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ODE |
Mathematica |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (x \right )^{3}
\] |
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\[
{}y^{\prime \prime }-y = \frac {1}{\sqrt {1-{\mathrm e}^{2 x}}}
\] |
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\[
{}y^{\prime \prime }-y = {\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 15 \,{\mathrm e}^{-x} \sqrt {1+x}
\] |
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\[
{}y^{\prime \prime }+4 y = 2 \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{2 x}}{\left (1+{\mathrm e}^{x}\right )^{2}}
\] |
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\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}}
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = \frac {5 \ln \left (x \right )}{x^{2}}
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 \ln \left (x \right ) x^{2}
\] |
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\[
{}\left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = 9 \,{\mathrm e}^{-2 t}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = 2 t^{2}+1
\] |
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\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 t \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 8 \,{\mathrm e}^{-t} \sin \left (t \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
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\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
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\[
{}y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right )
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right )
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right )
\] |
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\[
{}y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right )
\] |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 10 \,{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (t -1\right )
\] |
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\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 40 t^{2} \operatorname {Heaviside}\left (t -2\right )
\] |
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\[
{}y^{\prime \prime \prime \prime }+4 y = \left (2 t^{2}+t +1\right ) \delta \left (t -1\right )
\] |
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\[
{}[x^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = 0, x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 0]
\] |
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\[
{}[2 x^{\prime }\left (t \right )+x \left (t \right )-5 y^{\prime }\left (t \right )-4 y \left (t \right ) = 0, -y^{\prime }\left (t \right )-2 x \left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right ) = 0, 3 x \left (t \right )-y^{\prime }\left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime \prime }\left (t \right )+x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 0, x^{\prime }\left (t \right )+x \left (t \right )-y^{\prime }\left (t \right ) = 0]
\] |
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\[
{}[x^{\prime \prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = 0, x \left (t \right )+y^{\prime \prime }\left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right )-y_{2} \left (x \right ) = 0, 4 y_{1} \left (x \right )+y_{2}^{\prime }\left (x \right )-4 y_{2} \left (x \right )-2 y_{3} \left (x \right ) = 0, -2 y_{1} \left (x \right )+y_{2} \left (x \right )+y_{3}^{\prime }\left (x \right )+y_{3} \left (x \right ) = 0]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right )-2 y_{1} \left (x \right )+3 y_{2} \left (x \right )-3 y_{3} \left (x \right ) = 0, -4 y_{1} \left (x \right )+y_{2}^{\prime }\left (x \right )+5 y_{2} \left (x \right )-3 y_{3} \left (x \right ) = 0, -4 y_{1} \left (x \right )+4 y_{2} \left (x \right )+y_{3}^{\prime }\left (x \right )-2 y_{3} \left (x \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 8, 2 x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 2 \,{\mathrm e}^{-t}-8]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )+t \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )+{\mathrm e}^{-t}]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = {\mathrm e}^{t}, -4 x \left (t \right )+y^{\prime }\left (t \right )-3 y \left (t \right ) = 1]
\] |
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\[
{}[x^{\prime }\left (t \right )-4 x \left (t \right )+3 y \left (t \right ) = \sin \left (t \right ), -2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = -2 \cos \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-y \left (t \right ) = 0, -x \left (t \right )+y^{\prime }\left (t \right ) = {\mathrm e}^{t}+{\mathrm e}^{-t}]
\] |
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\[
{}[x^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right ) = 0, -x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = \sin \left (2 t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )+2 y^{\prime }\left (t \right ) = -4 \,{\mathrm e}^{2 t}, 2 x^{\prime }\left (t \right )-3 x \left (t \right )+3 y^{\prime }\left (t \right )-y \left (t \right ) = 0]
\] |
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\[
{}[3 x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )-6 y \left (t \right ) = 5 \,{\mathrm e}^{t}, 4 x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )-8 y \left (t \right ) = 5 \,{\mathrm e}^{t}+2 t -3]
\] |
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\[
{}[x^{\prime }\left (t \right )-5 x \left (t \right )+3 y \left (t \right ) = 2 \,{\mathrm e}^{3 t}, -x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = 5 \,{\mathrm e}^{-t}]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )+y \left (t \right ) = 0, x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = -5 \,{\mathrm e}^{t} \sin \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right )+4 x \left (t \right )+2 y \left (t \right ) = \frac {2}{{\mathrm e}^{t}-1}, 6 x \left (t \right )-y^{\prime }\left (t \right )+3 y \left (t \right ) = \frac {3}{{\mathrm e}^{t}-1}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = \sec \left (t \right ), -2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 16 t \,{\mathrm e}^{t}, 2 x \left (t \right )-y^{\prime }\left (t \right )-2 y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )+y \left (t \right ) = 5 \,{\mathrm e}^{t} \cos \left (t \right ), x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 10 \,{\mathrm e}^{t} \sin \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-4 x \left (t \right )+3 y \left (t \right ) = \sin \left (t \right ), 2 x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = 2 \cos \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )-y \left (t \right ) = 2 \,{\mathrm e}^{t}, x \left (t \right )-y^{\prime }\left (t \right )+2 y \left (t \right ) = 3 \,{\mathrm e}^{4 t}]
\] |
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\[
{}[x^{\prime \prime }\left (t \right )+x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 40 \,{\mathrm e}^{3 t}, x^{\prime }\left (t \right )+x \left (t \right )-y^{\prime }\left (t \right ) = 36 \,{\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )-y \left (t \right ) = 2 \,{\mathrm e}^{t}, y^{\prime }\left (t \right )-2 y \left (t \right )-4 z \left (t \right ) = 4 \,{\mathrm e}^{2 t}, x \left (t \right )-z^{\prime }\left (t \right )-z \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime \prime }\left (t \right )+2 x \left (t \right )-2 y^{\prime }\left (t \right ) = 0, 3 x^{\prime }\left (t \right )+y^{\prime \prime }\left (t \right )-8 y \left (t \right ) = 240 \,{\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 0, x \left (t \right )-y^{\prime }\left (t \right ) = 15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = 2 \sin \left (t \right ) \left (1-\operatorname {Heaviside}\left (t -\pi \right )\right ), 2 x \left (t \right )-y^{\prime }\left (t \right )-y \left (t \right ) = 0]
\] |
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\[
{}[2 x^{\prime }\left (t \right )+x \left (t \right )-5 y^{\prime }\left (t \right )-4 y \left (t \right ) = 28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ), 3 x^{\prime }\left (t \right )-2 x \left (t \right )-4 y^{\prime }\left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+26 \sin \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+8 x_{2} \left (t \right )+9 t, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3 \,{\mathrm e}^{-t}]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )+\frac {{\mathrm e}^{3 t}}{{\mathrm e}^{2 t}+1}\right ]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-2 x_{2} \left (t \right )+\frac {2}{{\mathrm e}^{t}-1}, x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+3 x_{2} \left (t \right )-\frac {3}{{\mathrm e}^{t}-1}\right ]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+\frac {4}{\sin \left (2 t \right )}\right ]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+27 t, x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+35 \,{\mathrm e}^{t} t^{{3}/{2}}\right ]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+6 \,{\mathrm e}^{-t}, x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+12 t, x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )-2 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-6 x_{2} \left (t \right )+5 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+4 \,{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+4 \sin \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+2 \,{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{3} \left (t \right )+24 t, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-x y = 0
\] |
✓ |
✓ |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+x y = 0
\] |
✓ |
✓ |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-2 x^{2} y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-2 x^{2} y^{\prime }+x y = 0
\] |
✓ |
✓ |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (4 x -1\right ) y^{\prime }+2 y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+\left (1+\cos \left (x \right )\right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }+\left (-2 x^{2}+x \right ) y^{\prime }-x y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+2 y = 0
\] |
✓ |
✓ |
|