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Mathematica |
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\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
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\[
{}y^{\prime }+\sqrt {x^{2}+1}\, y = 0
\] |
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\[
{}\cos \left (x \right ) y^{\prime }+y = 0
\] |
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\[
{}y^{\prime }+\sqrt {2 x^{2}+1}\, y = 0
\] |
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\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
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\[
{}y^{\prime \prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}\sqrt {x}\, y^{\prime \prime }+y^{\prime }+x y = 0
\] |
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\[
{}\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
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\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\] |
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\[
{}\left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y = 0
\] |
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\[
{}\left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime } = 0
\] |
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\[
{}3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0
\] |
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\[
{}\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{x -2}+\frac {2 y}{x +2} = 0
\] |
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\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
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\[
{}\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4} = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}} = 0
\] |
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\[
{}y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y = 0
\] |
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\[
{}\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1} = 0
\] |
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\[
{}\left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y = 0
\] |
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\[
{}\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {y}{1-x} = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y = 0
\] |
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\[
{}2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0
\] |
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\[
{}\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y = 0
\] |
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\[
{}\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y = 0
\] |
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\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x +2}+y = 0
\] |
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\[
{}4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}} = 0
\] |
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\[
{}\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (-x^{2}+2\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
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\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y = 0
\] |
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\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x y^{\prime }+\left (4 x^{3}-4\right ) y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (1-4 x \right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x +1\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
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\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
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\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+3 y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x -4\right ) y = 0
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 1-2 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )]
\] |
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\[
{}[t x^{\prime }\left (t \right )+2 x \left (t \right ) = 15 y \left (t \right ), t y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\] |
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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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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+2 y \left (t \right )-17, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )-13]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+2 y \left (t \right )+7 \,{\mathrm e}^{2 t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )-7 \,{\mathrm e}^{2 t}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )-6 \,{\mathrm e}^{3 t}, y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )+2 \,{\mathrm e}^{3 t}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+24 t]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+19 \cos \left (4 t \right )-13 \sin \left (4 t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )+5 \operatorname {Heaviside}\left (t -2\right ), y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )+17 \operatorname {Heaviside}\left (t -2\right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-7 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right )+4, y^{\prime }\left (t \right ) = 3 x \left (t \right )-7 y \left (t \right )+5]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-5]
\] |
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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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\[
{}y^{\prime \prime }+y^{\prime }-2 y = x^{3}
\] |
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\[
{}y y^{\prime }+y^{4} = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y = {\mathrm e}^{x}
\] |
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\[
{}{y^{\prime }}^{2}+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+2 y = 0
\] |
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\[
{}x {y^{\prime \prime }}^{2}+2 y = 2 x
\] |
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\[
{}x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right )
\] |
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\[
{}2 x -1-y^{\prime } = 0
\] |
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\[
{}2 x -y-y y^{\prime } = 0
\] |
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\[
{}y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime }+x y = 0
\] |
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\[
{}y^{\prime }+y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
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\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
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\[
{}x^{\prime \prime }+2 x^{\prime }-10 x = 0
\] |
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\[
{}x^{\prime \prime }+x = \cos \left (t \right ) t -\cos \left (t \right )
\] |
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\[
{}y^{\prime \prime }-12 y^{\prime }+40 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = 0
\] |
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\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0
\] |
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