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ODE |
Mathematica |
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\[
{}y^{\prime } = \frac {y \left (x^{2} y^{2}+y x \,{\mathrm e}^{x}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x} \left (x -1\right )}{x}
\] |
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\[
{}y^{\prime } = \frac {\left (x y+1\right ) \left (x^{2} y^{2}+x^{2} y+2 x y+1+x +x^{2}\right )}{x^{5}}
\] |
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\[
{}y^{\prime } = \frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+x y}{x^{2}}
\] |
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\[
{}y^{\prime } = -F \left (x \right ) \left (-a \,x^{2}+y^{2}\right )+\frac {y}{x}
\] |
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\[
{}y^{\prime } = -F \left (x \right ) \left (y^{2}-2 x y-x^{2}\right )+\frac {y}{x}
\] |
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\[
{}y^{\prime } = -F \left (x \right ) \left (-y^{2} a -b \,x^{2}\right )+\frac {y}{x}
\] |
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\[
{}y^{\prime } = -F \left (x \right ) \left (-y^{2}+2 x^{2} y+1-x^{4}\right )+2 x
\] |
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\[
{}y^{\prime } = -F \left (x \right ) \left (-y^{2}+2 x y+x^{2}\right )+\frac {y}{x}
\] |
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\[
{}y^{\prime } = -F \left (x \right ) \left (-7 x y^{2}-x^{3}\right )+\frac {y}{x}
\] |
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\[
{}y^{\prime } = -F \left (x \right ) \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{\ln \left (x \right ) x}
\] |
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\[
{}y^{\prime } = -x^{3} \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{\ln \left (x \right ) x}
\] |
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\[
{}y^{\prime } = \left (y-{\mathrm e}^{x}\right )^{2}+{\mathrm e}^{x}
\] |
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\[
{}y^{\prime } = \frac {\left (y-\operatorname {Si}\left (x \right )\right )^{2}+\sin \left (x \right )}{x}
\] |
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\[
{}y^{\prime } = \left (y+\cos \left (x \right )\right )^{2}+\sin \left (x \right )
\] |
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\[
{}y^{\prime } = \frac {\left (y-\ln \left (x \right )-\operatorname {Ci}\left (x \right )\right )^{2}+\cos \left (x \right )}{x}
\] |
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\[
{}y^{\prime } = \frac {\left (y-x +\ln \left (1+x \right )\right )^{2}+x}{1+x}
\] |
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\[
{}y^{\prime } = \frac {2 x^{2} y+x^{3}+y \ln \left (x \right ) x -y^{2}-x y}{x^{2} \left (x +\ln \left (x \right )\right )}
\] |
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\[
{}y^{\prime } = f \left (x \right )
\] |
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\[
{}y^{\prime } = f \left (y\right )
\] |
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\[
{}y^{\prime } = f \left (x \right ) g \left (y\right )
\] |
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\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{0} \left (x \right )
\] |
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\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n}
\] |
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\[
{}y^{\prime } = f \left (\frac {y}{x}\right )
\] |
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\[
{}y^{\prime } = y^{2} a +b x +c
\] |
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\[
{}y^{\prime } = y^{2}-a^{2} x^{2}+3 a
\] |
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\[
{}y^{\prime } = y^{2}+a^{2} x^{2}+b x +c
\] |
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\[
{}y^{\prime } = y^{2} a +b \,x^{n}
\] |
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\[
{}y^{\prime } = y^{2}+a n \,x^{n -1}-a^{2} x^{2 n}
\] |
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\[
{}y^{\prime } = y^{2} a +b \,x^{2 n}+c \,x^{n -1}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m}
\] |
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\[
{}y^{\prime } = y^{2}+k \left (a x +b \right )^{n} \left (c x +d \right )^{-n -4}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m}
\] |
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\[
{}y^{\prime } = \left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c
\] |
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\[
{}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0} = 0
\] |
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\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b
\] |
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\[
{}x^{2} y^{\prime } = x^{2} y^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right )
\] |
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\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \,x^{n}+c
\] |
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\[
{}x^{2} y^{\prime } = x^{2} y^{2}+a \,x^{2 m} \left (b \,x^{m}+c \right )^{n}-\frac {n^{2}}{4}+\frac {1}{4}
\] |
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\[
{}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} = 0
\] |
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\[
{}x^{4} y^{\prime } = -y^{2} x^{4}-a^{2}
\] |
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\[
{}a \,x^{2} \left (x -1\right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s = 0
\] |
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\[
{}\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
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\[
{}x^{n +1} y^{\prime } = a \,x^{2 n} y^{2}+c \,x^{m}+d
\] |
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\[
{}\left (a \,x^{n}+b \right ) y^{\prime } = b y^{2}+a \,x^{n -2}
\] |
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\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) \left (y^{\prime }-y^{2}\right )+a n \left (n -1\right ) x^{n -2}+b m \left (m -1\right ) x^{m -2} = 0
\] |
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\[
{}y^{\prime } = y^{2} a +b y+c x +k
\] |
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\[
{}y^{\prime } = y^{2}+a \,x^{n} y+a \,x^{n -1}
\] |
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\[
{}y^{\prime } = y^{2}+a \,x^{n} y+b \,x^{n -1}
\] |
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\[
{}y^{\prime } = y^{2}+\left (\alpha x +\beta \right ) y+a \,x^{2}+b x +c
\] |
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\[
{}y^{\prime } = y^{2}+a \,x^{n} y-a b \,x^{n}-b^{2}
\] |
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\[
{}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +m +1}-a \,x^{m}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+b c \,x^{m}-a \,c^{2} x^{n}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1}
\] |
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\[
{}y^{\prime } = -a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m}
\] |
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\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+c k \,x^{k -1}-b c \,x^{m +k}-a \,c^{2} x^{n +2 k}
\] |
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\[
{}x y^{\prime } = y^{2} a +b y+c \,x^{2 b}
\] |
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\[
{}x y^{\prime } = y^{2} a +b y+c \,x^{n}
\] |
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\[
{}x y^{\prime } = y^{2} a +\left (n +b \,x^{n}\right ) y+c \,x^{2 n}
\] |
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\[
{}x y^{\prime } = x y^{2}+a y+b \,x^{n}
\] |
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\[
{}x y^{\prime }+a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0} = 0
\] |
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\[
{}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{-n}
\] |
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\[
{}x y^{\prime } = a \,x^{n} y^{2}+m y-a \,b^{2} x^{n +2 m}
\] |
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\[
{}x y^{\prime } = x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m}
\] |
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\[
{}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{m}
\] |
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\[
{}x y^{\prime } = a \,x^{2 n} y^{2}+\left (b \,x^{n}-n \right ) y+c
\] |
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\[
{}x y^{\prime } = a \,x^{2 n +m} y^{2}+\left (b \,x^{n +m}-n \right ) y+c \,x^{m}
\] |
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\[
{}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (a_{1} x +b_{1} \right ) y+a_{0} x +b_{0} = 0
\] |
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\[
{}\left (a x +c \right ) y^{\prime } = \alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma
\] |
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\[
{}2 x^{2} y^{\prime } = 2 y^{2}+x y-2 x \,a^{2}
\] |
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\[
{}2 x^{2} y^{\prime } = 2 y^{2}+3 x y-2 x \,a^{2}
\] |
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\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c
\] |
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\[
{}x^{2} y^{\prime } = c \,x^{2} y^{2}+\left (a \,x^{2}+b x \right ) y+\alpha \,x^{2}+\beta x +\gamma
\] |
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\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \,x^{n}+s
\] |
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\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n}
\] |
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\[
{}x^{2} y^{\prime } = c \,x^{2} y^{2}+\left (a \,x^{n}+b \right ) x y+\alpha \,x^{2 n}+\beta \,x^{n}+\gamma
\] |
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\[
{}x^{2} y^{\prime } = \left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2}
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime }+\lambda \left (y^{2}-2 x y+1\right ) = 0
\] |
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\[
{}\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\frac {b \left (a +\beta \right )}{\alpha } = 0
\] |
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\[
{}\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma = 0
\] |
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\[
{}\left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 x y+\left (1-a \right ) x^{2}-b = 0
\] |
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\[
{}\left (a \,x^{2}+b x +c \right ) y^{\prime } = y^{2}+\left (2 \lambda x +b \right ) y+\lambda \left (\lambda -a \right ) x^{2}+\mu
\] |
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\[
{}\left (a \,x^{2}+b x +c \right ) y^{\prime } = y^{2}+\left (a x +\mu \right ) y-\lambda ^{2} x^{2}+\lambda \left (b -\mu \right ) x +\lambda c
\] |
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\[
{}\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime } = y^{2}+\left (a_{1} x +b_{1} \right ) y-\lambda \left (\lambda +a_{1} -a_{2} \right ) x^{2}+\lambda \left (b_{2} -b_{1} \right ) x +\lambda c_{2}
\] |
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\[
{}\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime } = y^{2}+\left (a_{1} x +b_{1} \right ) y+a_{0} x^{2}+b_{0} x +c_{0}
\] |
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\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (y+x -b \right ) = 0
\] |
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\[
{}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b_{1} x +a_{1} \right ) y+a_{0} = 0
\] |
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\[
{}x^{3} y^{\prime } = x^{3} a y^{2}+\left (b \,x^{2}+c \right ) y+s x
\] |
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\[
{}x^{3} y^{\prime } = x^{3} a y^{2}+x \left (b x +c \right ) y+\alpha x +\beta
\] |
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\[
{}x \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b \,x^{2}+c \right ) y+s x = 0
\] |
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\[
{}x^{2} \left (x +a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b x +c \right ) y+\alpha x +\beta = 0
\] |
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\[
{}\left (a \,x^{2}+b x +e \right ) \left (x y^{\prime }-y\right )-y^{2}+x^{2} = 0
\] |
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\[
{}x^{2} \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b \,x^{2}+c \right ) y+s = 0
\] |
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\[
{}a \left (x^{2}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+b x \left (x^{2}-1\right ) y+c \,x^{2}+d x +s = 0
\] |
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\[
{}x^{n +1} y^{\prime } = a \,x^{2 n} y^{2}+b \,x^{n} y+c \,x^{m}+d
\] |
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\[
{}x \left (a \,x^{k}+b \right ) y^{\prime } = \alpha \,x^{n} y^{2}+\left (\beta -a n \,x^{k}\right ) y+\gamma \,x^{-n}
\] |
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\[
{}x^{2} \left (a \,x^{n}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (p \,x^{n}+q \right ) x y+r \,x^{n}+s = 0
\] |
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\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = c y^{2}-b \,x^{m -1} y+a \,x^{n -2}
\] |
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\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = a \,x^{n -2} y^{2}+b \,x^{m -1} y+c
\] |
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\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = \alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s}
\] |
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