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Mathematica |
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\[
{} y^{\prime \prime }+\lambda y = 0
\]
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\[
{} y^{\prime \prime }+\lambda y = 0
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\[
{} y^{\prime \prime }-y = 0
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\[
{} y^{\prime \prime }+y = 0
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
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\[
{} y^{\prime \prime }+y = 0
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\[
{} y^{\prime \prime }-y = 0
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = 0
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\[
{} y^{\prime \prime }+\alpha y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }+\alpha ^{2} y = 1
\]
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\[
{} y^{\prime \prime }+y = 1
\]
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\[
{} y^{\prime \prime }+\lambda ^{2} y = 0
\]
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\[
{} y^{\prime \prime }+\lambda ^{2} y = 0
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }-\lambda ^{4} y = 0
\]
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\[
{} x y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0
\]
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\[
{} y^{\prime } = 1-x y
\]
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\[
{} y^{\prime } = \frac {y-x}{x +y}
\]
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\[
{} y^{\prime } = y \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+x y = 0
\]
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\[
{} y^{\prime \prime }-\sin \left (x \right ) y^{\prime } = 0
\]
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\[
{} x y^{\prime \prime }+y \sin \left (x \right ) = x
\]
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\[
{} \ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0
\]
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\[
{} y^{\prime \prime \prime }+x \sin \left (y\right ) = 0
\]
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\[
{} y^{\prime }-2 x y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }+y = 1
\]
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\[
{} y^{\prime \prime }-\left (x^{2}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime } = x^{2} y-y^{\prime }
\]
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\[
{} y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\]
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\[
{} y^{\prime } = {\mathrm e}^{y}+x y
\]
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\[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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\[
{} \left (1+x \right ) y^{\prime }-n y = 0
\]
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\[
{} 9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9} = 0
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+4 \left (x^{4}-1\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0
\]
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\[
{} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y = 0
\]
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\[
{} y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = \cos \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \pi ^{2}-x^{2}
\]
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\[
{} y^{\prime \prime }-4 y = \cos \left (\pi x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \arcsin \left (\sin \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }+9 y = \sin \left (x \right )^{3}
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = -2 t x_{1} \left (t \right )^{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )+t}{t}\right ]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = {\mathrm e}^{t -x_{1} \left (t \right )}, x_{2}^{\prime }\left (t \right ) = 2 \,{\mathrm e}^{x_{1} \left (t \right )}]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = \frac {y \left (t \right )^{2}}{x \left (t \right )}\right ]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )^{2}}{x_{2} \left (t \right )}, x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{1} \left (t \right )\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {{\mathrm e}^{-x \left (t \right )}}{t}, y^{\prime }\left (t \right ) = \frac {x \left (t \right ) {\mathrm e}^{-y \left (t \right )}}{t}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )-t}{x \left (t \right )+y \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {t -y \left (t \right )}{y \left (t \right )-x \left (t \right )}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )-t}{y \left (t \right )-x \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = -9 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+t, y^{\prime }\left (t \right ) = x \left (t \right )-t]
\]
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\[
{} [x^{\prime }\left (t \right )+3 x \left (t \right )+4 y \left (t \right ) = 0, y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right ) = 0]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-3 y \left (t \right )]
\]
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\[
{} [4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime \prime }\left (t \right ) = y \left (t \right ), y^{\prime \prime }\left (t \right ) = x \left (t \right )]
\]
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\[
{} [x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right ) = 0, x^{\prime }\left (t \right )+y^{\prime \prime }\left (t \right ) = 0]
\]
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\[
{} [x^{\prime \prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\]
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\[
{} [x^{\prime \prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) x^{\prime }\left (t \right )+x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -\frac {1}{y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {1}{x \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {x \left (t \right )}{y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {y \left (t \right )}{x \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )}{x \left (t \right )-y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{x \left (t \right )-y \left (t \right )}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = \sin \left (x \left (t \right )\right ) \cos \left (y \left (t \right )\right ), y^{\prime }\left (t \right ) = \cos \left (x \left (t \right )\right ) \sin \left (y \left (t \right )\right )]
\]
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\[
{} \left [{\mathrm e}^{t} x^{\prime }\left (t \right ) = \frac {1}{y \left (t \right )}, {\mathrm e}^{t} y^{\prime }\left (t \right ) = \frac {1}{x \left (t \right )}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \cos \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}+\sin \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}, y^{\prime }\left (t \right ) = -\frac {\sin \left (2 x \left (t \right )\right ) \sin \left (2 y \left (t \right )\right )}{2}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = 8 y \left (t \right )-x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )-2 x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )-2 z \left (t \right )-3 x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = -{\mathrm e}^{2 t}, y^{\prime }\left (t \right )+3 x \left (t \right )-2 y \left (t \right ) = 6 \,{\mathrm e}^{2 t}]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-\cos \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )-2 x \left (t \right )+\cos \left (t \right )+\sin \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+\tan \left (t \right )^{2}-1, y^{\prime }\left (t \right ) = \tan \left (t \right )-x \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = -4 x \left (t \right )-2 y \left (t \right )+\frac {2}{{\mathrm e}^{t}-1}, y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )-\frac {3}{{\mathrm e}^{t}-1}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {1}{\cos \left (t \right )}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = 1-x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 t]
\]
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\[
{} [x^{\prime }\left (t \right ) = -y \left (t \right )+\sin \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+\cos \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-{\mathrm e}^{t}]
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )+4 t -1, y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )+t]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+{\mathrm e}^{t}]
\]
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\[
{} [x^{\prime }\left (t \right )+y \left (t \right ) = t^{2}, y^{\prime }\left (t \right )-x \left (t \right ) = t]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{-t}, 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-2 z \left (t \right )+2-t, y^{\prime }\left (t \right ) = 1-x \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )+1-t]
\]
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\[
{} [x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 2 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = 1, z^{\prime }\left (t \right )+z \left (t \right ) = 1]
\]
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\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )]
\]
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