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ODE |
Mathematica |
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\[
{} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime \prime }+8 y = {\mathrm e}^{-2 x}
\]
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\[
{} y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1+x \right )^{2}}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x}
\]
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\[
{} y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime }-2 y = t^{3}
\]
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\[
{} y^{\prime }+3 y = \operatorname {Heaviside}\left (t -4\right )
\]
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\[
{} y^{\prime \prime }-4 y = t^{3}
\]
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\[
{} y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 7
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t}
\]
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\[
{} t y^{\prime \prime }+y^{\prime }+t y = 0
\]
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\[
{} y^{\prime \prime }-9 y = 0
\]
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\[
{} y^{\prime \prime }+9 y = 27 t^{3}
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-8 y^{\prime }+17 y = 0
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} t^{2}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+13 y = 0
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+17 y = 0
\]
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\[
{} y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 1
\]
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\[
{} y^{\prime \prime }+4 y = t
\]
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\[
{} y^{\prime \prime }+4 y = {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 1
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = t
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t}
\]
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\[
{} y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\]
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\[
{} y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\]
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\[
{} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right )
\]
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\[
{} y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\]
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\[
{} y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\]
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\[
{} y^{\prime } = 3 \delta \left (t -2\right )
\]
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\[
{} y^{\prime } = \delta \left (t -2\right )-\delta \left (t -4\right )
\]
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\[
{} y^{\prime \prime } = \delta \left (t -3\right )
\]
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\[
{} y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (t -4\right )
\]
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\[
{} y^{\prime }+2 y = 4 \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right )
\]
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\[
{} y^{\prime }+3 y = \delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+16 y = \delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }-16 y = \delta \left (t -10\right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right )
\]
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\[
{} y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right )
\]
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\[
{} y^{\prime }-2 y = 0
\]
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\[
{} y^{\prime }-2 x y = 0
\]
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\[
{} y^{\prime }+\frac {2 y}{2 x -1} = 0
\]
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\[
{} \left (x -3\right ) y^{\prime }-2 y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime }-2 x y = 0
\]
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\[
{} y^{\prime }+\frac {y}{x -1} = 0
\]
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\[
{} y^{\prime }+\frac {y}{x -1} = 0
\]
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\[
{} \left (1-x \right ) y^{\prime }-2 y = 0
\]
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\[
{} \left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y = 0
\]
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\[
{} \left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y = 0
\]
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\[
{} \left (1+x \right ) y^{\prime }-x y = 0
\]
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\[
{} \left (1+x \right ) y^{\prime }+\left (1-x \right ) y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+y = 0
\]
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\[
{} \left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }-3 x^{2} y = 0
\]
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\[
{} \left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\]
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\[
{} \left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0
\]
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\[
{} \left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-2 x y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\lambda y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-x^{2} y = 0
\]
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\[
{} y^{\prime \prime }+{\mathrm e}^{2 x} y = 0
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }-y = 0
\]
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\[
{} y^{\prime \prime }+x y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-x y = 0
\]
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\[
{} y^{\prime \prime }-y^{2} = 0
\]
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