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Mathematica |
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\[
{}y^{\prime } = \sqrt {x -y}
\] |
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\[
{}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0
\] |
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\[
{}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0
\] |
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\[
{}[x^{\prime }\left (t \right ) = t x \left (t \right )-{\mathrm e}^{t} y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+t^{2} y \left (t \right )-\sin \left (t \right )]
\] |
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\[
{}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0
\] |
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\[
{}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = {| y|}+1
\] |
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\[
{}\left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y = 0
\] |
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\[
{}y^{\prime } = 1+y+y^{2} \cos \left (t \right )
\] |
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\[
{}\sqrt {1+y^{2}}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}}
\] |
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\[
{}y^{\prime } = 1+y+y^{2} \cos \left (t \right )
\] |
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\[
{}y^{\prime } = t y^{a}
\] |
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\[
{}x^{2}+3 x y^{\prime } = y^{3}+2 y
\] |
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\[
{}2 x +y+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
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\[
{}y \left (y^{2}+x \right )+x \left (x -y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}1+x y \left (x y^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}+\left (x^{3}-2 x y\right ) y^{\prime } = 0
\] |
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\[
{}y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y y^{\prime \prime } = y^{3}+{y^{\prime }}^{2}
\] |
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\[
{}3 {y^{\prime }}^{4} x = y {y^{\prime }}^{3}+1
\] |
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\[
{}x y y^{\prime } = \left (1+x \right ) \left (1+y\right )
\] |
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\[
{}\cos \left (y\right )-x \sin \left (y\right ) y^{\prime } = \sec \left (x \right )^{2}
\] |
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\[
{}{y^{\prime }}^{3}+y^{2} = x y y^{\prime }
\] |
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\[
{}y = x y^{\prime }-x^{2} {y^{\prime }}^{3}
\] |
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\[
{}y \left (y-2 x y^{\prime }\right )^{3} = {y^{\prime }}^{2}
\] |
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\[
{}5 y+{y^{\prime }}^{2} = x \left (x +y^{\prime }\right )
\] |
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\[
{}2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x = y
\] |
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\[
{}y^{\prime }+f \left (x \right )^{2} = f^{\prime }\left (x \right )+y^{2}
\] |
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\[
{}x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (1-n \right ) x^{n -1} = 0
\] |
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\[
{}{y^{\prime }}^{3}-x y^{\prime }+a y = 0
\] |
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\[
{}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
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\[
{}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0
\] |
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\[
{}{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right ) = 0
\] |
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\[
{}{y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y} = 0
\] |
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\[
{}{y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a2} +\operatorname {a3} y = 0
\] |
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\[
{}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\] |
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\[
{}2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
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\[
{}8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y
\] |
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\[
{}x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0
\] |
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\[
{}y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0
\] |
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\[
{}y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2} = 0
\] |
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\[
{}{y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\] |
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\[
{}x +y+\left (3 x +3 y-4\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0
\] |
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\[
{}2 y^{\prime \prime }-3 y^{2} = 0
\] |
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\[
{}y^{\prime } = \sqrt {1+y^{2}}\, \sin \left (y\right )^{2}
\] |
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\[
{}y^{\prime } = -\frac {5+8 x}{3 y^{2}+1}
\] |
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\[
{}y^{\prime } = -\frac {5+8 x}{3 y^{2}+1}
\] |
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\[
{}y^{\prime } = -\frac {5+8 x}{3 y^{2}+1}
\] |
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\[
{}y^{\prime } = -\frac {5+8 x}{3 y^{2}+1}
\] |
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\[
{}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime } = y^{\prime } {\mathrm e}^{y}
\] |
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\[
{}y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\] |
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\[
{}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\] |
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\[
{}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
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\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0
\] |
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\[
{}{y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\] |
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\[
{}{y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\] |
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\[
{}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0
\] |
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\[
{}y^{\prime } = -4 \sin \left (x -y\right )-4
\] |
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\[
{}y^{2} y^{\prime \prime } = x
\] |
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\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0
\] |
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\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0
\] |
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\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x
\] |
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\[
{}t y^{\prime }+y = t
\] |
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\[
{}t y^{\prime }+y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\] |
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\[
{}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0
\] |
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\[
{}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0
\] |
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\[
{}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0
\] |
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\[
{}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0
\] |
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\[
{}\frac {y^{\prime } f_{\nu }\left (x \right ) \left (-y+y^{p +1}\right )}{y-1}-\frac {g_{\nu }\left (x \right ) \left (-y+y^{q +1}\right )}{y-1} = 0
\] |
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\[
{}\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0
\] |
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\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+\left (a \,x^{2}+b x +a \right ) y = 0
\] |
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\[
{}x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-2 x^{3} y^{\prime }-\left (\left (a -n \right ) \left (a +n +1\right ) x^{2} \left (x^{2}-1\right )+2 a \,x^{2}+n \left (n +1\right ) \left (x^{2}-1\right )\right ) y = 0
\] |
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\[
{}y^{\prime \prime } = -\frac {\left (\left (1-4 a \right ) x^{2}-1\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (\left (-v^{2}+x^{2}\right ) \left (x^{2}-1\right )^{2}+4 a \left (a +1\right ) x^{4}-2 a \,x^{2} \left (x^{2}-1\right )\right ) y}{x^{2} \left (x^{2}-1\right )^{2}}
\] |
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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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\[
{}y^{\prime \prime } = -\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}}
\] |
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\[
{}x^{2} y^{\prime \prime \prime }-\left (x +\nu \right ) x y^{\prime \prime }+\nu \left (2 x +1\right ) y^{\prime }-\nu \left (1+x \right ) y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2} = 0
\] |
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\[
{}\left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y = 0
\] |
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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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\[
{}x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0
\] |
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\[
{}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}+a x = 0
\] |
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\[
{}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\] |
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\[
{}\sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
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\[
{}\left (x y^{\prime }-y\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0
\] |
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\[
{}a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0
\] |
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\[
{}a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right )+z^{\prime }\left (t \right ) = y \left (t \right ) z \left (t \right ), x^{\prime }\left (t \right )+z^{\prime }\left (t \right ) = x \left (t \right ) z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = -y \left (t \right ) \left (z \left (t \right )^{2}+x \left (t \right )^{2}\right ), z^{\prime }\left (t \right ) = z \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\] |
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\[
{}a \,x^{2} \left (x -1\right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s = 0
\] |
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