| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.859 |
|
| \begin{align*}
4 y^{2} {y^{\prime }}^{2} x^{2}&=\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.381 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.842 |
|
| \begin{align*}
3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.823 |
|
| \begin{align*}
9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.864 |
|
| \begin{align*}
9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
153.231 |
|
| \begin{align*}
{y^{\prime }}^{3}&=b x +a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \begin{align*}
{y^{\prime }}^{3}&=a \,x^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.875 |
|
| \begin{align*}
{y^{\prime }}^{3}+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.006 |
|
| \begin{align*}
{y^{\prime }}^{3}&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
9.900 |
|
| \begin{align*}
{y^{\prime }}^{3}&=\left (y-a \right )^{2} \left (y-b \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.049 |
|
| \begin{align*}
{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.565 |
|
| \begin{align*}
{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.318 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }+a -b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
116.792 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{3}&={\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
11.115 |
|
| \begin{align*}
{y^{\prime }}^{3}-7 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
{y^{\prime }}^{3}-y^{\prime } x +a y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
57.150 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
2.862 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
118.776 |
|
| \begin{align*}
{y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.676 |
|
| \begin{align*}
{y^{\prime }}^{3}+a x y^{\prime }-a y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.393 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.649 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
54.885 |
|
| \begin{align*}
{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.553 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.181 |
|
| \begin{align*}
{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
10.638 |
|
| \begin{align*}
{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 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
20.389 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.597 |
|
| \begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.319 |
|
| \begin{align*}
{y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.026 |
|
| \begin{align*}
{y^{\prime }}^{3}+a_{0} {y^{\prime }}^{2}+a_{1} y^{\prime }+a_{2} +a_{3} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
3.951 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (1-3 x \right ) {y^{\prime }}^{2}-x \left (1-3 x \right ) y^{\prime }-1-x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.589 |
|
| \begin{align*}
{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
110.450 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.802 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+y x +y^{2}\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+x y^{2} \left (y^{4}+x y^{2}+x^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
11.019 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.483 |
|
| \begin{align*}
3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.055 |
|
| \begin{align*}
4 {y^{\prime }}^{3}+4 y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.368 |
|
| \begin{align*}
8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2}&=27 x +27 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.678 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.387 |
|
| \begin{align*}
x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.689 |
|
| \begin{align*}
4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.881 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.838 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
5.805 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.855 |
|
| \begin{align*}
2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 y x \right ) y y^{\prime }+2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
504.702 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{3}-y {y^{\prime }}^{2} x^{3}-x^{2} y^{2} y^{\prime }+x y^{3}&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
77.650 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{3}-y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
2.025 |
|
| \begin{align*}
y {y^{\prime }}^{3}-3 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.151 |
|
| \begin{align*}
2 y {y^{\prime }}^{3}-3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
37.506 |
|
| \begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.944 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{3}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
3.496 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.115 |
|
| \begin{align*}
4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.260 |
|
| \begin{align*}
16 y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.249 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✗ |
497.112 |
|
| \begin{align*}
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 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
3.257 |
|
| \begin{align*}
y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.411 |
|
| \begin{align*}
{y^{\prime }}^{4}&=\left (y-a \right )^{3} \left (y-b \right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.455 |
|
| \begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.088 |
|
| \begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.201 |
|
| \begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.802 |
|
| \begin{align*}
{y^{\prime }}^{4}+y^{\prime } x -3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
7.066 |
|
| \begin{align*}
{y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 y^{2} y^{\prime } x -16 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
315.697 |
|
| \begin{align*}
{y^{\prime }}^{4}+4 y {y^{\prime }}^{3}+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
124.345 |
|
| \begin{align*}
2 {y^{\prime }}^{4}-y y^{\prime }-2&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
95.340 |
|
| \begin{align*}
{y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1521.023 |
|
| \begin{align*}
3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.019 |
|
| \begin{align*}
{y^{\prime }}^{6}&=\left (y-a \right )^{4} \left (y-b \right )^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.754 |
|
| \begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
34.794 |
|
| \begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
37.089 |
|
| \begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
37.614 |
|
| \begin{align*}
x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right )&=a^{2} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
1.040 |
|
| \begin{align*}
2 \sqrt {a y^{\prime }}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
51.257 |
|
| \begin{align*}
\left (x -y\right ) \sqrt {y^{\prime }}&=a \left (1+y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.773 |
|
| \begin{align*}
2 \left (1+y\right )^{{3}/{2}}+3 y^{\prime } x -3 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
64.575 |
|
| \begin{align*}
\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.618 |
|
| \begin{align*}
\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.856 |
|
| \begin{align*}
\sqrt {1+{y^{\prime }}^{2}}&=y^{\prime } x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.931 |
|
| \begin{align*}
\sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
13.010 |
|
| \begin{align*}
a \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
3.118 |
|
| \begin{align*}
a x \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
53.815 |
|
| \begin{align*}
a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+y^{\prime } x -y&=0 \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
44.141 |
|
| \begin{align*}
\cos \left (y^{\prime }\right )+y^{\prime } x&=y \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.369 |
|
| \begin{align*}
a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.440 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )+y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.414 |
|
| \begin{align*}
y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right )&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
62.823 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right )&=y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.137 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2}&=1 \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
9.422 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.063 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
29.763 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+y^{\prime } x +a&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.185 |
|