Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x^{2} {y^{\prime }}^{2}-y^{2} = 0 \] |
2 |
1 |
2 |
separable |
[_separable] |
✓ |
✓ |
0.528 |
|
|
\[ {}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0 \] |
2 |
1 |
2 |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.503 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0 \] |
2 |
1 |
2 |
separable |
[_separable] |
✓ |
✓ |
0.602 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+x y^{\prime }-y^{2}-y = 0 \] |
2 |
1 |
2 |
separable |
[_separable] |
✓ |
✓ |
0.618 |
|
|
\[ {}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0 \] |
2 |
1 |
2 |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.421 |
|
|
\[ {}{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y = 0 \] |
2 |
1 |
2 |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.398 |
|
|
\[ {}x {y^{\prime }}^{2}-\left (1+x y\right ) y^{\prime }+y = 0 \] |
2 |
1 |
2 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.282 |
|
|
\[ {}{y^{\prime }}^{2}-x^{2} y^{2} = 0 \] |
2 |
1 |
2 |
separable |
[_separable] |
✓ |
✓ |
0.465 |
|
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2} \] |
2 |
1 |
3 |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.195 |
|
|
\[ {}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0 \] |
2 |
2 |
3 |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.532 |
|
|
\[ {}{y^{\prime }}^{2}-x y \left (x +y\right ) y^{\prime }+x^{3} y^{3} = 0 \] |
2 |
1 |
2 |
separable |
[_separable] |
✓ |
✓ |
0.546 |
|
|
\[ {}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0 \] |
2 |
1 |
3 |
quadrature, homogeneousTypeD2 |
[_quadrature] |
✓ |
✓ |
0.836 |
|
|
\[ {}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2} \] |
2 |
1 |
3 |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.11 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y = 0 \] |
2 |
2 |
3 |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.536 |
|
|
\[ {}\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2} \] |
2 |
1 |
5 |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.7 |
|
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (y-x \right ) = 0 \] |
2 |
1 |
4 |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.439 |
|
|
\[ {}x y \left (x^{2}+y^{2}\right ) \left ({y^{\prime }}^{2}-1\right ) = y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right ) \] |
2 |
1 |
6 |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.103 |
|
|
\[ {}x {y^{\prime }}^{3}-\left (x^{2}+x +y\right ) {y^{\prime }}^{2}+\left (x^{2}+x y+y\right ) y^{\prime }-x y = 0 \] |
3 |
1 |
3 |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.477 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0 \] |
2 |
2 |
3 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.403 |
|
|
\[ {}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0 \] |
2 |
3 |
3 |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.368 |
|
|
\[ {}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
2 |
5 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.311 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.498 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }+y = 0 \] |
2 |
2 |
2 |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.262 |
|
|
\[ {}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \] |
2 |
2 |
2 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.935 |
|
|
\[ {}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \] |
2 |
2 |
6 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
6.27 |
|
|
\[ {}4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y = 0 \] |
2 |
1 |
3 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
22.549 |
|
|
\[ {}{y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0 \] |
3 |
5 |
4 |
dAlembert |
[_dAlembert] |
✓ |
✓ |
151.773 |
|
|
\[ {}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0 \] |
3 |
1 |
10 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
114.33 |
|
|
\[ {}{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y = 0 \] |
2 |
2 |
2 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.641 |
|
|
\[ {}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \] |
2 |
2 |
2 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.579 |
|
|
\[ {}2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0 \] |
3 |
1 |
4 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
108.481 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }+y = 0 \] |
2 |
2 |
2 |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.292 |
|
|
\[ {}y = x y^{\prime }+k {y^{\prime }}^{2} \] |
2 |
2 |
2 |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.302 |
|
|
\[ {}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0 \] |
2 |
2 |
3 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.955 |
|
|
\[ {}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0 \] |
2 |
2 |
4 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.307 |
|
|
\[ {}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0 \] |
2 |
3 |
3 |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.375 |
|
|
\[ {}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
2 |
5 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.55 |
|
|
\[ {}x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0 \] |
2 |
3 |
3 |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.401 |
|
|
\[ {}y^{\prime } \left (x y^{\prime }-y+k \right )+a = 0 \] |
2 |
3 |
3 |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.422 |
|
|
\[ {}x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0 \] |
3 |
1 |
3 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
23.949 |
|
|
\[ {}y = x^{6} {y^{\prime }}^{3}-x y^{\prime } \] |
3 |
1 |
3 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
94.164 |
|
|
\[ {}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0 \] |
4 |
0 |
5 |
unknown |
[[_1st_order, _with_linear_symmetries]] |
✗ |
N/A |
3.405 |
|
|
\[ {}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0 \] |
3 |
4 |
4 |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.012 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.461 |
|
|
\[ {}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0 \] |
3 |
4 |
2 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
94.181 |
|
|
\[ {}2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0 \] |
2 |
3 |
1 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.528 |
|
|
\[ {}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
3 |
4 |
4 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
6.592 |
|
|
\[ {}4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0 \] |
2 |
2 |
4 |
dAlembert |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
0.581 |
|
|
\[ {}{y^{\prime }}^{3}-x y^{\prime }+2 y = 0 \] |
3 |
4 |
2 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
92.384 |
|
|
\[ {}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0 \] |
2 |
3 |
2 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.694 |
|
|
\[ {}2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0 \] |
2 |
3 |
1 |
dAlembert |
[_rational, _dAlembert] |
✓ |
✓ |
1.139 |
|
|
\[ {}5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.63 |
|
|
\[ {}{y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.612 |
|
|
\[ {}y = x y^{\prime }+x^{3} {y^{\prime }}^{2} \] |
2 |
2 |
0 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
25.161 |
|
|
\[ {}y^{\prime \prime } = x {y^{\prime }}^{3} \] |
1 |
2 |
2 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.338 |
|
|
\[ {}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.013 |
|
|
\[ {}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.807 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
2 |
3 |
second_order_integrable_as_is, second_order_ode_missing_x, exact nonlinear second order ode |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.438 |
|
|
\[ {}y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
1 |
3 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.994 |
|
|
\[ {}\left (y+1\right ) y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
2 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.032 |
|
|
\[ {}2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
2 |
2 |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.347 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{5} \] |
1 |
1 |
1 |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.078 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x = 0 \] |
1 |
1 |
1 |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.556 |
|
|
\[ {}y^{\prime \prime } = 2 y {y^{\prime }}^{3} \] |
1 |
3 |
4 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
142.67 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
3 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.911 |
|
|
\[ {}y^{\prime \prime }+\beta ^{2} y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.576 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
1 |
3 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.004 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime } = y^{\prime } \] |
1 |
1 |
1 |
second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.085 |
|
|
\[ {}y^{\prime \prime } = x {y^{\prime }}^{2} \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.128 |
|
|
\[ {}y^{\prime \prime } = x {y^{\prime }}^{2} \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.937 |
|
|
\[ {}y^{\prime \prime } = -{\mathrm e}^{-2 y} \] |
1 |
2 |
1 |
second_order_ode_missing_x, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
63.49 |
|
|
\[ {}y^{\prime \prime } = -{\mathrm e}^{-2 y} \] |
1 |
2 |
1 |
second_order_ode_missing_x, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
62.529 |
|
|
\[ {}2 y^{\prime \prime } = \sin \left (2 y\right ) \] |
1 |
2 |
1 |
second_order_ode_missing_x, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
10.706 |
|
|
\[ {}2 y^{\prime \prime } = \sin \left (2 y\right ) \] |
1 |
2 |
1 |
second_order_ode_missing_x, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
6.464 |
|
|
\[ {}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3 \] |
1 |
1 |
1 |
kovacic, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.612 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.592 |
|
|
\[ {}y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2} \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.592 |
|
|
\[ {}2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right ) \] |
1 |
2 |
2 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
3.171 |
|
|
\[ {}x^{2} y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.645 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.585 |
|
|
\[ {}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
2 |
3 |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.48 |
|
|
\[ {}y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-y y^{\prime } \cos \left (y\right )\right ) \] |
1 |
1 |
2 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
5.556 |
|
|
\[ {}\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0 \] |
1 |
1 |
4 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.111 |
|
|
\[ {}\left (y y^{\prime \prime }+1+{y^{\prime }}^{2}\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3} \] |
2 |
4 |
7 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
11.033 |
|
|
\[ {}x^{2} y^{\prime \prime } = y^{\prime } \left (2 x -y^{\prime }\right ) \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.155 |
|
|
\[ {}x^{2} y^{\prime \prime } = y^{\prime } \left (3 x -2 y^{\prime }\right ) \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.875 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime } \left (2-3 x y^{\prime }\right ) \] |
1 |
1 |
1 |
second_order_ode_missing_y, second_order_nonlinear_solved_by_mainardi_lioville_method |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.083 |
|
|
\[ {}x^{4} y^{\prime \prime } = y^{\prime } \left (y^{\prime }+x^{3}\right ) \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.091 |
|
|
\[ {}y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2} \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.299 |
|
|
\[ {}{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0 \] |
2 |
4 |
2 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
141.525 |
|
|
\[ {}{y^{\prime \prime }}^{2}-x y^{\prime \prime }+y^{\prime } = 0 \] |
2 |
2 |
2 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.686 |
|
|
\[ {}{y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \] |
3 |
1 |
3 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✗ |
126.669 |
|
|
\[ {}3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1 \] |
1 |
3 |
3 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
8.366 |
|
|
\[ {}4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3 \] |
1 |
4 |
4 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.635 |
|
|
|
|||||||||
|
|
|||||||||