|
# |
ODE |
CAS classification |
Solved? |
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\[
{}x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }-x^{\prime }-2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+8 x^{\prime }+15 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+x = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+9 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+2 x = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+25 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }-6 x^{\prime }+8 x = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }-4 x = 3 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+8 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+18 x = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+9 x = 6 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25} = 6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 1+\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = t +\delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 2 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+9 x = \delta \left (t -3 \pi \right )+\cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+5 x = \delta \left (t -\pi \right )+\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = \delta \left (t \right )-\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+9 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+8 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+8 x = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = t^{2} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+7 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+7 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 1+{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \left (t -3\right ) \operatorname {Heaviside}\left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+7 y = \left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 2 \delta \left (t -1\right )-\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}+3 \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 36
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 12-6 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 6 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \left (t \right )+\sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 9 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = \operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{-t +1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 9 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 2 t^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 8 \,{\mathrm e}^{-t} \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 y^{\prime \prime }-6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-5 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{\pi -t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+3 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+2 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 1+t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = \delta \left (t -1\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{\prime \prime }-x^{\prime }-6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+9 x = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }-2 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (-t +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{\prime \prime }-x = \delta \left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+x = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = t \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-20 y^{\prime }+51 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}3 y^{\prime \prime }+8 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+34 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = 9 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = t +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-9 y = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right .
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (x -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 7
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 27 t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+17 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} t^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+17 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _quadrature]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -3\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (t -4\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-16 y = \delta \left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
|
|
\[
{}x^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
|
|
\[
{}x^{\prime \prime } = \cos \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+x = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime } = 12 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}2 x^{\prime \prime }-2 x^{\prime } = \left (1+t \right ) {\mathrm e}^{t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}x^{\prime \prime }+x = 2 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = t^{2} {\mathrm e}^{t}+7
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }-6 y = t^{2}+7
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = t \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+29 y = {\mathrm e}^{-2 t} \sin \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+w^{2} y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 18 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = 2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = -20 \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -4 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }+6 y = \delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{5}+y = k \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{10}+y = k \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+w^{2} y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = \sin \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+17 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = g \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 3 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+a^{2} y = f \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
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\[
{}y^{\prime \prime }+y^{\prime }-6 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
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\[
{}y^{\prime \prime }-y^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|