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ODE |
Mathematica |
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 3 x^{{3}/{2}} \sin \left (x \right )
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = g \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\]
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\[
{} t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \left (x \right )
\]
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\[
{} t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2}
\]
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\[
{} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t
\]
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\[
{} y^{\prime \prime }+y = g \left (t \right )
\]
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\[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }-y = {\mathrm e}^{2 t} t^{2}
\]
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\[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = t^{2} {\mathrm e}^{t}+7
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }-6 y = t^{2}+7
\]
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\[
{} y^{\prime \prime }+4 y = 3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = t \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+16 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = t
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+29 y = {\mathrm e}^{-2 t} \sin \left (5 t \right )
\]
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\[
{} y^{\prime \prime }+w^{2} y = \cos \left (2 t \right )
\]
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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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\[
{} y^{\prime \prime }+4 y = \sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\]
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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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\[
{} 2 \left (2 a -y\right ) y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{2} \left (x^{2} y^{\prime \prime }-x y^{\prime }+y\right ) = x^{3}
\]
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\[
{} x^{2} y^{2} y^{\prime \prime }-3 x y^{2} y^{\prime }+4 y^{3}+x^{6} = 0
\]
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\[
{} x \left (y^{\prime } x^{2}+2 x y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} x +8 x y y^{\prime }+4 y^{2}-1 = 0
\]
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\[
{} x \left (x y+1\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 x y+2\right ) y^{\prime }+y^{2}+1 = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 2 x^{3}
\]
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\[
{} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1
\]
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\[
{} y^{\prime \prime }+\frac {y}{x^{2} \ln \left (x \right )} = {\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right )
\]
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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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\[
{} y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right )
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime } = x +y^{2}
\]
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\[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} x y^{\prime \prime }+y^{\prime } = 4 x
\]
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\[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
\]
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\[
{} \left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime \prime } = 2 x y-{\mathrm e}^{y}-x
\]
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\[
{} x y^{\prime \prime }-y^{\prime } = 3 x^{2}
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 4 x
\]
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\[
{} x^{3} y^{\prime \prime }+y^{\prime } x^{2}+x y = 1
\]
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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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