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Mathematica |
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\[
{}y^{\prime \prime }+3 y^{\prime }-5 y = 1
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{-t +\pi }
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+3 y = 2
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+2 y = t
\] |
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\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t}
\] |
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\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0
\] |
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\[
{}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
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\[
{}y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
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\[
{}x y^{\prime \prime }+3 y^{\prime }+x y = 0
\] |
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\[
{}x y^{\prime \prime }-y^{\prime }+x y = 0
\] |
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\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0
\] |
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\[
{}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0
\] |
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\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
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\[
{}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0
\] |
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\[
{}y^{\prime \prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
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\[
{}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )
\] |
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\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{t}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t}
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3}
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
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\[
{}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\] |
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\[
{}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = t +1
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+8 y^{\prime }+20 y = 0
\] |
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\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (t -2 \pi \right )
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )
\] |
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\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right )
\] |
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\[
{}y^{\prime \prime }+9 y = \cos \left (3 t \right )
\] |
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\[
{}y^{\prime \prime }+y = \sin \left (t \right )
\] |
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\[
{}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right .
\] |
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\[
{}t y^{\prime \prime }-y^{\prime } = 2 t^{2}
\] |
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\[
{}2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\] |
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\[
{}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right )
\] |
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\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )
\] |
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\[
{}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right )
\] |
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\[
{}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right )
\] |
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\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime } = \delta \left (t -1\right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (t -1\right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right )
\] |
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\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right )
\] |
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\[
{}y^{\prime \prime } = x {y^{\prime }}^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
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\[
{}y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
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\[
{}\left (1+y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\] |
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\[
{}2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
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\[
{}x y^{\prime \prime } = y^{\prime }+x^{5}
\] |
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\[
{}x y^{\prime \prime }+y^{\prime }+x = 0
\] |
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\[
{}y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime }+\beta ^{2} y = 0
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
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\[
{}y^{\prime \prime } \cos \left (x \right ) = y^{\prime }
\] |
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\[
{}y^{\prime \prime } = x {y^{\prime }}^{2}
\] |
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\[
{}y^{\prime \prime } = x {y^{\prime }}^{2}
\] |
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\[
{}y^{\prime \prime } = -{\mathrm e}^{-2 y}
\] |
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\[
{}y^{\prime \prime } = -{\mathrm e}^{-2 y}
\] |
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\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
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\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
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\[
{}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3
\] |
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\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
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\[
{}y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2}
\] |
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\[
{}2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right )
\] |
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