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ODE |
Mathematica |
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\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 y^{2} y^{\prime } x = 0
\] |
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\[
{}{y^{\prime }}^{2}-a \,x^{3} = 0
\] |
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\[
{}{y^{\prime }}^{3} \left (x +2 y\right )+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (y+2 x \right ) y^{\prime } = 0
\] |
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\[
{}{y^{\prime }}^{3} = a \,x^{4}
\] |
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\[
{}4 y^{2} {y^{\prime }}^{2}+2 y^{\prime } x y \left (1+3 x \right )+3 x^{3} = 0
\] |
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\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
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\[
{}x -y y^{\prime } = a {y^{\prime }}^{2}
\] |
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\[
{}y = -a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}}
\] |
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\[
{}4 y = x^{2}+{y^{\prime }}^{2}
\] |
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\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
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\[
{}y = 2 y^{\prime }+3 {y^{\prime }}^{2}
\] |
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\[
{}x \left (1+{y^{\prime }}^{2}\right ) = 1
\] |
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\[
{}x^{2} = a^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
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\[
{}y^{2} = a^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
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\[
{}y^{2}+x y y^{\prime }-x^{2} {y^{\prime }}^{2} = 0
\] |
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\[
{}y = y {y^{\prime }}^{2}+2 x y^{\prime }
\] |
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\[
{}y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2}
\] |
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\[
{}x^{2} \left (-x y^{\prime }+y\right ) = y {y^{\prime }}^{2}
\] |
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\[
{}y = x y^{\prime }+\arcsin \left (y^{\prime }\right )
\] |
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\[
{}{\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2} = 0
\] |
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\[
{}x y \left (-x y^{\prime }+y\right ) = x +y y^{\prime }
\] |
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\[
{}y^{\prime }+2 x y = x^{2}+y^{2}
\] |
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\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2} = 0
\] |
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\[
{}y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\] |
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\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{\prime } y^{3}+x^{3}
\] |
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\[
{}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\] |
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\[
{}{y^{\prime }}^{2}-9 y^{\prime }+18 = 0
\] |
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\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
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\[
{}\left (x y^{\prime }-y\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\] |
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\[
{}\left (x y^{\prime }-y\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\] |
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\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
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\[
{}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
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\[
{}\left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\] |
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\[
{}y^{2} \left (1-{y^{\prime }}^{2}\right ) = b
\] |
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\[
{}\left (x y^{\prime }-y\right ) \left (x +y y^{\prime }\right ) = h^{2} y^{\prime }
\] |
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\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
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\[
{}\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\] |
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\[
{}x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} = a
\] |
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\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
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\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
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\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
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\[
{}{y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\] |
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\[
{}{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{y^{\prime }}^{3} {\mathrm e}^{2 y} = 0
\] |
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\[
{}\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\] |
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\[
{}y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = b
\] |
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\[
{}y = x y^{\prime }+\frac {m}{y^{\prime }}
\] |
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\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
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\[
{}y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
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\[
{}y^{\prime } \sqrt {x} = \sqrt {y}
\] |
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\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2}+x^{3} = 0
\] |
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\[
{}\left (1+y^{\prime }\right )^{3} = \frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a}
\] |
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\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = r^{2}
\] |
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\[
{}x {y^{\prime }}^{2}-\left (x -a \right )^{2} = 0
\] |
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\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
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\[
{}a {y^{\prime }}^{3} = 27 y
\] |
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\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
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\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\] |
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\[
{}y^{2}-2 x y y^{\prime }+\left (x^{2}-1\right ) {y^{\prime }}^{2} = m^{2}
\] |
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\[
{}y = x y^{\prime }+\sqrt {b^{2}+a^{2} y^{\prime }}
\] |
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\[
{}y = x y^{\prime }-{y^{\prime }}^{2}
\] |
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\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
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\[
{}4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0
\] |
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\[
{}\left (8 {y^{\prime }}^{3}-27\right ) x = 12 y {y^{\prime }}^{2}
\] |
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\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}-b^{2} = 0
\] |
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\[
{}\left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }-54 y = 0
\] |
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\[
{}y^{\prime \prime }-m^{2} y = 0
\] |
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\[
{}2 y^{\prime \prime }+5 y^{\prime }-12 y = 0
\] |
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\[
{}9 y^{\prime \prime }+18 y^{\prime }-16 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0
\] |
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\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-m^{2} y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\] |
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\[
{}y^{\prime \prime }-y = 2+5 x
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y = X \left (x \right )
\] |
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\[
{}y^{\prime \prime \prime }+y = 3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime \prime }-y = \left (1+{\mathrm e}^{x}\right )^{2}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}}
\] |
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\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}
\] |
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\[
{}y^{\prime \prime \prime }+8 y = x^{4}+2 x +1
\] |
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\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\] |
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\[
{}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\] |
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\[
{}y^{\prime \prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2}
\] |
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\[
{}y^{\prime \prime \prime \prime }+y = {\mathrm e}^{2 x} x
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right ) {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
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\[
{}y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0
\] |
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\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x}+x^{2}+x
\] |
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\[
{}y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x}
\] |
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\[
{}y^{\prime \prime }-a^{2} y = {\mathrm e}^{a x}+{\mathrm e}^{n x}
\] |
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\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-6 y^{\prime }+8 y = x
\] |
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