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# |
ODE |
CAS classification |
Solved? |
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\[
{}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
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\[
{}y^{\prime }+y = 8 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
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\[
{}y^{\prime }+3 y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
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|
\[
{}y^{\prime }+2 y = 4 t
\] |
[[_linear, ‘class A‘]] |
✓ |
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\[
{}y^{\prime }-y = 6 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }-y = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{t} \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = 2 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \delta \left (t -5\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+4 y = 3 \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-5 y = 2 \,{\mathrm e}^{-t}+\delta \left (t -3\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime }+2 y = 2
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+\frac {26 y}{5} = \frac {97 \sin \left (2 t \right )}{5}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime }-6 y = 0
\] |
[_quadrature] |
✓ |
|
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\[
{}L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}L i^{\prime }+R i = E_{0} \delta \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}L i^{\prime }+R i = E_{0} \sin \left (\omega t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+6 y = {\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (5 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+y = {\mathrm e}^{-3 t} \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+4 y = {\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }-y = 1+t \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = t \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }-y = t \,{\mathrm e}^{t} \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }-3 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+x = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}x^{\prime } = 2 x+\operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}x^{\prime } = x-2 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
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\[
{}x^{\prime } = -x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}x^{\prime }+3 x = \delta \left (t -1\right )+\operatorname {Heaviside}\left (-4+t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+y = 2 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
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\[
{}2 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
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\[
{}y^{\prime }-y = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
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\[
{}y^{\prime }-2 y = 4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
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\[
{}10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime }+2 y = 4
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime } = {\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }-2 y = 6
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+3 y = \delta \left (-2+x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }-3 y = \delta \left (x -1\right )+2 \operatorname {Heaviside}\left (-2+x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+4 y = 0
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime }-2 y = t^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+3 y = \operatorname {Heaviside}\left (-4+t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 3 \delta \left (t -2\right )
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime } = \delta \left (t -2\right )-\delta \left (-4+t \right )
\] |
[_quadrature] |
✓ |
|
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\[
{}y^{\prime }+2 y = 4 \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime }+3 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}x^{\prime }+3 x = {\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}x^{\prime }+x = 2 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
|
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\[
{}y^{\prime }+y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
|