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Mathematica |
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 18 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -3 \pi \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )
\]
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\[
{} u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2}
\]
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\[
{} u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .
\]
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\[
{} u^{\prime \prime }+\frac {u^{\prime }}{4}+u = 2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right )
\]
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\[
{} y^{\prime \prime }-y = -20 \delta \left (t -3\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\]
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\[
{} y^{\prime \prime }+4 y = \delta \left (t -4 \pi \right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\]
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\[
{} y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right )
\]
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\[
{} 2 y^{\prime \prime }+y^{\prime }+6 y = \delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{5}+y = k \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{10}+y = k \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+w^{2} y = g \left (t \right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+25 y = \sin \left (\alpha t \right )
\]
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\[
{} 4 y^{\prime \prime }+4 y^{\prime }+17 y = g \left (t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 1-\operatorname {Heaviside}\left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = g \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (\alpha t \right )
\]
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\[
{} \frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\]
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\[
{} \frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\]
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\[
{} y^{\prime \prime } = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{x}+{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 x \right ) x
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )
\]
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\[
{} y^{\prime \prime }-y = \frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}}
\]
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\[
{} y^{\prime \prime }-2 y = 4 x^{2} {\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime \prime }+y = \sin \left (x \right ) \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right )
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 4 x
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = 6
\]
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\[
{} y^{\prime \prime }-2 y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = 4
\]
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\[
{} y^{\prime \prime }-y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = 6 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime }+4 y = 3 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y = 2 \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = 12 x -10
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime } = 10 x^{4}+2
\]
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\[
{} y^{\prime \prime }+k^{2} y = \sin \left (b x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x
\]
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\[
{} y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 x
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+4 y = \tan \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right )
\]
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\[
{} 2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \cot \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = \cot \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y = x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y = {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-y = x^{2} {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 10 x^{3} {\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-y = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }-y^{\prime }+y = x^{3}-3 x^{2}+1
\]
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\[
{} 4 y^{\prime \prime }+y = x^{4}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-y = -x^{4}+3 x
\]
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\[
{} y^{\prime \prime }+y = x^{4}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = x^{3} {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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