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Mathematica |
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\[
{}y^{\prime } = y^{2}+x^{2}-1
\] |
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\[
{}x^{2} y^{\prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime } = 2 y
\] |
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\[
{}x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+x y = 0
\] |
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\[
{}3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
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\[
{}x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+x y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime } = 2 y
\] |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y = {\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right )
\] |
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\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0
\] |
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\[
{}t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0
\] |
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\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\] |
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\[
{}2 x +3 y+2+\left (y-x \right ) y^{\prime } = 0
\] |
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\[
{}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0
\] |
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\[
{}\left (x^{2}+y^{2}-2 y\right ) y^{\prime } = 2 x
\] |
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\[
{}\sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \sin \left (x \right )
\] |
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\[
{}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-\left (1+x \right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y}{z^{3}} = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )} = 0
\] |
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\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right )
\] |
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\[
{}2 y^{\prime } = 2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right )
\] |
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\[
{}\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime } = y^{3} \csc \left (x \right ) \sec \left (x \right )
\] |
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\[
{}\left (x \,a^{2}+y \left (x^{2}-y^{2}\right )\right ) y^{\prime }+x \left (x^{2}-y^{2}\right ) = a^{2} y
\] |
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\[
{}{y^{\prime }}^{2}+a \,x^{2}+b y = 0
\] |
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\[
{}{y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y = 0
\] |
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\[
{}x^{3} {y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
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\[
{}x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
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\[
{}x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y = 0
\] |
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\[
{}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0
\] |
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\[
{}y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime \prime }-\left (2 x -1\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}} = 0
\] |
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\[
{}x^{3} y^{\prime \prime }+y = x^{{3}/{2}}
\] |
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\[
{}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = \sqrt {x}
\] |
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\[
{}s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }+3 y^{\prime }-x y = 0
\] |
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\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}}
\] |
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\[
{}x y^{\prime \prime }-2 y^{\prime }+y = \cos \left (x \right )
\] |
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\[
{}y^{\prime }-\frac {y}{x} = \cos \left (x \right )
\] |
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\[
{}x^{2} y^{\prime \prime }+y^{\prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime \prime }+\left (1+x \right ) y = 0
\] |
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\[
{}t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0
\] |
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\[
{}m^{\prime } = -\frac {k}{m^{2}}
\] |
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\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
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\[
{}x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+\lambda y = 0
\] |
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\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
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\[
{}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y = \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2}
\] |
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\[
{}x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y = 0
\] |
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\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
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\[
{}x y y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3}
\] |
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\[
{}x^{2} y^{\prime } = y
\] |
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\[
{}x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
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\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\] |
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\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
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\[
{}x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0
\] |
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\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t, z^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t]
\] |
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\[
{}y = x y^{\prime }+x^{3} {y^{\prime }}^{2}
\] |
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\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1+x
\] |
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\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x
\] |
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\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+x +1
\] |
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\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )
\] |
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\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )+1
\] |
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\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \cos \left (x \right )+\sin \left (x \right )
\] |
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\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = 1
\] |
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\[
{}y^{\prime }+y = \frac {1}{x}
\] |
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\[
{}y^{\prime }+y = \frac {1}{x^{2}}
\] |
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\[
{}y^{\prime } = \frac {1}{x}
\] |
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\[
{}y^{\prime \prime } = \frac {1}{x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{x}
\] |
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\[
{}y^{\prime \prime }+y = \frac {1}{x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = \frac {1}{x}
\] |
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\[
{}t y^{\prime }+y = \sin \left (t \right )
\] |
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\[
{}{y^{\prime }}^{2}+a y+b \,x^{2} = 0
\] |
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\[
{}{y^{\prime }}^{2}+a x y^{\prime }+b y+c \,x^{2} = 0
\] |
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\[
{}\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x y+x^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\] |
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\[
{}\left (a \left (x^{2}+y^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (x^{2}+y^{2}\right )^{{3}/{2}}-y^{2} = 0
\] |
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\[
{}{y^{\prime }}^{2} \sin \left (y\right )+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4} = 0
\] |
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\[
{}x^{3} {y^{\prime }}^{3}-3 y {y^{\prime }}^{2} x^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y = 0
\] |
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\[
{}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0
\] |
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\[
{}y^{\prime } = \frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )}
\] |
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\[
{}y^{\prime } = -\frac {\ln \left (x -1\right )-\coth \left (1+x \right ) x^{2}-2 \coth \left (1+x \right ) x y-\coth \left (1+x \right )-\coth \left (1+x \right ) y^{2}}{\ln \left (x -1\right )}
\] |
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\[
{}y^{\prime } = \frac {2 x \ln \left (\frac {1}{x -1}\right )-\coth \left (\frac {1+x}{x -1}\right )+\coth \left (\frac {1+x}{x -1}\right ) y^{2}-2 \coth \left (\frac {1+x}{x -1}\right ) x^{2} y+\coth \left (\frac {1+x}{x -1}\right ) x^{4}}{\ln \left (\frac {1}{x -1}\right )}
\] |
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\[
{}y^{\prime } = \frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 x \,a^{3}+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}}
\] |
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