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\[
{}\frac {2 t y}{t^{2}+1}+y^{\prime } = \frac {1}{t^{2}+1}
\] |
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\[
{}y^{\prime }+y = {\mathrm e}^{t} t
\] |
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\[
{}t^{2} y+y^{\prime } = 1
\] |
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\[
{}t^{2} y+y^{\prime } = t^{2}
\] |
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\[
{}\frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1}
\] |
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\[
{}\sqrt {t^{2}+1}\, y+y^{\prime } = 0
\] |
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\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
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\[
{}y^{\prime }-2 t y = t
\] |
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\[
{}t y+y^{\prime } = t +1
\] |
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\[
{}y^{\prime }+y = \frac {1}{t^{2}+1}
\] |
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\[
{}y^{\prime }-2 t y = 1
\] |
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\[
{}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{{5}/{2}}
\] |
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\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = t
\] |
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\[
{}y^{\prime }+\frac {y}{t} = \frac {1}{t^{2}}
\] |
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\[
{}y^{\prime }+\frac {y}{\sqrt {t}} = {\mathrm e}^{\frac {\sqrt {t}}{2}}
\] |
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\[
{}y^{\prime }+\frac {y}{t} = \cos \left (t \right )+\frac {\sin \left (t \right )}{t}
\] |
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\[
{}y^{\prime }+\tan \left (t \right ) y = \cos \left (t \right ) \sin \left (t \right )
\] |
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\[
{}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
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\[
{}y^{\prime } = \left (t +1\right ) \left (y+1\right )
\] |
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\[
{}y^{\prime } = 1-t +y^{2}-t y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{3+t +y}
\] |
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\[
{}\cos \left (y\right ) \sin \left (t \right ) y^{\prime } = \cos \left (t \right ) \sin \left (y\right )
\] |
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\[
{}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \frac {2 t}{y+t^{2} y}
\] |
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\[
{}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}}
\] |
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\[
{}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y}
\] |
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\[
{}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1}
\] |
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\[
{}y^{\prime } = k \left (a -y\right ) \left (b -y\right )
\] |
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\[
{}3 t y^{\prime } = \cos \left (t \right ) y
\] |
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\[
{}t y^{\prime } = y+\sqrt {t^{2}+y^{2}}
\] |
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\[
{}2 t y y^{\prime } = 3 y^{2}-t^{2}
\] |
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\[
{}\left (t -\sqrt {t y}\right ) y^{\prime } = y
\] |
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\[
{}y^{\prime } = \frac {y+t}{t -y}
\] |
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\[
{}{\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\] |
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\[
{}y^{\prime } = \frac {t +y+1}{t -y+3}
\] |
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\[
{}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
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\[
{}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0
\] |
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\[
{}2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}1+{\mathrm e}^{t y} \left (1+t y\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime } = 0
\] |
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\[
{}\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime } = 0
\] |
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\[
{}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0
\] |
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\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
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\[
{}2 t \cos \left (y\right )+3 t^{2} y+\left (t^{3}-\sin \left (y\right ) t^{2}-y\right ) y^{\prime } = 0
\] |
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\[
{}3 t^{2}+4 t y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0
\] |
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\[
{}2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime } = 0
\] |
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\[
{}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = y^{2}+\cos \left (t^{2}\right )
\] |
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\[
{}y^{\prime } = 1+y+y^{2} \cos \left (t \right )
\] |
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\[
{}y^{\prime } = t +y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{\left (y-t \right )^{2}}
\] |
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\[
{}y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\] |
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\[
{}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800}
\] |
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\[
{}y^{\prime } = t^{2}+y^{2}
\] |
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\[
{}y^{\prime } = t \left (y+1\right )
\] |
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\[
{}y^{\prime } = t \sqrt {1-y^{2}}
\] |
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\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-y = 0
\] |
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\[
{}6 y^{\prime \prime }-7 y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
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\[
{}3 y^{\prime \prime }+6 y^{\prime }+3 y = 0
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }-4 y = 0
\] |
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\[
{}2 y^{\prime \prime }+y^{\prime }-10 y = 0
\] |
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\[
{}5 y^{\prime \prime }+5 y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
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\[
{}2 y^{\prime \prime }+3 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = 0
\] |
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\[
{}4 y^{\prime \prime }-y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
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\[
{}2 y^{\prime \prime }-y^{\prime }+3 y = 0
\] |
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\[
{}3 y^{\prime \prime }-2 y^{\prime }+4 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
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\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
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\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
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\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
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\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\] |
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\[
{}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
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\[
{}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\] |
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\[
{}\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
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