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Mathematica |
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\[
{} \left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y = 0
\]
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\[
{} \left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\]
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\[
{} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\]
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\[
{} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-3\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+\frac {8}{9}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\left (2 x^{2}+\frac {5}{9}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0
\]
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\[
{} 2 x y^{\prime \prime }+y^{\prime }+2 y = 0
\]
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\[
{} 3 x y^{\prime \prime }-\left (x -2\right ) y^{\prime }-2 y = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }+x y = 0
\]
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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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\[
{} x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y = 0
\]
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\[
{} x y^{\prime \prime }-\left (x^{2}+2\right ) y^{\prime }+x y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\]
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\[
{} \left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\frac {3 y}{4} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -1\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+8 \left (x^{2}-1\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4} = 0
\]
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\[
{} x y^{\prime \prime }+y^{\prime }+2 y = 0
\]
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\[
{} 2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-3\right ) y = 0
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{4 t}]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right ) = -2 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right ) = t^{2}]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right ) = {\mathrm e}^{3 t}]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 2 \,{\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{2 t}]
\]
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\[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = {\mathrm e}^{-t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}]
\]
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\[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right ) = t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-4 x \left (t \right )-y \left (t \right ) = {\mathrm e}^{t}]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-6 y \left (t \right ) = {\mathrm e}^{3 t}, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-6 y \left (t \right ) = t]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = 3 t, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-3 y \left (t \right ) = 1]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 0]
\]
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\[
{} [x^{\prime }\left (t \right )-y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right ) = t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 1]
\]
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\[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right ) = 4 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right ) = 2]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )+5 y \left (t \right ) = t^{2}, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right ) = 1+2 t]
\]
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\[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right ) = t^{2}+4 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right ) = 2 t^{2}-2 t]
\]
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\[
{} [3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = t -1, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right ) = t +2]
\]
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\[
{} [2 x^{\prime }\left (t \right )+4 y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right ) = 3 \,{\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right ) = {\mathrm e}^{t}]
\]
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\[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = -2 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right ) = t^{2}]
\]
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\[
{} [2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 1, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = t]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )+5 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right )+17 t]
\]
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\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+7 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right )-4 z \left (t \right ), z^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )-4 z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )-6 y \left (t \right )+6 z \left (t \right )]
\]
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\[
{} y^{\prime }-y = {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime }+y = 2 \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }-12 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 8
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = t \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 20 \sin \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 36 t \,{\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 \pi -4 t & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .
\]
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\[
{} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x = 0
\]
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\[
{} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x = 0
\]
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\[
{} \left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0
\]
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\[
{} t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x = 0
\]
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\[
{} t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x = 0
\]
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\[
{} \left (1+2 t \right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
\]
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\[
{} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0
\]
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\[
{} t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x = 0
\]
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\[
{} t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x = 0
\]
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\[
{} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
\]
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\[
{} \frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}} = 0
\]
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\[
{} t^{2} x^{\prime \prime }+t x^{\prime }+x = 0
\]
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\[
{} \left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x = 0
\]
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\[
{} x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x = 0
\]
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\[
{} f \left (t \right ) x^{\prime \prime }+g \left (t \right ) x = 0
\]
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\[
{} x^{\prime \prime }+\left (t +1\right ) x = 0
\]
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\[
{} y^{\prime \prime }+\lambda y = 0
\]
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\[
{} y^{\prime \prime }+\lambda y = 0
\]
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