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Mathematica |
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\[
{}\left (y^{2}+x^{2}+x \right ) y^{\prime }-y = 0
\] |
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\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
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\[
{}\left (y^{2}+x^{4}\right ) y^{\prime }-4 x^{3} y = 0
\] |
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\[
{}\left (y^{2}+4 \sin \left (x \right )\right ) y^{\prime }-\cos \left (x \right ) = 0
\] |
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\[
{}\left (y^{2}+2 y+x \right ) y^{\prime }+\left (x +y\right )^{2} y^{2}+y \left (1+y\right ) = 0
\] |
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\[
{}\left (x +y\right )^{2} y^{\prime }-a^{2} = 0
\] |
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\[
{}\left (y^{2}+2 x y-x^{2}\right ) y^{\prime }-y^{2}+2 x y+x^{2} = 0
\] |
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\[
{}\left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0
\] |
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\[
{}3 \left (y^{2}-x^{2}\right ) y^{\prime }+2 y^{3}-6 x \left (1+x \right ) y-3 \,{\mathrm e}^{x} = 0
\] |
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\[
{}\left (x^{2}+4 y^{2}\right ) y^{\prime }-x y = 0
\] |
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\[
{}\left (4 y^{2}+2 x y+3 x^{2}\right ) y^{\prime }+y^{2}+6 x y+2 x^{2} = 0
\] |
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\[
{}\left (2 y-3 x +1\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2} = 0
\] |
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\[
{}\left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2} = 0
\] |
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\[
{}\left (6 y^{2}-3 x^{2} y+1\right ) y^{\prime }-3 x y^{2}+x = 0
\] |
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\[
{}\left (6 y-x \right )^{2} y^{\prime }-6 y^{2}+2 x y+a = 0
\] |
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\[
{}\left (y^{2} a +2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0
\] |
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\[
{}\left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (a x +b y\right ) = 0
\] |
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\[
{}\left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2} = 0
\] |
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\[
{}x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 x y = 0
\] |
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\[
{}x \left (y^{2}+x^{2}-a \right ) y^{\prime }-y \left (y^{2}+x^{2}+a \right ) = 0
\] |
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\[
{}x \left (y^{2}+x y-x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y = 0
\] |
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\[
{}x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 x^{2} y^{2}+x^{4} = 0
\] |
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\[
{}2 x \left (y^{2}+5 x^{2}\right ) y^{\prime }+y^{3}-x^{2} y = 0
\] |
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\[
{}3 y^{2} y^{\prime } x +y^{3}-2 x = 0
\] |
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\[
{}\left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 x y = 0
\] |
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\[
{}6 y^{2} y^{\prime } x +2 y^{3}+x = 0
\] |
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\[
{}\left (x^{2}+6 x y^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right ) = 0
\] |
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\[
{}\left (x^{2} y^{2}+x \right ) y^{\prime }+y = 0
\] |
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\[
{}\left (x y-1\right )^{2} x y^{\prime }+\left (x^{2} y^{2}+1\right ) y = 0
\] |
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\[
{}\left (10 y^{2} x^{3}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2} = 0
\] |
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\[
{}\left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2} = 0
\] |
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\[
{}\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y = 0
\] |
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\[
{}\left (y^{2}+x^{2}+a \right ) y y^{\prime }+\left (y^{2}+x^{2}-a \right ) x = 0
\] |
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\[
{}2 y^{3} y^{\prime }+x y^{2} = 0
\] |
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\[
{}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0
\] |
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\[
{}\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3} = 0
\] |
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\[
{}\left (20 y^{3}-3 x y^{2}+6 x^{2} y+3 x^{3}\right ) y^{\prime }-y^{3}+6 x y^{2}+9 x^{2} y+4 x^{3} = 0
\] |
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\[
{}\left (\frac {y^{2}}{b}+\frac {x^{2}}{a}\right ) \left (y y^{\prime }+x \right )+\frac {\left (a -b \right ) \left (y y^{\prime }-x \right )}{a +b} = 0
\] |
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\[
{}\left (2 a y^{3}+3 a x y^{2}-b \,x^{3}+c \,x^{2}\right ) y^{\prime }-a y^{3}+c y^{2}+3 b \,x^{2} y+2 b \,x^{3} = 0
\] |
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\[
{}x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right ) = 0
\] |
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\[
{}\left (2 x y^{3}-x^{4}\right ) y^{\prime }-y^{4}+2 x^{3} y = 0
\] |
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\[
{}\left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2} = 0
\] |
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\[
{}\left (2 x y^{3}+x y+x^{2}\right ) y^{\prime }+y^{2}-x y = 0
\] |
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\[
{}\left (3 x y^{3}-4 x y+y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right ) = 0
\] |
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\[
{}\left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y = 0
\] |
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\[
{}\left (x^{2} y^{3}+x y\right ) y^{\prime }-1 = 0
\] |
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\[
{}\left (2 x^{2} y^{3}+x^{2} y^{2}-2 x \right ) y^{\prime }-2 y-1 = 0
\] |
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\[
{}\left (10 x^{2} y^{3}-3 y^{2}-2\right ) y^{\prime }+5 y^{4} x +x = 0
\] |
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\[
{}\left (a x y^{3}+c \right ) x y^{\prime }+\left (b \,x^{3} y+c \right ) y = 0
\] |
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\[
{}\left (2 x^{3} y^{3}-x \right ) y^{\prime }+2 x^{3} y^{3}-y = 0
\] |
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\[
{}y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x = 0
\] |
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\[
{}y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right ) = 0
\] |
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\[
{}\left (y^{4} x +2 x^{2} y^{3}+2 y+x \right ) y^{\prime }+y^{5}+y = 0
\] |
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\[
{}a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y = 0
\] |
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\[
{}y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y = 0
\] |
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\[
{}\left (f \left (x +y\right )+1\right ) y^{\prime }+f \left (x +y\right ) = 0
\] |
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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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\[
{}\left (\sqrt {x y}-1\right ) x y^{\prime }-\left (\sqrt {x y}+1\right ) y = 0
\] |
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\[
{}\left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y = 0
\] |
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\[
{}\left (\sqrt {x +y}+1\right ) y^{\prime }+1 = 0
\] |
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\[
{}\sqrt {y^{2}-1}\, y^{\prime }-\sqrt {x^{2}-1} = 0
\] |
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\[
{}\left (\sqrt {1+y^{2}}+a x \right ) y^{\prime }+\sqrt {x^{2}+1}+a y = 0
\] |
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\[
{}\left (\sqrt {x^{2}+y^{2}}+x \right ) y^{\prime }-y = 0
\] |
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\[
{}\left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right ) = 0
\] |
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\[
{}\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }-y \sqrt {1+x^{2}+y^{2}}-x \left (x^{2}+y^{2}\right ) = 0
\] |
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\[
{}\left (\frac {\operatorname {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) = 0
\] |
✗ |
✗ |
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\[
{}\left (x \,{\mathrm e}^{y}+{\mathrm e}^{x}\right ) y^{\prime }+{\mathrm e}^{y}+y \,{\mathrm e}^{x} = 0
\] |
✓ |
✓ |
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\[
{}x \left (3 \,{\mathrm e}^{x y}+2 \,{\mathrm e}^{-x y}\right ) \left (x y^{\prime }+y\right )+1 = 0
\] |
✓ |
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\[
{}\left (\ln \left (y\right )+x \right ) y^{\prime }-1 = 0
\] |
✓ |
✓ |
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\[
{}\left (\ln \left (y\right )+2 x -1\right ) y^{\prime }-2 y = 0
\] |
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\[
{}x \left (2 x^{2} y \ln \left (y\right )+1\right ) y^{\prime }-2 y = 0
\] |
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\[
{}x \left (y \ln \left (x y\right )+y-a x \right ) y^{\prime }-y \left (a x \ln \left (x y\right )-y+a x \right ) = 0
\] |
✓ |
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\[
{}y^{\prime } \left (\sin \left (x \right )+1\right ) \sin \left (y\right )+\cos \left (x \right ) \left (\cos \left (y\right )-1\right ) = 0
\] |
✓ |
✓ |
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\[
{}\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right )+\sin \left (y\right ) = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime } \cot \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) x -y \cot \left (\frac {y}{x}\right ) = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime } \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right )^{2}-\sin \left (y\right ) = 0
\] |
✓ |
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\[
{}y^{\prime } \cos \left (y\right )+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3} = 0
\] |
✓ |
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\[
{}y^{\prime } \left (\cos \left (y\right )-\sin \left (\alpha \right ) \sin \left (x \right )\right ) \cos \left (y\right )+\left (\cos \left (x \right )-\sin \left (\alpha \right ) \sin \left (y\right )\right ) \cos \left (x \right ) = 0
\] |
✓ |
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\[
{}x \cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 0
\] |
✓ |
✓ |
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\[
{}\left (x \sin \left (y\right )-1\right ) y^{\prime }+\cos \left (y\right ) = 0
\] |
✓ |
✓ |
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\[
{}\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-y \sin \left (x \right )+\sin \left (y\right ) = 0
\] |
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\[
{}\left (x^{2} \cos \left (y\right )+2 y \sin \left (x \right )\right ) y^{\prime }+2 x \sin \left (y\right )+y^{2} \cos \left (x \right ) = 0
\] |
✓ |
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\[
{}x y^{\prime } \ln \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \left (1-x \cos \left (y\right )\right ) = 0
\] |
✓ |
✓ |
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\[
{}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
✓ |
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\[
{}3 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }+5 \cos \left (x \right )^{4} y = 0
\] |
✓ |
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\[
{}y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos \left (a y\right )^{2}-1+c \cos \left (a y\right )} = 0
\] |
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\[
{}\left (x \sin \left (x y\right )+\cos \left (x +y\right )-\sin \left (y\right )\right ) y^{\prime }+y \sin \left (x y\right )+\cos \left (x +y\right )+\cos \left (x \right ) = 0
\] |
✓ |
✓ |
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\[
{}\left (x^{2} y \sin \left (x y\right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (x y\right )-y = 0
\] |
✓ |
✓ |
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\[
{}\left (x y^{\prime }-y\right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0
\] |
✓ |
✓ |
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\[
{}\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = 0
\] |
✓ |
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\[
{}\left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right ) = 0
\] |
✓ |
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\[
{}f \left (x^{2}+y^{2} a \right ) \left (a y y^{\prime }+x \right )-y-x y^{\prime } = 0
\] |
✓ |
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\[
{}f \left (x^{c} y\right ) \left (b x y^{\prime }-a \right )-x^{a} y^{b} \left (x y^{\prime }+c y\right ) = 0
\] |
✗ |
✗ |
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\[
{}y^{\prime }-1 = 0
\] |
✓ |
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\[
{}y^{\prime } = F \left (\frac {y}{x +a}\right )
\] |
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\[
{}y^{\prime } = 2 x +F \left (y-x^{2}\right )
\] |
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\[
{}y^{\prime } = -\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right )
\] |
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\[
{}y^{\prime } = F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x}
\] |
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\[
{}y^{\prime } = \frac {1+2 F \left (\frac {1+4 x^{2} y}{4 x^{2}}\right ) x}{2 x^{3}}
\] |
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\[
{}y^{\prime } = \frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}}
\] |
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