\] |
✗ |
✗ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+5 \,{\mathrm e}^{x}, y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 \,{\mathrm e}^{-x}]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )-2 y_{1} \left (x \right )+\sin \left (2 x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+y_{2} \left (x \right )-2 \cos \left (3 x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{3} \left (x \right )-y_{1} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 x y_{1} \left (x \right )-x^{2} y_{2} \left (x \right )+4 x, y_{2}^{\prime }\left (x \right ) = {\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right )]
\] |
✗ |
✗ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+4 x -2, y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )+3 x]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}\right ]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x\right ]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+y_{2} \left (x \right )-3 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 5 y_{1} \left (x \right )-5 y_{2} \left (x \right )-5 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+4 y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-5 y_{2} \left (x \right )-3 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 4 y_{1} \left (x \right )+6 y_{2} \left (x \right )+6 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+3 y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = -y_{1} \left (x \right )-4 y_{2} \left (x \right )-3 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+2 y_{2} \left (x \right )-3 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = -2 y_{1} \left (x \right )-y_{2} \left (x \right )+y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )-2 y_{2} \left (x \right )-y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{2} \left (x \right )-2 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+2 y_{2} \left (x \right )+4 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+2 y_{2} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{3} \left (x \right )-4 y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 4 y_{3} \left (x \right )+3 y_{4} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-5 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -2 y_{1} \left (x \right )+3 y_{2} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{3} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 2 y_{4} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )+y_{4} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )-y \left (t \right )+2, y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )-3]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )-6, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+2]
\] |
✓ |
✓ |
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