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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} y^{\prime } = y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n}
\]
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\[
{} y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \sin \left (\lambda x \right ) y-a \tan \left (\lambda x \right )
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \arcsin \left (x \right )^{n} \left (x^{k +1} y-1\right )
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \arccos \left (x \right )^{n} \left (x^{k +1} y-1\right )
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \arctan \left (x \right )^{n} \left (x^{k +1} y-1\right )
\]
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\[
{} y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} \left (x^{k +1} y-1\right )
\]
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\[
{} y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+x^{n +1} f \left (x \right ) y-f \left (x \right )
\]
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\[
{} y^{\prime } = -a \ln \left (x \right ) y^{2}+a f \left (x \right ) \left (x \ln \left (x \right )-x \right ) y-f \left (x \right )
\]
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\[
{} y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+f \left (x \right ) \cos \left (\lambda x \right ) y-f \left (x \right )
\]
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\[
{} y^{\prime } = y^{2}-f \left (x \right )^{2}+f^{\prime }\left (x \right )
\]
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\[
{} y^{\prime } = -f^{\prime }\left (x \right ) y^{2}+f \left (x \right ) g \left (x \right ) y-g \left (x \right )
\]
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\[
{} y y^{\prime }-y = 2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right )
\]
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\[
{} y y^{\prime }-y = A x +\frac {B}{x}-\frac {B^{2}}{x^{3}}
\]
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\[
{} y y^{\prime }-y = A +B \,{\mathrm e}^{-\frac {2 x}{A}}
\]
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\[
{} y y^{\prime }-y = A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right )
\]
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\[
{} y y^{\prime }-y = \frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}}
\]
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\[
{} y y^{\prime }-y = -\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4}
\]
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\[
{} y y^{\prime }-y = \frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}}
\]
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\[
{} y y^{\prime }-y = -\frac {4 x}{25}+\frac {A}{\sqrt {x}}
\]
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\[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49}
\]
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\[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98}
\]
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\[
{} y y^{\prime }-y = A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right )
\]
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\[
{} y y^{\prime }-y = A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right )
\]
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\[
{} y y^{\prime }-y = A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}}
\]
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\[
{} y y^{\prime }-y = 2 A^{2}-A \sqrt {x}
\]
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\[
{} y y^{\prime }-y = -\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}}
\]
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\[
{} y y^{\prime }-y = 12 x +\frac {A}{x^{{5}/{2}}}
\]
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\[
{} y y^{\prime }-y = 2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right )
\]
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\[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49}
\]
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\[
{} y y^{\prime }-y = -\frac {12 x}{49}+A \sqrt {x}
\]
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\[
{} y y^{\prime }-y = -\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49}
\]
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\[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49}
\]
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\[
{} y y^{\prime }-y = -\frac {6 x}{25}+\frac {4 B^{2} \left (\left (-A +2\right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75}
\]
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\[
{} y y^{\prime } = \frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1
\]
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\[
{} y y^{\prime } = \left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1
\]
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\[
{} y y^{\prime } = \left (a x +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x
\]
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\[
{} 2 y y^{\prime } = \left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x
\]
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\[
{} y y^{\prime } = x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (x +a \right )
\]
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\[
{} y y^{\prime }-\frac {a \left (\left (m -1\right ) x +1\right ) y}{x} = \frac {a^{2} \left (m x +1\right ) \left (x -1\right )}{x}
\]
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\[
{} y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x} = -\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x}
\]
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\[
{} y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}}
\]
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\[
{} y y^{\prime }-\frac {a \left (1+x \right ) y}{2 x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +5\right )}{4 x^{{5}/{2}}}
\]
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\[
{} y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}} = \frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}}
\]
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\[
{} y y^{\prime }+\frac {a \left (x -2\right ) y}{x} = \frac {2 a^{2} \left (x -1\right )}{x}
\]
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\[
{} y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}}
\]
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\[
{} y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{11}/{5}}}
\]
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\[
{} y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +1\right )}{2 x^{4}}
\]
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\[
{} y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}} = \frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}}
\]
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\[
{} y y^{\prime }-\frac {a \left (\left (k +1\right ) x -1\right ) y}{x^{2}} = \frac {a^{2} \left (k +1\right ) \left (x -1\right )}{x^{2}}
\]
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\[
{} y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y = n \left (-a +x \right ) x^{-2 n}
\]
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\[
{} y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y = -\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n}
\]
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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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\[
{} y y^{\prime } = {\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right )
\]
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\[
{} y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y = -a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x}
\]
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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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\[
{} y y^{\prime } = \left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right )
\]
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\[
{} \left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\]
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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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\[
{} y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\]
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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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\[
{} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+x^{n} \left (a \,x^{2}+\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (m +1\right ) x^{m -1}\right ) y = 0
\]
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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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\[
{} x y^{\prime \prime }-\left (2 a x +1\right ) y^{\prime }+b \,x^{3} y = 0
\]
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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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\[
{} x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{n -2} y = 0
\]
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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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\[
{} x^{2} y^{\prime \prime }-\left (a^{2} x^{2 n}+a \left (2 b +n -1\right ) x^{n}+b \left (b -1\right )\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\left (a \,x^{3 n}+b \,x^{2 n}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x \left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{3}+B \,x^{2}+C x +d \right ) y = 0
\]
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\[
{} \left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y = 0
\]
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\[
{} \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0
\]
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\[
{} 2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\lambda y = 0
\]
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\[
{} x^{4} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y = 0
\]
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\[
{} x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\]
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\[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (a -1\right ) y = 0
\]
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\[
{} x^{n} y^{\prime \prime }+\left (2 x^{n -1}+a \,x^{2}+b x \right ) y^{\prime }+b y = 0
\]
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\[
{} \left (a \,x^{n}+b x +c \right ) y^{\prime \prime } = a n \left (n -1\right ) x^{n -2} y
\]
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\[
{} x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y = 0
\]
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\[
{} \left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{n -2} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y = 0
\]
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\[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y = 0
\]
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\[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0
\]
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\[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{x \mu } \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+\mu \right ) y = 0
\]
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\[
{} y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 x \mu }+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 x \mu }\right )-\mu \right ) y = 0
\]
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\[
{} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\]
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\[
{} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\]
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\[
{} {\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 n x \left (1+x \right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\]
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\[
{} x^{4} y^{\prime \prime }+2 x^{3} \left (1+x \right ) y^{\prime }+n^{2} y = 0
\]
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\[
{} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
\]
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\[
{} y = {y^{\prime }}^{4}-{y^{\prime }}^{3}-2
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\]
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\[
{} x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|