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ODE |
Mathematica |
Maple |
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\[
{}y^{\prime \prime } = -\frac {2 n \cosh \left (x \right ) y^{\prime }}{\sinh \left (x \right )}-\left (-a^{2}+n^{2}\right ) y
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (2 n +1\right ) \cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\left (v +n +1\right ) \left (v -n \right ) y
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (\sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }}{\sin \left (x \right )}-y \sin \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime } = -\frac {x \sin \left (x \right ) y^{\prime }}{x \cos \left (x \right )-\sin \left (x \right )}+\frac {\sin \left (x \right ) y}{x \cos \left (x \right )-\sin \left (x \right )}
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (x^{2} \sin \left (x \right )-2 x \cos \left (x \right )\right ) y^{\prime }}{x^{2} \cos \left (x \right )}-\frac {\left (2 \cos \left (x \right )-x \sin \left (x \right )\right ) y}{x^{2} \cos \left (x \right )}
\] |
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\[
{}\cos \left (x \right )^{2} y^{\prime \prime }-\left (a \cos \left (x \right )^{2}+n \left (n -1\right )\right ) y = 0
\] |
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\[
{}y^{\prime \prime } = -\frac {a \left (n -1\right ) \sin \left (2 a x \right ) y^{\prime }}{\cos \left (a x \right )^{2}}-\frac {n \,a^{2} \left (\left (n -1\right ) \sin \left (a x \right )^{2}+\cos \left (a x \right )^{2}\right ) y}{\cos \left (a x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = \frac {2 y}{\sin \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = -\frac {a y}{\sin \left (x \right )^{2}}
\] |
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\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-\left (a \sin \left (x \right )^{2}+n \left (n -1\right )\right ) y = 0
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}}
\] |
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\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-\left (a^{2} \cos \left (x \right )^{2}+b \cos \left (x \right )+\frac {b^{2}}{\left (2 a -3\right )^{2}}+3 a +2\right ) y = 0
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (-\left (a^{2} b^{2}-\left (a +1\right )^{2}\right ) \sin \left (x \right )^{2}-a \left (a +1\right ) b \sin \left (2 x \right )-a \left (a -1\right )\right ) y}{\sin \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (a \cos \left (x \right )^{2}+b \sin \left (x \right )^{2}+c \right ) y}{\sin \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}+\frac {y}{\sin \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = \frac {\cos \left (2 x \right ) y^{\prime }}{\sin \left (2 x \right )}-2 y
\] |
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\[
{}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = -\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )}
\] |
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\[
{}y^{\prime \prime } = -\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = -\frac {4 \sin \left (3 x \right ) y}{\sin \left (x \right )^{3}}
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (4 v \left (v +1\right ) \sin \left (x \right )^{2}-\cos \left (x \right )^{2}+2-4 n^{2}\right ) y}{4 \sin \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = \frac {\left (3 \sin \left (x \right )^{2}+1\right ) y^{\prime }}{\cos \left (x \right ) \sin \left (x \right )}+\frac {\sin \left (x \right )^{2} y}{\cos \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = \frac {\phi ^{\prime }\left (x \right ) y^{\prime }}{\phi \left (x \right )-\phi \left (a \right )}-\frac {\left (-n \left (n +1\right ) \left (\phi \left (x \right )-\phi \left (a \right )\right )^{2}+D^{\left (2\right )}\left (\phi \right )\left (a \right )\right ) y}{\phi \left (x \right )-\phi \left (a \right )}
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (\phi \left (x^{3}\right )-\phi \left (x \right ) \phi ^{\prime }\left (x \right )-\phi ^{\prime \prime }\left (x \right )\right ) y^{\prime }}{\phi ^{\prime }\left (x \right )+\phi \left (x \right )^{2}}-\frac {\left ({\phi ^{\prime }\left (x \right )}^{2}-\phi \left (x \right )^{2} \phi ^{\prime }\left (x \right )-\phi \left (x \right ) \phi ^{\prime \prime }\left (x \right )\right ) y}{\phi ^{\prime }\left (x \right )+\phi \left (x \right )^{2}}
\] |
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\[
{}y^{\prime \prime } = \frac {2 \,\operatorname {JacobiSN}\left (x , k\right ) \operatorname {JacobiCN}\left (x , k\right ) \operatorname {JacobiDN}\left (x , k\right ) y^{\prime }-2 \left (1-2 \left (k^{2}+1\right ) \operatorname {JacobiSN}\left (a , k\right )^{2}+3 k^{2} \operatorname {JacobiSN}\left (a , k\right )^{4}\right ) y}{\operatorname {JacobiSN}\left (x , k\right )^{2}-\operatorname {JacobiSN}\left (a , k\right )}
\] |
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\[
{}y^{\prime \prime } = -\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )}
\] |
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\[
{}y^{\prime \prime } = -\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )}
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (2 f \left (x \right ) {g^{\prime }\left (x \right )}^{2} g \left (x \right )-\left (g \left (x \right )^{2}-1\right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )\right ) y^{\prime }}{f \left (x \right ) g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}-\frac {\left (\left (g \left (x \right )^{2}-1\right ) \left (f^{\prime }\left (x \right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )-f \left (x \right ) f^{\prime \prime }\left (x \right ) g^{\prime }\left (x \right )\right )-\left (2 f^{\prime }\left (x \right ) g \left (x \right )+v \left (v +1\right ) f \left (x \right ) g^{\prime }\left (x \right )\right ) f \left (x \right ) {g^{\prime }\left (x \right )}^{2}\right ) y}{f \left (x \right )^{2} g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}
\] |
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\[
{}y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (x -1\right ) y}{x^{4}}
\] |
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\[
{}y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}}
\] |
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\[
{}y^{\prime \prime } = -\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}}
\] |
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\[
{}y^{\prime \prime }-y^{2} = 0
\] |
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\[
{}y^{\prime \prime }-6 y^{2} = 0
\] |
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\[
{}y^{\prime \prime }-6 y^{2}-x = 0
\] |
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\[
{}y^{\prime \prime }-6 y^{2}+4 y = 0
\] |
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\[
{}y^{\prime \prime }+y^{2} a +b x +c = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{3}-x y+a = 0
\] |
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\[
{}y^{\prime \prime }-a y^{3} = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{3} a^{2}+2 a b x y-b = 0
\] |
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\[
{}y^{\prime \prime }+d +b x y+c y+a y^{3} = 0
\] |
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\[
{}y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0
\] |
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\[
{}y^{\prime \prime }+a \,x^{r} y^{2} = 0
\] |
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\[
{}y^{\prime \prime }+6 a^{10} y^{11}-y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {1}{\left (y^{2} a +b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0
\] |
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\[
{}y^{\prime \prime }-{\mathrm e}^{y} = 0
\] |
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\[
{}y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0
\] |
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\[
{}y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+a \sin \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0
\] |
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\[
{}y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0
\] |
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\[
{}y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime }-y^{3} = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime }-y^{3}+a y = 0
\] |
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\[
{}y^{\prime \prime }+\left (y+3 a \right ) y^{\prime }-y^{3}+y^{2} a +2 a^{2} y = 0
\] |
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\[
{}y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+y^{2} f \left (x \right )+y \left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}\right ) = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime }-y^{3}-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+f \left (x \right )\right ) \left (3 y^{\prime }+y^{2}\right )+\left (a f \left (x \right )^{2}+3 f^{\prime }\left (x \right )+\frac {3 {f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}\right ) y+b f \left (x \right )^{3} = 0
\] |
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\[
{}y^{\prime \prime }+\left (y-\frac {3 f^{\prime }\left (x \right )}{2 f \left (x \right )}\right ) y^{\prime }-y^{3}-\frac {f^{\prime }\left (x \right ) y^{2}}{2 f \left (x \right )}+\frac {\left (f \left (x \right )+\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-f^{\prime \prime }\left (x \right )\right ) y}{2 f \left (x \right )} = 0
\] |
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\[
{}y^{\prime \prime }+2 y y^{\prime }+f \left (x \right ) y^{\prime }+f^{\prime }\left (x \right ) y = 0
\] |
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\[
{}y^{\prime \prime }+2 y y^{\prime }+f \left (x \right ) \left (y^{\prime }+y^{2}\right )-g \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+3 y y^{\prime }+y^{3}+f \left (x \right ) y-g \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }-3 y y^{\prime }-3 y^{2} a -4 a^{2} y-b = 0
\] |
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\[
{}y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }-2 a y y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+a y y^{\prime }+b y^{3} = 0
\] |
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\[
{}y^{\prime \prime }+f \left (x , y\right ) y^{\prime }+g \left (x , y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b y = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b y^{\prime }+c y = 0
\] |
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\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{\prime }+c y = 0
\] |
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\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b \sin \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+a y {y^{\prime }}^{2}+b y = 0
\] |
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\[
{}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (x \right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }-\frac {D\left (f \right )\left (y\right ) {y^{\prime }}^{3}}{f \left (y\right )}+g \left (x \right ) y^{\prime }+h \left (x \right ) f \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+\phi \left (y\right ) {y^{\prime }}^{2}+f \left (x \right ) y^{\prime }+g \left (x \right ) \Phi \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (y\right ) y^{\prime }+h \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+\left (1+{y^{\prime }}^{2}\right ) \left (f \left (x , y\right ) y^{\prime }+g \left (x , y\right )\right ) = 0
\] |
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\[
{}y^{\prime \prime }+a y \left (1+{y^{\prime }}^{2}\right )^{2} = 0
\] |
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\[
{}y^{\prime \prime }-a \left (x y^{\prime }-y\right )^{v} = 0
\] |
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\[
{}y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0
\] |
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\[
{}y^{\prime \prime }+\left (y^{\prime }-\frac {y}{x}\right )^{a} f \left (x , y\right ) = 0
\] |
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\[
{}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b
\] |
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\[
{}y^{\prime \prime } = a \sqrt {{y^{\prime }}^{2}+b y^{2}}
\] |
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\[
{}y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
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\[
{}y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
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\[
{}y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
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\[
{}y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
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\[
{}y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0
\] |
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