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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} y y^{\prime } = \left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2}
\]
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\[
{} y y^{\prime } = \left (a \left (2 \mu +\lambda \right ) {\mathrm e}^{\lambda x}+b \right ) {\mathrm e}^{x \mu } y+\left (-a^{2} \mu \,{\mathrm e}^{2 \lambda x}-a b \,{\mathrm e}^{\lambda x}+c \right ) {\mathrm e}^{2 x \mu }
\]
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\[
{} y y^{\prime } = \left ({\mathrm e}^{\lambda x} a +b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right )
\]
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\[
{} y y^{\prime } = {\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right )
\]
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\[
{} y y^{\prime } = {\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right )
\]
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\[
{} y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y = -a^{2} b \,x^{2} {\mathrm e}^{2 b x}
\]
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\[
{} y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y = -a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x}
\]
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\[
{} y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y = -a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}}
\]
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\[
{} y y^{\prime } = \left (a \cosh \left (x \right )+b \right ) y-a b \sinh \left (x \right )+c
\]
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\[
{} y y^{\prime } = \left (a \sinh \left (x \right )+b \right ) y-a b \cosh \left (x \right )+c
\]
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\[
{} y y^{\prime } = \left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right )
\]
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\[
{} y y^{\prime } = \left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right )
\]
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\[
{} y y^{\prime } = a x \cos \left (\lambda \,x^{2}\right ) y+x
\]
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\[
{} y y^{\prime } = a x \sin \left (\lambda \,x^{2}\right ) y+x
\]
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\[
{} \left (y A +B x +a \right ) y^{\prime }+B y+k x +b = 0
\]
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\[
{} \left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\]
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\[
{} \left (y+a k \,x^{2}+b x +c \right ) y^{\prime } = -y^{2} a +2 a k x y+m y+k \left (k +b -m \right ) x +s
\]
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\[
{} \left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y+k \,x^{m}+b = 0
\]
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\[
{} \left (y+a \,x^{n +1}+b \,x^{n}\right ) y^{\prime } = \left (a n \,x^{n}+c \,x^{n -1}\right ) y
\]
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\[
{} x y y^{\prime } = y^{2} a +b y+c \,x^{n}+s
\]
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\[
{} x y y^{\prime } = -n y^{2}+a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c
\]
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\[
{} y^{\prime \prime }+a y = 0
\]
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\[
{} y^{\prime \prime }-\left (a x +b \right ) y = 0
\]
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\[
{} y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0
\]
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\[
{} y^{\prime \prime }-\left (a \,x^{2}+b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y = 0
\]
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\[
{} y^{\prime \prime }-\left (a \,x^{2}+b c x \right ) y = 0
\]
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\[
{} y^{\prime \prime }-a \,x^{n} y = 0
\]
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\[
{} y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+\left (n -1\right ) y = 0
\]
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\[
{} y^{\prime \prime }-2 x y^{\prime }+2 n y = 0
\]
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\[
{} y^{\prime \prime }+a x y^{\prime }+b y = 0
\]
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\[
{} y^{\prime \prime }+a x y^{\prime }+b x y = 0
\]
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\[
{} y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 a x y^{\prime }+\left (b \,x^{4}+a^{2} x^{2}+c x +a \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (-c +a \right ) x^{2}+b x +1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{n +1}+b \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (a \,x^{2}+b -c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+2 b \right ) y^{\prime }+\left (a b \,x^{2}-a x +b^{2}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a b \,x^{2}+b x +2 a \right ) y^{\prime }+a^{2} \left (b \,x^{2}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+x \left (a b \,x^{2}+b c +2 a \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (a b \,x^{3}+a c \,x^{2}+b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a b \,x^{3}-a \,x^{2}+b^{2}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 a \,x^{2}+b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a b \,x^{3}+b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{n} y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y = 0
\]
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\[
{} y^{\prime \prime }+2 a \,x^{n} y^{\prime }+a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{n +m}+b \,x^{2 m}+m \,x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+a n \,x^{n -1}+c \,x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-a^{2} x \right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-a^{2} x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+x^{n} \left (a \,x^{2}+\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (m +1\right ) x^{m -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a b \,x^{n +m}+b \left (m +1\right ) x^{m -1}-a \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a b \,x^{n +m}+b c \,x^{m}+a n \,x^{n -1}\right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+b y = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+b x y = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+n y^{\prime }+b \,x^{-2 n +1} y = 0
\]
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\[
{} x y^{\prime \prime }+\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+b \,x^{n} y = 0
\]
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\[
{} x y^{\prime \prime }+a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+a x y^{\prime }+a y = 0
\]
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\[
{} x y^{\prime \prime }+\left (b -x \right ) y^{\prime }-a y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (-c +a \right ) x +b \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a \left (a x +b \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (\left (a +b \right ) x +n +m \right ) y^{\prime }+\left (a b x +a n +b m \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\]
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\[
{} x y^{\prime \prime }-\left (a x +1\right ) y^{\prime }-b \,x^{2} \left (b x +a \right ) y = 0
\]
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\[
{} x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+a^{2} x +a \right ) y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right ) = 0
\]
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\[
{} x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y = 0
\]
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\[
{} x y^{\prime \prime }+\left (a b \,x^{2}+b -5\right ) y^{\prime }+2 a^{2} \left (b -2\right ) x^{3} y = 0
\]
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