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ODE |
Mathematica |
Maple |
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\[
{}\left [x^{\prime }\left (t \right ) = -\frac {4 x \left (t \right )}{5}+2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {6 y \left (t \right )}{5}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = a x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+a y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+a y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = a x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = a x \left (t \right )+\frac {5 y \left (t \right )}{4}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+a y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+a y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = a x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+a y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )]
\] |
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\[
{}\left [i^{\prime }\left (t \right ) = \frac {i \left (t \right )}{2}-\frac {v \left (t \right )}{8}, v^{\prime }\left (t \right ) = 2 i \left (t \right )-\frac {v \left (t \right )}{2}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{4}-\frac {y \left (t \right )}{4}\right ]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{2}+y \left (t \right ), y^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{4}-\frac {y \left (t \right )}{2}\right ]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -3 x \left (t \right )+\frac {5 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right )\right ]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -x \left (t \right )-\frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )\right ]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = 2 x \left (t \right )+\frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}+y \left (t \right )\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+\frac {3 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{2}+\frac {y \left (t \right )}{2}\right ]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = 2 x \left (t \right )+\frac {3 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{2}-y \left (t \right )\right ]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = -\frac {3 x \left (t \right )}{4}-\frac {y \left (t \right )}{4}\right ]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -3 x \left (t \right )+\frac {5 y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right )\right ]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = 2 x \left (t \right )+\frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}+y \left (t \right )\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -8 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+x \left (t \right )^{2}, y^{\prime }\left (t \right ) = y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )^{2} y \left (t \right )-3 x \left (t \right )^{2}-4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) y \left (t \right )^{2}+6 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )-3 y \left (t \right )+2]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+2 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = \frac {y \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{4}-\frac {3 x \left (t \right ) y \left (t \right )}{4}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -\left (x \left (t \right )-y \left (t \right )\right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right ) \left (2+y \left (t \right )\right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ) \left (2-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = \left (x \left (t \right )+2\right ) \left (y \left (t \right )-x \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {x \left (t \right )^{3}}{5}-\frac {y \left (t \right )}{5}\right ]
\] |
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\[
{}x^{\prime } = \frac {x \sqrt {6 x-9}}{3}
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = x \left (t \right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (\frac {3}{4}-y \left (t \right )-\frac {x \left (t \right )}{2}\right )\right ]
\] |
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\[
{}y^{\prime \prime }+t y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y+y^{3} = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-t y = \frac {1}{\pi }
\] |
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\[
{}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = d
\] |
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\[
{}y^{\prime \prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+9 y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+16 y = 0
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime }+4 y = 0
\] |
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\[
{}t y^{\prime \prime }+3 y = t
\] |
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\[
{}\left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y = \sin \left (t \right )
\] |
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\[
{}t \left (t -4\right ) y^{\prime \prime }+3 t y^{\prime }+4 y = 2
\] |
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\[
{}y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 \ln \left (t \right ) y = 0
\] |
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\[
{}\left (x +3\right ) y^{\prime \prime }+x y^{\prime }+y \ln \left (x \right ) = 0
\] |
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\[
{}\left (x -2\right ) y^{\prime \prime }+y^{\prime }+\left (x -2\right ) \tan \left (x \right ) y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {\alpha \left (\alpha +1\right ) \mu ^{2} y}{-x^{2}+1} = 0
\] |
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\[
{}y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi }
\] |
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\[
{}t^{2} y^{\prime \prime }-2 y = 0
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
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\[
{}\left (1-x \cot \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
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\[
{}a y^{\prime \prime }+b y^{\prime }+c y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0
\] |
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\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
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\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0
\] |
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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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\[
{}x y^{\prime \prime }-\left (x +n \right ) y^{\prime }+n y = 0
\] |
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\[
{}y^{\prime \prime }+a \left (x y^{\prime }+y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 0
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
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\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+6 y = 0
\] |
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\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
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\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
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\[
{}6 y^{\prime \prime }-y^{\prime }-y = 0
\] |
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\[
{}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }-8 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
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\[
{}4 y^{\prime \prime }-9 y = 0
\] |
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\[
{}25 y^{\prime \prime }-20 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+16 y = 0
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0
\] |
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