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ODE |
Mathematica |
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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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\[
{}y^{\prime \prime }+\lambda y = 0
\] |
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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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\[
{}y^{\prime \prime }-2 y^{\prime }+\left (\lambda +1\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\lambda y = 0
\] |
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\[
{}y^{\prime \prime }-4 y = 0
\] |
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\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 0
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = 0
\] |
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\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
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\[
{}2 y^{\prime \prime }+2 y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime } = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = 0
\] |
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\[
{}y^{\prime \prime }-4 y = 3 \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-4 y = x +{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-6 y = x^{3}
\] |
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\[
{}-2 y^{\prime \prime }+3 y = x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x} \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = 5 \cos \left (6 x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = \left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }+4 y = 12 \cos \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }+y = {\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }+y = 3 x \sin \left (x \right )
\] |
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\[
{}2 y^{\prime \prime }+5 y^{\prime }-3 y = \sin \left (x \right )-8 x
\] |
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\[
{}8 y^{\prime \prime }-y = x \,{\mathrm e}^{-\frac {x}{2}}
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+4 y = x^{2}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+y = 4 \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = 2 x -2 \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-y = 3 x +5 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{x}+\sin \left (4 x \right )
\] |
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\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\] |
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\[
{}y^{\prime \prime }+4 y = \sec \left (x \right ) \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 y = {\mathrm e}^{-x} \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = \sec \left (x \right ) \csc \left (x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = \csc \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+y = \tan \left (\frac {x}{3}\right )^{2}
\] |
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\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{\frac {x}{2}} \ln \left (x \right )
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\] |
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\[
{}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+3 y = 3 \,{\mathrm e}^{-4 x}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime \prime }+2 y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = {\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right )
\] |
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\[
{}y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y = \sin \left (k x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }+4 y = x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}-8
\] |
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\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\] |
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\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = {\mathrm e}^{x} x^{2}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2} \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{2} \sin \left (x \right )
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\[
{}y^{\prime \prime }-y = \sin \left (2 x \right ) x
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0
\] |
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