# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
\[ {}x \left (x -2 y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-2 x y+y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.077 |
|
\[ {}x \left (x -2 y\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-2 x y+y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
221.604 |
|
\[ {}y^{2} {y^{\prime }}^{2} = a^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.414 |
|
\[ {}y^{2} {y^{\prime }}^{2}-a^{2}+y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.568 |
|
\[ {}y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
4.924 |
|
\[ {}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.02 |
|
\[ {}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 x a +y^{2} = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.564 |
|
\[ {}y^{2} {y^{\prime }}^{2}-\left (1+x \right ) y y^{\prime }+x = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.453 |
|
\[ {}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.355 |
|
\[ {}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a -y^{2} = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
8.827 |
|
\[ {}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.358 |
|
\[ {}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2} = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.385 |
|
\[ {}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +x^{2} a +\left (1-a \right ) y^{2} = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
3.305 |
|
\[ {}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.752 |
|
\[ {}\left (a^{2}-y^{2}\right ) {y^{\prime }}^{2} = y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.974 |
|
\[ {}\left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
4.385 |
|
\[ {}\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.087 |
|
\[ {}\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
183.437 |
|
\[ {}\left (\left (-a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.123 |
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2} \] |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.948 |
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-\left (x -y\right ) y = 0 \] |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.136 |
|
\[ {}\left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
11.89 |
|
\[ {}2 y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-1+x^{2}+y^{2} = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
74.107 |
|
\[ {}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.616 |
|
\[ {}4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.59 |
|
\[ {}\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0 \] |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.957 |
|
\[ {}9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
3.781 |
|
\[ {}\left (2-3 y\right )^{2} {y^{\prime }}^{2} = 4-4 y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.474 |
|
\[ {}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
11.996 |
|
\[ {}\left (-b +a \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2} = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
3.382 |
|
\[ {}a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
19.815 |
|
\[ {}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x \,a^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.448 |
|
\[ {}x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0 \] |
unknown |
[_rational] |
✗ |
N/A |
7.855 |
|
\[ {}2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.208 |
|
\[ {}4 x^{2} y^{2} {y^{\prime }}^{2} = \left (x^{2}+y^{2}\right )^{2} \] |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.309 |
|
\[ {}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
5.898 |
|
\[ {}3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1 = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.103 |
|
\[ {}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.038 |
|
\[ {}9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2} = 0 \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.399 |
|
\[ {}{y^{\prime }}^{3} = b x +a \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.587 |
|
\[ {}{y^{\prime }}^{3} = a \,x^{n} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.45 |
|
\[ {}{y^{\prime }}^{3}+x -y = 0 \] |
dAlembert, first_order_nonlinear_p_but_linear_in_x_y |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.728 |
|
\[ {}{y^{\prime }}^{3} = \left (a +b y+c y^{2}\right ) f \left (x \right ) \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.733 |
|
\[ {}{y^{\prime }}^{3} = \left (y-a \right )^{2} \left (y-b \right )^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.214 |
|
\[ {}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} = 0 \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.263 |
|
\[ {}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} = 0 \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
188.713 |
|
\[ {}{y^{\prime }}^{3}+y^{\prime }+a -b x = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.565 |
|
\[ {}{y^{\prime }}^{3}+y^{\prime }-y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.901 |
|
\[ {}{y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.155 |
|
\[ {}{y^{\prime }}^{3}-7 y^{\prime }+6 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.286 |
|
\[ {}{y^{\prime }}^{3}-x y^{\prime }+a y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
169.119 |
|
\[ {}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
3.142 |
|
\[ {}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
99.775 |
|
\[ {}{y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.445 |
|
\[ {}{y^{\prime }}^{3}+a x y^{\prime }-a y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.434 |
|
\[ {}{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.503 |
|
\[ {}{y^{\prime }}^{3}-2 y y^{\prime }+y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.445 |
|
\[ {}{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
16.117 |
|
\[ {}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
17.514 |
|
\[ {}{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right ) = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.973 |
|
\[ {}{y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y} = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
104.449 |
|
\[ {}{y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.296 |
|
\[ {}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.492 |
|
\[ {}{y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.56 |
|
\[ {}{y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
167.053 |
|
\[ {}{y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a2} +\operatorname {a3} y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.897 |
|
\[ {}{y^{\prime }}^{3}+\left (-3 x +1\right ) {y^{\prime }}^{2}-x \left (-3 x +1\right ) y^{\prime }-1-x^{3} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.723 |
|
\[ {}{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.787 |
|
\[ {}{y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.78 |
|
\[ {}{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.313 |
|
\[ {}{y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0 \] |
linear, quadrature |
[_quadrature] |
✓ |
✓ |
0.622 |
|
\[ {}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+x y+y^{2}\right ) y^{\prime }-x^{3} y^{3} = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.481 |
|
\[ {}{y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.987 |
|
\[ {}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
100.448 |
|
\[ {}2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.233 |
|
\[ {}3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
86.383 |
|
\[ {}4 {y^{\prime }}^{3}+4 y^{\prime } = x \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.579 |
|
\[ {}8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.527 |
|
\[ {}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.745 |
|
\[ {}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.448 |
|
\[ {}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
93.679 |
|
\[ {}2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.613 |
|
\[ {}4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
13.632 |
|
\[ {}8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
23.288 |
|
\[ {}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
3.786 |
|
\[ {}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.54 |
|
\[ {}x {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
315.692 |
|
\[ {}2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
21.441 |
|
\[ {}x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3} = 1 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
18.007 |
|
\[ {}x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
100.911 |
|
\[ {}y {y^{\prime }}^{3}-3 x y^{\prime }+3 y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
173.355 |
|
\[ {}2 y {y^{\prime }}^{3}-3 x y^{\prime }+2 y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
154.286 |
|
\[ {}\left (2 y+x \right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (y+2 x \right ) y^{\prime } = 0 \] |
quadrature, homogeneousTypeD2 |
[_quadrature] |
✓ |
✓ |
1.062 |
|
\[ {}y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
81.401 |
|
\[ {}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
87.318 |
|
\[ {}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
47.616 |
|
\[ {}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
86.735 |
|
\[ {}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
175.365 |
|
\[ {}y^{3} {y^{\prime }}^{3}-\left (-3 x +1\right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2} = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
134.116 |
|
\[ {}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
143.295 |
|
|
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|
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