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Mathematica |
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\[
{}x^{\prime \prime }-x = \delta \left (t -5\right )
\] |
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\[
{}x^{\prime \prime }+x = \delta \left (t -2\right )
\] |
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\[
{}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right )
\] |
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\[
{}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right )
\] |
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\[
{}x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -6 y \left (t \right ), y^{\prime }\left (t \right ) = 6 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-14]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-1]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\] |
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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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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-10 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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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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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )+1, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+2]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-10 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\cos \left (w t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+3, y^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )+2 t]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+7 y \left (t \right )]
\] |
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\[
{}y^{\prime }+y = 1+x
\] |
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\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 0
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
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\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
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\[
{}x y^{\prime }+y = x^{3} y^{3}
\] |
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\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
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\[
{}y^{\prime }+4 x y = 8 x
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0
\] |
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\[
{}y^{\prime }+2 y = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right )
\] |
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\[
{}{y^{\prime }}^{2}-4 y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
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\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
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\[
{}y^{\prime \prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\] |
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\[
{}y^{\prime } = x^{2} \sin \left (y\right )
\] |
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\[
{}y^{\prime } = \frac {y^{2}}{x -2}
\] |
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\[
{}y^{\prime } = y^{{1}/{3}}
\] |
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\[
{}3 x +2 y+\left (y+2 x \right ) y^{\prime } = 0
\] |
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\[
{}y^{2}+3+\left (2 x y-4\right ) y^{\prime } = 0
\] |
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\[
{}2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0
\] |
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\[
{}3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0
\] |
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\[
{}6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0
\] |
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\[
{}y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime } = 0
\] |
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\[
{}\frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime } = 0
\] |
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\[
{}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0
\] |
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\[
{}\frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime } = 0
\] |
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\[
{}2 x y-3+\left (x^{2}+4 y\right ) y^{\prime } = 0
\] |
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\[
{}3 x^{2} y^{2}-y^{3}+2 x +\left (2 x^{3} y-3 x y^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}2 y \sin \left (x \right ) \cos \left (x \right )+y^{2} \sin \left (x \right )+\left (\sin \left (x \right )^{2}-2 y \cos \left (x \right )\right ) y^{\prime } = 0
\] |
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\[
{}y \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 x y\right ) y^{\prime } = 0
\] |
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\[
{}\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}} = 0
\] |
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\[
{}\frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0
\] |
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\[
{}4 x +3 y^{2}+2 x y y^{\prime } = 0
\] |
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\[
{}y^{2}+2 x y-x^{2} y^{\prime } = 0
\] |
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\[
{}y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime } = 0
\] |
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\[
{}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0
\] |
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\[
{}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0
\] |
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\[
{}\csc \left (y\right )+\sec \left (x \right ) y^{\prime } = 0
\] |
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\[
{}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0
\] |
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\[
{}\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime } = 0
\] |
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\[
{}\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0
\] |
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\[
{}x +y-x y^{\prime } = 0
\] |
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\[
{}2 x y+3 y^{2}-\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0
\] |
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\[
{}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0
\] |
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