|
# |
ODE |
CAS classification |
Solved? |
|
\[
{}y = y^{\prime } x -\frac {{y^{\prime }}^{2}}{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x -\sqrt {y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\frac {3}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{{2}/{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +{\mathrm e}^{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}\left (y-y^{\prime } x \right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y^{\prime } y-2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}\left (y-y^{\prime } x \right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}2 {y^{\prime }}^{2} \left (y-y^{\prime } x \right ) = 1
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (2-x \right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-4 \left (x +1\right ) y^{\prime }+4 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-a x y^{\prime }+a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c = b y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y^{\prime } y+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +\left (-y+a \right ) y^{\prime }+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +\left (a +x -y\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (a -x \right ) {y^{\prime }}^{2}+y^{\prime } y-b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (2+y\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+1+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (a +2 x y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+b +y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+a x y^{\prime }-a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}2 \sqrt {a y^{\prime }}+y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
|
|
\[
{}\sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}a \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+y^{\prime } x -y = 0
\] |
[_Clairaut] |
✓ |
|
|
\[
{}\cos \left (y^{\prime }\right )+y^{\prime } x = y
\] |
[_Clairaut] |
✓ |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2} = 1
\] |
[_Clairaut] |
✓ |
|
|
\[
{}\ln \left (y^{\prime }\right )+y^{\prime } x +a = y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}\ln \left (y^{\prime }\right )+a \left (-y+y^{\prime } x \right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x +y = 0
\] |
[_Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}
\] |
[_Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +y^{\prime }-{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x -2 {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +k {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}y^{\prime } \left (y^{\prime } x -y+k \right )+a = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+1+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}\left (1+y^{\prime }\right )^{2} \left (y-y^{\prime } x \right ) = 1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x +\left (k -x -y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}\frac {{y^{\prime }}^{2}}{4}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}}
\] |
[_Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (a x +b \right ) y^{\prime }-a y+c = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y^{\prime } y+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (2+y\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}\left (3 x +5\right ) {y^{\prime }}^{2}-\left (x +3 y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (a +2 x y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}\sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}\ln \left (y^{\prime }\right )+a \left (-y+y^{\prime } x \right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2}-1 = 0
\] |
[_Clairaut] |
✓ |
|
|
\[
{}\left (-y+y^{\prime } x \right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } y = \left (x -b \right ) {y^{\prime }}^{2}+a
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 \left (x y-2\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime }-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\sqrt {1-{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x -\frac {1}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime }+2 x = 2 \sqrt {y+x^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } t -{y^{\prime }}^{3} = y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } t -y-2 \left (y^{\prime } t -y\right )^{2} = y^{\prime }+1
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } t -y-1 = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}1+y-y^{\prime } t = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}1-2 y^{\prime } t +2 y = \frac {1}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } t +3 {y^{\prime }}^{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y-y^{\prime } t = -2 {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y-y^{\prime } t = -4 {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\frac {a}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y^{\prime } y-y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}x = \frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\sqrt {a^{2} {y^{\prime }}^{2}+b^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +y^{\prime }-{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} \left (x^{2}-1\right )-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -x +\sqrt {x^{2}+2 y}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{\prime } = -x -\sqrt {x^{2}+2 y}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +y^{\prime }-{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\arcsin \left (y^{\prime }\right )
\] |
[_Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\frac {m}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = m^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\sqrt {b^{2}+a^{2} y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}-b^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\frac {a}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +y^{\prime }-{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +a y^{\prime } \left (1-y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\sqrt {1+{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}\left (y-y^{\prime } x \right ) \left (y^{\prime }-1\right ) = y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} x -y^{\prime } y+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}+a^{4} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = 1
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = m
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+b^{2}-y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
|