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ODE |
Mathematica |
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = \left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 2 \cos \left (t \right )^{2}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 2 \cos \left (t \right )^{2} {\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = \sin \left (t \right )+t \,{\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+4 y = t^{2}+\left (2 t +3\right ) \left (1+\cos \left (t \right )\right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t}+{\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = 1+t^{2}+{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+y = \cos \left (t \right ) \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+y = \cos \left (t \right ) \cos \left (2 t \right ) \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = t^{{3}/{2}} {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-t y = 0
\]
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\[
{} \left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y = 0
\]
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\[
{} y^{\prime \prime }-t^{3} y = 0
\]
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\[
{} t \left (-t +2\right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y = 0
\]
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\[
{} y^{\prime \prime }+t^{2} y = 0
\]
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\[
{} y^{\prime \prime }-t^{3} y = 0
\]
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\[
{} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0
\]
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\[
{} y^{\prime \prime }-2 t y^{\prime }+\lambda y = 0
\]
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\[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\]
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\[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y = 0
\]
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\[
{} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = {\mathrm e}^{t}
\]
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\[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }+t y = 0
\]
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\[
{} y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\]
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\[
{} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\]
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\[
{} \left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\]
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\[
{} t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\]
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\[
{} \left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\]
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\[
{} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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\[
{} t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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\[
{} \sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0
\]
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\[
{} \left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0
\]
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\[
{} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0
\]
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\[
{} t^{3} y^{\prime \prime }+\sin \left (t^{2}\right ) y^{\prime }+t y = 0
\]
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\[
{} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y = 0
\]
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\[
{} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0
\]
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\[
{} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0
\]
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\[
{} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0
\]
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\[
{} 4 t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\]
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\[
{} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0
\]
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\[
{} t^{2} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0
\]
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\[
{} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0
\]
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\[
{} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y = 0
\]
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\[
{} t y^{\prime \prime }+t y^{\prime }+2 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y = 0
\]
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\[
{} t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y = 0
\]
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\[
{} t \left (1-t \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) t \right ) y^{\prime }-\alpha \beta y = 0
\]
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\[
{} 2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t +1\right ) y = 0
\]
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\[
{} t y^{\prime \prime }+y^{\prime }-4 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y = 0
\]
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\[
{} t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y = 0
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{2 t}
\]
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\[
{} 2 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+y = t^{2} \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+7 y = \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = t^{3}
\]
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\[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+y = \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+y = t \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} t
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+7 y = \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = 1+{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 \left (t -3\right ) \operatorname {Heaviside}\left (t -3\right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y^{\prime }+7 y = \left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (t \right )+\delta \left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = 2 \delta \left (t -1\right )-\delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}+3 \delta \left (t -3\right )
\]
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\[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )+t, y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )-1]
\]
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\[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
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