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Mathematica |
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0
\]
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\[
{} 3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\]
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\[
{} 9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = 4 x -8
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }-6 y = \ln \left (x \right )
\]
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\[
{} \left (x +2\right )^{2} y^{\prime \prime }-\left (x +2\right ) y^{\prime }-3 y = 0
\]
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\[
{} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0
\]
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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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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\]
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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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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .
\]
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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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\[
{} \left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0
\]
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\[
{} t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x = 0
\]
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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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\[
{} y^{\prime \prime }+\lambda y = 0
\]
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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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\[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\]
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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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\[
{} x^{\prime \prime }-3 x^{\prime }+2 x = 0
\]
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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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\[
{} t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y = 0
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} \left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\]
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\[
{} \left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (-t +2\right ) x = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} \tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{x}
\]
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\[
{} x^{\prime \prime }-x = \frac {1}{t}
\]
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