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ODE |
Mathematica |
Maple |
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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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\[
{}y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-x \,a^{2}\right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-x \,a^{2}\right ) y = 0
\] |
✗ |
✗ |
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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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\[
{}x y^{\prime \prime }+\left (-x +b \right ) y^{\prime }-a y = 0
\] |
✓ |
✓ |
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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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\[
{}x y^{\prime \prime }+\left (\left (a +b \right ) x +m +n \right ) y^{\prime }+\left (a b x +a n +b m \right ) y = 0
\] |
✓ |
✓ |
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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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\[
{}x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+\left (b \,x^{3}+x \,a^{2}+a \right ) y = 0
\] |
✓ |
✓ |
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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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\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }-\left (a c \,x^{2}+\left (b c +c^{2}+a \right ) x +b +2 c \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +2\right ) y^{\prime }+b y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (2 a x +b \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (c -1\right ) \left (a x +b \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y = 0
\] |
✗ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +2\right ) y^{\prime }+\left (c \,x^{2}+d x +b \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+x \left (a \,x^{2}+b \right ) y^{\prime }+\left (3 a \,x^{2}+b \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+2\right ) y^{\prime }+b x y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a b \,x^{3}+b \,x^{2}+a x -1\right ) y^{\prime }+a^{2} b \,x^{3} y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (a \,x^{2}+b x +c \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y = 0
\] |
✗ |
✗ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{n}+2\right ) y^{\prime }+a \,x^{n -1} y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{2 n -1} y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a n \,x^{n -1} y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b -1\right ) x^{n -1} y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b +n -1\right ) x^{n -1} y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y = 0
\] |
✗ |
✗ |
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\[
{}x y^{\prime \prime }+\left (a b \,x^{n}+b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y = 0
\] |
✗ |
✗ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{2 n -1}+d \,x^{n -1}\right ) y = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{n -2} y = 0
\] |
✗ |
✓ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b x \right ) y^{\prime }+\left (a b \,x^{n}+a n \,x^{n -1}-b \right ) y = 0
\] |
✗ |
✗ |
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\[
{}x y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+a x -1\right ) y^{\prime }+a^{2} b \,x^{n} y = 0
\] |
✗ |
✗ |
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\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\] |
✗ |
✗ |
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\[
{}x y^{\prime \prime }+\left (a b \,x^{n +m}+a n \,x^{n}+b \,x^{m}+1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y = 0
\] |
✗ |
✗ |
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\[
{}\left (x +a \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+b y = 0
\] |
✓ |
✓ |
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\[
{}\left (a_{1} x +a_{0} \right ) y^{\prime \prime }+\left (b_{1} x +b_{0} \right ) y^{\prime }-m b_{1} y = 0
\] |
✓ |
✓ |
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\[
{}\left (a x +b \right ) y^{\prime \prime }+s \left (c x +d \right ) y^{\prime }-s^{2} \left (\left (a +c \right ) x +b +d \right ) y = 0
\] |
✓ |
✓ |
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\[
{}\left (a_{2} x +b_{2} \right ) y^{\prime \prime }+\left (a_{1} x +b_{1} \right ) y^{\prime }+\left (a_{0} x +b_{0} \right ) y = 0
\] |
✓ |
✓ |
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\[
{}\left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y = 0
\] |
✗ |
✓ |
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\[
{}x^{2} y^{\prime \prime }+a y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }+\left (a x +b \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-n \left (n +1\right )\right ) y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+n \left (n +1\right )\right ) y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+2 a b x +b^{2}-b \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }-\left (a^{2} x^{4}+a \left (2 b -1\right ) x^{2}+b \left (b +1\right )\right ) y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }-\left (a^{2} x^{2 n}+a \left (2 b +n -1\right ) x^{n}+b \left (b -1\right )\right ) y = 0
\] |
✗ |
✓ |
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\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n}+c \right ) y = 0
\] |
✓ |
✓ |
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\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{3 n}+b \,x^{2 n}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y = 0
\] |
✗ |
✓ |
|