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Mathematica |
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\[
{}y^{\prime }-2 y = t^{2} {\mathrm e}^{2 t}
\] |
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\[
{}y^{\prime }+y = t \,{\mathrm e}^{-t}+1
\] |
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\[
{}y^{\prime }+\frac {y}{t} = 5+\cos \left (2 t \right )
\] |
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\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{t}
\] |
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\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
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\[
{}y^{\prime }+2 t y = 16 t \,{\mathrm e}^{-t^{2}}
\] |
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\[
{}\left (t^{2}+1\right ) y^{\prime }+4 t y = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
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\[
{}2 y^{\prime }+y = 3 t
\] |
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\[
{}t y^{\prime }-y = t^{3} {\mathrm e}^{-t}
\] |
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\[
{}y^{\prime }+y = 5 \sin \left (2 t \right )
\] |
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\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
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\[
{}y^{\prime }-y = 2 t \,{\mathrm e}^{2 t}
\] |
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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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\[
{}y^{\prime }+\frac {2 y}{t} = \frac {\cos \left (t \right )}{t^{2}}
\] |
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\[
{}y^{\prime }-2 y = {\mathrm e}^{2 t}
\] |
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\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
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\[
{}t^{3} y^{\prime }+4 t^{2} y = {\mathrm e}^{-t}
\] |
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\[
{}t y^{\prime }+\left (t +1\right ) y = t
\] |
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\[
{}y^{\prime }-\frac {y}{3} = 3 \cos \left (t \right )
\] |
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\[
{}2 y^{\prime }-y = {\mathrm e}^{\frac {t}{3}}
\] |
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\[
{}3 y^{\prime }-2 y = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
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\[
{}t y^{\prime }+\left (t +1\right ) y = 2 t \,{\mathrm e}^{-t}
\] |
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\[
{}t y^{\prime }+2 y = \frac {\sin \left (t \right )}{t}
\] |
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\[
{}\sin \left (t \right ) y^{\prime }+y \cos \left (t \right ) = {\mathrm e}^{t}
\] |
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\[
{}y^{\prime }+\frac {y}{2} = 2 \cos \left (t \right )
\] |
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\[
{}y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4}
\] |
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\[
{}y^{\prime }+\frac {y}{4} = 3+2 \cos \left (2 t \right )
\] |
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\[
{}y^{\prime }-y = 1+3 \sin \left (t \right )
\] |
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\[
{}y^{\prime }-\frac {3 y}{2} = 3 t +3 \,{\mathrm e}^{t}
\] |
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\[
{}y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t}
\] |
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\[
{}y^{\prime }+\frac {y}{t} = 3 \cos \left (2 t \right )
\] |
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\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
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\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
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\[
{}\left (t -3\right ) y^{\prime }+\ln \left (t \right ) y = 2 t
\] |
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\[
{}t \left (t -4\right ) y^{\prime }+y = 0
\] |
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\[
{}y^{\prime }+\tan \left (t \right ) y = \sin \left (t \right )
\] |
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\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
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\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
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\[
{}\ln \left (t \right ) y^{\prime }+y = \cot \left (t \right )
\] |
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\[
{}y^{\prime } = \frac {t -y}{2 t +5 y}
\] |
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\[
{}y^{\prime } = \sqrt {1-t^{2}-y^{2}}
\] |
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\[
{}y^{\prime } = \frac {\ln \left (t y\right )}{1-t^{2}+y^{2}}
\] |
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\[
{}y^{\prime } = \left (t^{2}+y^{2}\right )^{{3}/{2}}
\] |
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\[
{}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}}
\] |
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\[
{}y^{\prime } = \frac {\cot \left (t \right ) y}{y+1}
\] |
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\[
{}y^{\prime } = y^{{1}/{3}}
\] |
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\[
{}y^{\prime } = -\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2}
\] |
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\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
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\[
{}y^{\prime } = 2 t y^{2}
\] |
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\[
{}y^{\prime }+y^{3} = 0
\] |
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\[
{}y^{\prime } = \frac {t^{2}}{y \left (t^{3}+1\right )}
\] |
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\[
{}y^{\prime } = t y \left (3-y\right )
\] |
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\[
{}y^{\prime } = y \left (3-t y\right )
\] |
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\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
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\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right .
\] |
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\[
{}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0
\] |
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\[
{}2 x +3+\left (2 y-2\right ) y^{\prime } = 0
\] |
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\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
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\[
{}3 x^{2}-2 x y+2+\left (6 y^{2}-x^{2}+3\right ) y^{\prime } = 0
\] |
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\[
{}2 x y^{2}+2 y+\left (2 x^{2} y+2 x \right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = -\frac {2 y+4 x}{2 x +3 y}
\] |
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\[
{}y^{\prime } = -\frac {4 x -2 y}{2 x -3 y}
\] |
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\[
{}{\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left ({\mathrm e}^{x} \cos \left (y\right )+2 \cos \left (x \right )\right ) y^{\prime } = 0
\] |
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\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
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\[
{}y \,{\mathrm e}^{x y} \cos \left (2 x \right )-2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+2 x +\left (x \,{\mathrm e}^{x y} \cos \left (2 x \right )-3\right ) y^{\prime } = 0
\] |
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\[
{}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0
\] |
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\[
{}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
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\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
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\[
{}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0
\] |
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\[
{}9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime } = 0
\] |
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\[
{}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}\frac {\sin \left (y\right )}{y}-2 \sin \left (x \right ) {\mathrm e}^{-x}+\frac {\left (\cos \left (y\right )+2 \,{\mathrm e}^{-x} \cos \left (x \right )\right ) y^{\prime }}{y} = 0
\] |
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\[
{}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
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\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
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\[
{}3 x^{2} y+2 x y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = {\mathrm e}^{2 x}+y-1
\] |
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\[
{}\frac {y^{\prime }}{\frac {x}{y}-\sin \left (y\right )} = 0
\] |
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\[
{}y+\left (2 x y-{\mathrm e}^{-2 y}\right ) y^{\prime } = 0
\] |
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\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0
\] |
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\[
{}\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\] |
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\[
{}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\] |
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\[
{}3 x y+y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y y^{\prime } = 1+x
\] |
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\[
{}\left (y^{4}+1\right ) y^{\prime } = x^{4}+1
\] |
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\[
{}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1
\] |
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\[
{}x \left (x -1\right ) y^{\prime } = y \left (1+y\right )
\] |
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\[
{}\sqrt {x^{2}-y^{2}}+y = x y^{\prime }
\] |
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\[
{}x y y^{\prime } = \left (x +y\right )^{2}
\] |
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\[
{}y^{\prime } = \frac {4 y-7 x}{5 x -y}
\] |
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\[
{}x y^{\prime }-4 \sqrt {y^{2}-x^{2}} = y
\] |
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\[
{}y^{\prime } = \frac {y^{4}+2 x y^{3}-3 x^{2} y^{2}-2 x^{3} y}{2 x^{2} y^{2}-2 x^{3} y-2 x^{4}}
\] |
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\[
{}\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = y \,{\mathrm e}^{\frac {x}{y}}
\] |
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\[
{}x y y^{\prime } = x^{2}+y^{2}
\] |
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\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
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\[
{}t y^{\prime }+y = t^{2} y^{2}
\] |
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\[
{}y^{\prime } = y \left (t y^{3}-1\right )
\] |
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\[
{}y^{\prime }+\frac {3 y}{t} = t^{2} y^{2}
\] |
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\[
{}t^{2} y^{\prime }+2 t y-y^{3} = 0
\] |
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\[
{}5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right )
\] |
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