|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x {y^{\prime }}^{2}-\left (3 x -y\right ) y^{\prime }+y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.56 |
|
|
\[ {}x {y^{\prime }}^{2}+a +b x -y-b y = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
1.33 |
|
|
\[ {}x {y^{\prime }}^{2}-2 y y^{\prime }+a = 0 \] |
dAlembert |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
0.435 |
|
|
\[ {}x {y^{\prime }}^{2}-2 y y^{\prime }+x a = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.293 |
|
|
\[ {}x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.315 |
|
|
\[ {}x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
5.328 |
|
|
\[ {}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.382 |
|
|
\[ {}x {y^{\prime }}^{2}-a y y^{\prime }+b = 0 \] |
dAlembert |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
54.294 |
|
|
\[ {}x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.714 |
|
|
\[ {}x {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.249 |
|
|
\[ {}x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2} = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.321 |
|
|
\[ {}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.332 |
|
|
\[ {}\left (1+x \right ) {y^{\prime }}^{2} = y \] |
dAlembert, first_order_nonlinear_p_but_separable |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.651 |
|
|
\[ {}\left (1+x \right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.295 |
|
|
\[ {}\left (a -x \right ) {y^{\prime }}^{2}+y y^{\prime }-b = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.297 |
|
|
\[ {}2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0 \] |
dAlembert |
[_rational, _dAlembert] |
✓ |
✓ |
0.555 |
|
|
\[ {}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.287 |
|
|
\[ {}\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.311 |
|
|
\[ {}\left (5+3 x \right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y = 0 \] |
dAlembert |
[_rational, _dAlembert] |
✓ |
✓ |
1.172 |
|
|
\[ {}4 x {y^{\prime }}^{2} = \left (a -3 x \right )^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.289 |
|
|
\[ {}4 x {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.264 |
|
|
\[ {}4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0 \] |
dAlembert |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
0.332 |
|
|
\[ {}4 x {y^{\prime }}^{2}+4 y y^{\prime } = 1 \] |
dAlembert |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
0.421 |
|
|
\[ {}4 x {y^{\prime }}^{2}+4 y y^{\prime }-y^{4} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.632 |
|
|
\[ {}4 \left (2-x \right ) {y^{\prime }}^{2}+1 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.267 |
|
|
\[ {}16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
3.387 |
|
|
\[ {}x^{2} {y^{\prime }}^{2} = a^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.255 |
|
|
\[ {}x^{2} {y^{\prime }}^{2} = y^{2} \] |
separable |
[_separable] |
✓ |
✓ |
0.419 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+x^{2}-y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.098 |
|
|
\[ {}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2} \] |
linear |
[_linear] |
✓ |
✓ |
0.527 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+y^{2}-y^{4} = 0 \] |
first_order_nonlinear_p_but_separable |
[_separable] |
✓ |
✓ |
0.937 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-x y^{\prime }+y \left (1-y\right ) = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.51 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y = 0 \] |
unknown |
[_rational] |
✗ |
N/A |
1.644 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x +y \left (y+1\right ) = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
3.608 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2} = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.108 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-\left (2 x y+1\right ) y^{\prime }+1+y^{2} = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.423 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-\left (a +2 x y\right ) y^{\prime }+y^{2} = 0 \] |
clairaut |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.525 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.512 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+2 x \left (y+2 x \right ) y^{\prime }-4 a +y^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
4.254 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
9.777 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.542 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+x^{3}+2 y^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
16.458 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.556 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y = 0 \] |
separable |
[_separable] |
✓ |
✓ |
3.259 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.499 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+x \left (x^{2}+x y-2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y = 0 \] |
unknown |
[_rational] |
❇ |
N/A |
7.028 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+\left (y+2 x \right ) y y^{\prime }+y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.978 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.935 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.434 |
|
|
\[ {}\left (-x^{2}+1\right ) {y^{\prime }}^{2} = 1-y^{2} \] |
first_order_nonlinear_p_but_separable |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.449 |
|
|
\[ {}\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+4 x^{2} = 0 \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
143.288 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2} = b^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.341 |
|
|
\[ {}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.347 |
|
|
\[ {}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2} = b^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.466 |
|
|
\[ {}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2} = x^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.342 |
|
|
\[ {}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
90.2 |
|
|
\[ {}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.523 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+b +y^{2} = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
2.242 |
|
|
\[ {}4 x^{2} {y^{\prime }}^{2}-4 x y y^{\prime } = 8 x^{3}-y^{2} \] |
linear |
[_linear] |
✓ |
✓ |
0.633 |
|
|
\[ {}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+a \left (1-a \right ) x^{2}+y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.332 |
|
|
\[ {}\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-a^{2} x^{2}+y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
240.952 |
|
|
\[ {}x^{3} {y^{\prime }}^{2} = a \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.247 |
|
|
\[ {}x^{3} {y^{\prime }}^{2}+x y^{\prime }-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
16.725 |
|
|
\[ {}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
5.416 |
|
|
\[ {}x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
6.466 |
|
|
\[ {}4 x \left (a -x \right ) \left (-x +b \right ) {y^{\prime }}^{2} = \left (a b -2 x \left (a +b \right )+2 x^{2}\right )^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.593 |
|
|
\[ {}x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.308 |
|
|
\[ {}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.475 |
|
|
\[ {}x^{4} {y^{\prime }}^{2}+x y^{2} y^{\prime }-y^{3} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
38.073 |
|
|
\[ {}x^{2} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+1 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.56 |
|
|
\[ {}3 x^{4} {y^{\prime }}^{2}-x y-y = 0 \] |
first_order_nonlinear_p_but_separable |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
0.737 |
|
|
\[ {}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
5.716 |
|
|
\[ {}x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.532 |
|
|
\[ {}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.646 |
|
|
\[ {}y {y^{\prime }}^{2} = a \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.413 |
|
|
\[ {}y {y^{\prime }}^{2} = x \,a^{2} \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.892 |
|
|
\[ {}y {y^{\prime }}^{2} = {\mathrm e}^{2 x} \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.884 |
|
|
\[ {}y {y^{\prime }}^{2}+2 a x y^{\prime }-a y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.69 |
|
|
\[ {}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.92 |
|
|
\[ {}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
16.224 |
|
|
\[ {}y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.815 |
|
|
\[ {}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
6.483 |
|
|
\[ {}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.442 |
|
|
\[ {}y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.855 |
|
|
\[ {}y {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+x = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.249 |
|
|
\[ {}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.379 |
|
|
\[ {}y {y^{\prime }}^{2}+y = a \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.975 |
|
|
\[ {}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.695 |
|
|
\[ {}\left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.658 |
|
|
\[ {}2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.544 |
|
|
\[ {}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
6.322 |
|
|
\[ {}\left (1-a y\right ) {y^{\prime }}^{2} = a y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.126 |
|
|
\[ {}\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y y^{\prime } = 0 \] |
quadrature, first_order_ode_lie_symmetry_calculated |
[_quadrature] |
✓ |
✓ |
0.816 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.343 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.481 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.465 |
|
|
\[ {}x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.448 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-x y = 0 \] |
unknown |
[_rational] |
❇ |
N/A |
233.874 |
|
|
\[ {}x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[_rational] |
✓ |
✓ |
66.336 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.702 |
|
|
|
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