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Mathematica |
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\[
{}y^{\prime }+2 x y = 2 x^{3}
\] |
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\[
{}y^{\prime }+\frac {2 x y}{-x^{2}+1} = 4 x
\] |
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\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {4}{\left (x^{2}+1\right )^{2}}
\] |
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\[
{}2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right ) = 4 \cos \left (x \right )^{4}
\] |
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\[
{}y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2}
\] |
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\[
{}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3}
\] |
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\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
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\[
{}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right )
\] |
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\[
{}1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }-\frac {y}{x} = 2 \ln \left (x \right ) x^{2}
\] |
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\[
{}y^{\prime }+\alpha y = {\mathrm e}^{\beta x}
\] |
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\[
{}y^{\prime }+\frac {m y}{x} = \ln \left (x \right )
\] |
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\[
{}y^{\prime }+\frac {2 y}{x} = 4 x
\] |
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\[
{}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
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\[
{}x^{\prime }+\frac {2 x}{-t +4} = 5
\] |
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\[
{}y-{\mathrm e}^{x}+y^{\prime } = 0
\] |
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\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right .
\] |
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\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right .
\] |
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\[
{}y^{\prime }+\frac {y}{x} = \cos \left (x \right )
\] |
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\[
{}y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
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\[
{}x y^{\prime }-y = \ln \left (x \right ) x^{2}
\] |
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\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
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\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
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\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
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\[
{}\sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right ) = x \cos \left (\frac {y}{x}\right )
\] |
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\[
{}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y
\] |
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\[
{}x y^{\prime }-y = \sqrt {9 x^{2}+y^{2}}
\] |
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\[
{}y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )
\] |
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\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
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\[
{}2 x y y^{\prime }-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}-2 y^{2} = 0
\] |
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\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
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\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
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\[
{}2 x \left (y+2 x \right ) y^{\prime } = \left (4 x -y\right ) y
\] |
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\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
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\[
{}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y}
\] |
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\[
{}y^{\prime } = \frac {-2 x +4 y}{x +y}
\] |
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\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
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\[
{}y^{\prime } = \frac {y-\sqrt {x^{2}+y^{2}}}{x}
\] |
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\[
{}x y^{\prime }-y = \sqrt {4 x^{2}-y^{2}}
\] |
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\[
{}y^{\prime } = \frac {a y+x}{a x -y}
\] |
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\[
{}y^{\prime } = \frac {x +\frac {y}{2}}{\frac {x}{2}-y}
\] |
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\[
{}y^{\prime }-\frac {y}{x} = \frac {4 x^{2} \cos \left (x \right )}{y}
\] |
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\[
{}y^{\prime }+\frac {y \tan \left (x \right )}{2} = 2 y^{3} \sin \left (x \right )
\] |
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\[
{}y^{\prime }-\frac {3 y}{2 x} = 6 y^{{1}/{3}} x^{2} \ln \left (x \right )
\] |
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\[
{}y^{\prime }+\frac {2 y}{x} = 6 \sqrt {x^{2}+1}\, \sqrt {y}
\] |
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\[
{}y^{\prime }+\frac {2 y}{x} = 6 y^{2} x^{4}
\] |
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\[
{}2 x \left (y^{\prime }+x^{2} y^{3}\right )+y = 0
\] |
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\[
{}\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right ) = 2 \left (b -a \right ) y
\] |
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\[
{}y^{\prime }+\frac {6 y}{x} = \frac {3 y^{{2}/{3}} \cos \left (x \right )}{x}
\] |
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\[
{}y^{\prime }+4 x y = 4 x^{3} \sqrt {y}
\] |
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\[
{}y^{\prime }-\frac {y}{2 x \ln \left (x \right )} = 2 x y^{3}
\] |
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\[
{}y^{\prime }-\frac {y}{\left (\pi -1\right ) x} = \frac {3 x y^{\pi }}{1-\pi }
\] |
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\[
{}2 y^{\prime }+y \cot \left (x \right ) = \frac {8 \cos \left (x \right )^{3}}{y}
\] |
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\[
{}\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right ) = y^{\sqrt {3}} \sec \left (x \right )
\] |
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\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = x y^{2}
\] |
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\[
{}y^{\prime }+y \cot \left (x \right ) = y^{3} \sin \left (x \right )^{3}
\] |
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\[
{}y^{\prime } = \left (9 x -y\right )^{2}
\] |
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\[
{}y^{\prime } = \left (4 x +y+2\right )^{2}
\] |
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\[
{}y^{\prime } = \sin \left (3 x -3 y+1\right )^{2}
\] |
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\[
{}y^{\prime } = \frac {y \left (\ln \left (x y\right )-1\right )}{x}
\] |
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\[
{}y^{\prime } = 2 x \left (x +y\right )^{2}-1
\] |
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\[
{}y^{\prime } = \frac {x +2 y-1}{2 x -y+3}
\] |
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\[
{}y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right )
\] |
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\[
{}y^{\prime }+\frac {2 y}{x}-y^{2} = -\frac {2}{x^{2}}
\] |
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\[
{}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}}
\] |
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\[
{}\frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right ) = q \left (x \right )
\] |
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\[
{}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x}
\] |
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\[
{}\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {1+x}} = \frac {1}{2 \sqrt {1+x}}
\] |
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\[
{}y \,{\mathrm e}^{x y}+\left (2 y-x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
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\[
{}\cos \left (x y\right )-x y \sin \left (x y\right )-x^{2} \sin \left (x y\right ) y^{\prime } = 0
\] |
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\[
{}y+3 x^{2}+x y^{\prime } = 0
\] |
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\[
{}2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
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\[
{}2 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}-2 x +2 x y y^{\prime } = 0
\] |
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\[
{}4 \,{\mathrm e}^{2 x}+2 x y-y^{2}+\left (x -y\right )^{2} y^{\prime } = 0
\] |
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\[
{}\frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}} = 0
\] |
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\[
{}y \cos \left (x y\right )-\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0
\] |
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\[
{}2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime } = 0
\] |
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\[
{}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
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\[
{}\sin \left (y\right )+y \cos \left (x \right )+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t}
\] |
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\[
{}y+y^{\prime } = 8 \,{\mathrm e}^{3 t}
\] |
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\[
{}y^{\prime }+3 y = 2 \,{\mathrm e}^{-t}
\] |
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\[
{}2 y+y^{\prime } = 4 t
\] |
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\[
{}y^{\prime }-y = 6 \cos \left (t \right )
\] |
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\[
{}y^{\prime }-y = 5 \sin \left (2 t \right )
\] |
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\[
{}y+y^{\prime } = 5 \,{\mathrm e}^{t} \sin \left (t \right )
\] |
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\[
{}2 y+y^{\prime } = 2 \operatorname {Heaviside}\left (t -1\right )
\] |
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\[
{}y^{\prime }-2 y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}
\] |
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\[
{}y^{\prime }-y = 4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right )
\] |
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\[
{}2 y+y^{\prime } = \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )
\] |
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\[
{}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
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\[
{}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right .
\] |
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\[
{}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right )
\] |
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\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
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\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
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\[
{}y+y^{\prime } = \delta \left (t -5\right )
\] |
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\[
{}y^{\prime }-2 y = \delta \left (t -2\right )
\] |
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