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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )+4 t -1, y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )+t]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+{\mathrm e}^{t}]
\]
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\[
{} [x^{\prime }\left (t \right )+y \left (t \right ) = t^{2}, -x \left (t \right )+y^{\prime }\left (t \right ) = t]
\]
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\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{-t}, 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-2 z \left (t \right )+2-t, y^{\prime }\left (t \right ) = 1-x \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )+1-t]
\]
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\[
{} [x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 2 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = 1, z^{\prime }\left (t \right )+z \left (t \right ) = 1]
\]
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\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+5 y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t}]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+\sin \left (t \right )]
\]
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\[
{} x^{\prime }+3 x = {\mathrm e}^{-2 t}
\]
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\[
{} x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1
\]
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\[
{} x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right )
\]
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\[
{} 2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t}
\]
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\[
{} x^{\prime }+x = 2 \sin \left (t \right )
\]
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\[
{} x^{\prime \prime } = 0
\]
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\[
{} x^{\prime \prime } = 1
\]
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\[
{} x^{\prime \prime } = \cos \left (t \right )
\]
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\[
{} x^{\prime \prime }+x^{\prime } = 0
\]
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\[
{} x^{\prime \prime }+x^{\prime } = 0
\]
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\[
{} x^{\prime \prime }-x^{\prime } = 1
\]
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\[
{} x^{\prime \prime }+x = t
\]
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\[
{} x^{\prime \prime }+6 x^{\prime } = 12 t +2
\]
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\[
{} x^{\prime \prime }-2 x^{\prime }+2 x = 2
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+4 x = 4
\]
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\[
{} 2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }+x = 2 \cos \left (t \right )
\]
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\[
{} y^{\prime } = \frac {x^{4}}{y}
\]
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\[
{} y^{\prime } = \frac {x^{2} \left (x^{3}+1\right )}{y}
\]
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\[
{} y^{\prime }+y^{3} \sin \left (x \right ) = 0
\]
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\[
{} y^{\prime } = \frac {7 x^{2}-1}{7+5 y}
\]
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\[
{} y^{\prime } = \sin \left (2 x \right )^{2} \cos \left (y\right )^{2}
\]
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\[
{} x y^{\prime } = \sqrt {1-y^{2}}
\]
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\[
{} y y^{\prime } = \left (x y^{2}+x \right ) {\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime } = \frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}}
\]
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\[
{} y^{\prime } = \frac {x^{2}}{1+y^{2}}
\]
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\[
{} y^{\prime } = \frac {\sec \left (x \right )^{2}}{1+y^{3}}
\]
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\[
{} y^{\prime } = 4 \sqrt {x y}
\]
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\[
{} y^{\prime } = x \left (y-y^{2}\right )
\]
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\[
{} y^{\prime } = \left (1-12 x \right ) y^{2}
\]
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\[
{} y^{\prime } = \frac {3-2 x}{y}
\]
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\[
{} x +y y^{\prime } {\mathrm e}^{-x} = 0
\]
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\[
{} r^{\prime } = \frac {r^{2}}{\theta }
\]
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\[
{} y^{\prime } = \frac {3 x}{y+x^{2} y}
\]
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\[
{} y^{\prime } = \frac {2 x}{1+2 y}
\]
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\[
{} y^{\prime } = 2 x y^{2}+4 x^{3} y^{2}
\]
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\[
{} y^{\prime } = x^{2} {\mathrm e}^{-3 y}
\]
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\[
{} y^{\prime } = \left (1+y^{2}\right ) \tan \left (2 x \right )
\]
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\[
{} y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6}
\]
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\[
{} y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11}
\]
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\[
{} y^{\prime } x^{2} = y-x y
\]
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\[
{} y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y}
\]
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\[
{} 2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-4}}
\]
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\[
{} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\]
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\[
{} \sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right )
\]
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\[
{} y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y}
\]
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\[
{} y^{\prime } = \frac {2 x^{2}}{2 y^{2}-6}
\]
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\[
{} y^{\prime } = 2 y^{2}+x y^{2}
\]
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\[
{} y^{\prime } = \frac {6-{\mathrm e}^{x}}{3+2 y}
\]
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\[
{} y^{\prime } = \frac {2 \cos \left (2 x \right )}{10+2 y}
\]
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\[
{} y^{\prime } = 2 \left (1+x \right ) \left (1+y^{2}\right )
\]
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\[
{} y^{\prime } = \frac {t \left (4-y\right ) y}{3}
\]
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\[
{} y^{\prime } = \frac {t y \left (4-y\right )}{t +1}
\]
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\[
{} y^{\prime } = \frac {b +a y}{d +c y}
\]
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\[
{} y^{\prime }+4 y = {\mathrm e}^{-2 t}+t
\]
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\[
{} -2 y+y^{\prime } = {\mathrm e}^{2 t} t^{2}
\]
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\[
{} y+y^{\prime } = 1+t \,{\mathrm e}^{-t}
\]
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\[
{} \frac {y}{t}+y^{\prime } = 5+\cos \left (2 t \right )
\]
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\[
{} -2 y+y^{\prime } = 3 \,{\mathrm e}^{t}
\]
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\[
{} 2 y+t y^{\prime } = \sin \left (t \right )
\]
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\[
{} 2 t y+y^{\prime } = 16 t \,{\mathrm e}^{-t^{2}}
\]
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\[
{} 4 t y+\left (t^{2}+1\right ) y^{\prime } = \frac {1}{\left (t^{2}+1\right )^{2}}
\]
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\[
{} y+2 y^{\prime } = 3 t
\]
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\[
{} -y+t y^{\prime } = t^{3} {\mathrm e}^{-t}
\]
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\[
{} y+y^{\prime } = 5 \sin \left (2 t \right )
\]
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\[
{} y+2 y^{\prime } = 3 t^{2}
\]
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\[
{} -y+y^{\prime } = 2 t \,{\mathrm e}^{2 t}
\]
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\[
{} y^{\prime }+2 y = t \,{\mathrm e}^{-2 t}
\]
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\[
{} t y^{\prime }+4 y = t^{2}-t +1
\]
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\[
{} \frac {2 y}{t}+y^{\prime } = \frac {\cos \left (t \right )}{t^{2}}
\]
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\[
{} -2 y+y^{\prime } = {\mathrm e}^{2 t}
\]
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\[
{} 2 y+t y^{\prime } = \sin \left (t \right )
\]
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\[
{} 4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t}
\]
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\[
{} \left (t +1\right ) y+t y^{\prime } = t
\]
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\[
{} y^{\prime }-\frac {y}{3} = 3 \cos \left (t \right )
\]
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\[
{} -y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}}
\]
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\[
{} -2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}}
\]
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\[
{} \left (t +1\right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t}
\]
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\[
{} 2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t}
\]
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\[
{} \cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t}
\]
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\[
{} \frac {y}{2}+y^{\prime } = 2 \cos \left (t \right )
\]
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\[
{} y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4}
\]
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\[
{} \frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right )
\]
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\[
{} -y+y^{\prime } = 1+3 \sin \left (t \right )
\]
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\[
{} -\frac {3 y}{2}+y^{\prime } = 3 t +3 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t}
\]
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\[
{} \frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right )
\]
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\[
{} 2 y+t y^{\prime } = \sin \left (t \right )
\]
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\[
{} y+2 y^{\prime } = 3 t^{2}
\]
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