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\[
{} y^{\prime \prime }+\lambda y = 0
\]
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\[
{} y^{\prime \prime }+\lambda y = 0
\]
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\[
{} y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
\]
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\[
{} y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
\]
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\[
{} 2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0
\]
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\[
{} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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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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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+5 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+7 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+5 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )+b y \left (t \right ), y^{\prime }\left (t \right ) = c x \left (t \right )+d y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+4 y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right )+\frac {x \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}, y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {y \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}\right ]
\]
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\[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\]
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\[
{} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\]
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\[
{} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\]
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\[
{} x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3} = 0
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{2}]
\]
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\[
{} x^{\prime } = \sin \left (t \right )+\cos \left (t \right )
\]
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\[
{} y^{\prime } = \frac {1}{x^{2}-1}
\]
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\[
{} u^{\prime } = 4 t \ln \left (t \right )
\]
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\[
{} z^{\prime } = x \,{\mathrm e}^{-2 x}
\]
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\[
{} T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right )
\]
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\[
{} x^{\prime } = \sec \left (t \right )^{2}
\]
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\[
{} y^{\prime } = x -\frac {1}{3} x^{3}
\]
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\[
{} x^{\prime } = 2 \sin \left (t \right )^{2}
\]
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\[
{} x V^{\prime } = x^{2}+1
\]
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\[
{} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t}
\]
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\[
{} x^{\prime } = -x+1
\]
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\[
{} x^{\prime } = x \left (2-x\right )
\]
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\[
{} x^{\prime } = \left (1+x\right ) \left (2-x\right ) \sin \left (x\right )
\]
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\[
{} x^{\prime } = -x \left (-x+1\right ) \left (2-x\right )
\]
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\[
{} x^{\prime } = x^{2}-x^{4}
\]
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\[
{} x^{\prime } = t^{3} \left (-x+1\right )
\]
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\[
{} y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\]
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\[
{} x^{\prime } = t^{2} x
\]
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\[
{} x^{\prime } = -x^{2}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-t^{2}} y^{2}
\]
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\[
{} x^{\prime }+p x = q
\]
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\[
{} x y^{\prime } = k y
\]
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\[
{} i^{\prime } = p \left (t \right ) i
\]
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\[
{} x^{\prime } = \lambda x
\]
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\[
{} m v^{\prime } = -m g +k v^{2}
\]
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\[
{} x^{\prime } = k x-x^{2}
\]
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\[
{} x^{\prime } = -x \left (k^{2}+x^{2}\right )
\]
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\[
{} y^{\prime }+\frac {y}{x} = x^{2}
\]
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\[
{} x^{\prime }+t x = 4 t
\]
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\[
{} z^{\prime } = z \tan \left (y \right )+\sin \left (y \right )
\]
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\[
{} y^{\prime }+{\mathrm e}^{-x} y = 1
\]
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\[
{} x^{\prime }+x \tanh \left (t \right ) = 3
\]
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\[
{} y^{\prime }+2 \cot \left (x \right ) y = 5
\]
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\[
{} x^{\prime }+5 x = t
\]
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\[
{} x^{\prime }+\left (a +\frac {1}{t}\right ) x = b
\]
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\[
{} T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right )
\]
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\[
{} 2 x y-\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime } = 0
\]
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\[
{} 1+y \,{\mathrm e}^{x}+x \,{\mathrm e}^{x} y+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime } = 0
\]
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\[
{} \left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }+\sin \left (y\right )-y \sin \left (x \right ) = 0
\]
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\[
{} {\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime } = 0
\]
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\[
{} {\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime } = 0
\]
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\[
{} V^{\prime }\left (x \right )+2 y y^{\prime } = 0
\]
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\[
{} \left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b = 0
\]
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\[
{} x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0
\]
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\[
{} x^{\prime } = \frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x}
\]
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\[
{} x^{\prime } = k x-x^{2}
\]
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\[
{} x^{\prime \prime }-3 x^{\prime }+2 x = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
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\[
{} z^{\prime \prime }-4 z^{\prime }+13 z = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime } = 0
\]
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\[
{} \theta ^{\prime \prime }+4 \theta = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+10 y = 0
\]
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\[
{} 2 z^{\prime \prime }+7 z^{\prime }-4 z = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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\[
{} x^{\prime \prime }+6 x^{\prime }+10 x = 0
\]
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\[
{} 4 x^{\prime \prime }-20 x^{\prime }+21 x = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = 0
\]
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\[
{} y^{\prime \prime }-4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+\omega ^{2} y = 0
\]
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\[
{} x^{\prime \prime }-4 x = t^{2}
\]
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\[
{} x^{\prime \prime }-4 x^{\prime } = t^{2}
\]
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\[
{} x^{\prime \prime }+x^{\prime }-2 x = 3 \,{\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }+x^{\prime }-2 x = {\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+x = {\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }+\omega ^{2} x = \sin \left (\alpha t \right )
\]
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\[
{} x^{\prime \prime }+\omega ^{2} x = \sin \left (\omega t \right )
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right )
\]
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\[
{} x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right )
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+4 x = {\mathrm e}^{2 t}
\]
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\[
{} x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right )
\]
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\[
{} x^{\prime \prime }+\omega ^{2} x = \cos \left (\alpha t \right )
\]
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\[
{} x^{\prime \prime }+\omega ^{2} x = \cos \left (\omega t \right )
\]
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