|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}{y^{\prime }}^{2} = x^{2} y^{2} \] |
separable |
[_separable] |
✓ |
✓ |
0.364 |
|
|
\[ {}{y^{\prime }}^{2} = \left (y-1\right ) y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.499 |
|
|
\[ {}{y^{\prime }}^{2} = \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.505 |
|
|
\[ {}{y^{\prime }}^{2} = a^{2} y^{n} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.709 |
|
|
\[ {}{y^{\prime }}^{2} = a^{2} \left (1-\ln \left (y\right )^{2}\right ) y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.108 |
|
|
\[ {}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) = 0 \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.375 |
|
|
\[ {}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) = 0 \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
0.869 |
|
|
\[ {}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) = 0 \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.198 |
|
|
\[ {}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right ) = 0 \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
4.577 |
|
|
\[ {}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2} \] |
first_order_nonlinear_p_but_separable |
[_separable] |
✓ |
✓ |
5.11 |
|
|
\[ {}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right ) \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
2.323 |
|
|
\[ {}{y^{\prime }}^{2}+2 y^{\prime }+x = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.255 |
|
|
\[ {}{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right ) = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.232 |
|
|
\[ {}{y^{\prime }}^{2}-2 y^{\prime }-y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.415 |
|
|
\[ {}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.228 |
|
|
\[ {}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.191 |
|
|
\[ {}{y^{\prime }}^{2}+a y^{\prime }+b = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.222 |
|
|
\[ {}{y^{\prime }}^{2}+a y^{\prime }+b x = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.295 |
|
|
\[ {}{y^{\prime }}^{2}+a y^{\prime }+b y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.654 |
|
|
\[ {}{y^{\prime }}^{2}+x y^{\prime }+1 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.368 |
|
|
\[ {}{y^{\prime }}^{2}+x y^{\prime }-y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.206 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }+y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.213 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.34 |
|
|
\[ {}{y^{\prime }}^{2}+x y^{\prime }+x -y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.307 |
|
|
\[ {}{y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.199 |
|
|
\[ {}{y^{\prime }}^{2}-\left (1+x \right ) y^{\prime }+y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.222 |
|
|
\[ {}{y^{\prime }}^{2}-\left (2-x \right ) y^{\prime }+1-y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.239 |
|
|
\[ {}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.212 |
|
|
\[ {}{y^{\prime }}^{2}-2 x y^{\prime }+1 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.351 |
|
|
\[ {}{y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.238 |
|
|
\[ {}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.315 |
|
|
\[ {}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.279 |
|
|
\[ {}{y^{\prime }}^{2}-2 x y^{\prime }+2 y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.225 |
|
|
\[ {}{y^{\prime }}^{2}-\left (2 x +1\right ) y^{\prime }-x \left (1-x \right ) = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.326 |
|
|
\[ {}{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.299 |
|
|
\[ {}{y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.36 |
|
|
\[ {}{y^{\prime }}^{2}-4 \left (1+x \right ) y^{\prime }+4 y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.201 |
|
|
\[ {}{y^{\prime }}^{2}+a x y^{\prime } = b c \,x^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.256 |
|
|
\[ {}{y^{\prime }}^{2}-a x y^{\prime }+a y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.234 |
|
|
\[ {}{y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.085 |
|
|
\[ {}{y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c = b y \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.229 |
|
|
\[ {}{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 x y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.228 |
|
|
\[ {}{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
9.748 |
|
|
\[ {}{y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.714 |
|
|
\[ {}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 y x^{4} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.308 |
|
|
\[ {}{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.265 |
|
|
\[ {}{y^{\prime }}^{2}+y y^{\prime } = x \left (x +y\right ) \] |
linear, quadrature |
[_quadrature] |
✓ |
✓ |
0.347 |
|
|
\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.498 |
|
|
\[ {}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.279 |
|
|
\[ {}{y^{\prime }}^{2}-2 y y^{\prime }-2 x = 0 \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
0.417 |
|
|
\[ {}{y^{\prime }}^{2}+\left (2 y+1\right ) y^{\prime }+y \left (y-1\right ) = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
142.175 |
|
|
\[ {}{y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 x y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.291 |
|
|
\[ {}{y^{\prime }}^{2}-\left (1+4 y\right ) y^{\prime }+\left (1+4 y\right ) y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.342 |
|
|
\[ {}{y^{\prime }}^{2}-2 \left (-3 y+1\right ) y^{\prime }-\left (4-9 y\right ) y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.604 |
|
|
\[ {}{y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right ) = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.172 |
|
|
\[ {}{y^{\prime }}^{2}+a y y^{\prime }-x a = 0 \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
0.776 |
|
|
\[ {}{y^{\prime }}^{2}-a y y^{\prime }-x a = 0 \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
0.467 |
|
|
\[ {}{y^{\prime }}^{2}+\left (x a +b y\right ) y^{\prime }+a b x y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.336 |
|
|
\[ {}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
4.219 |
|
|
\[ {}{y^{\prime }}^{2}-\left (2 x y+1\right ) y^{\prime }+2 x y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.297 |
|
|
\[ {}{y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.833 |
|
|
\[ {}{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3} = 0 \] |
quadrature, separable |
[_separable] |
✓ |
✓ |
0.333 |
|
|
\[ {}{y^{\prime }}^{2}+x y^{2} y^{\prime }+y^{3} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
75.362 |
|
|
\[ {}{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
18.745 |
|
|
\[ {}{y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.554 |
|
|
\[ {}{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.079 |
|
|
\[ {}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
4.494 |
|
|
\[ {}{y^{\prime }}^{2}-3 x y^{\frac {2}{3}} y^{\prime }+9 y^{\frac {5}{3}} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
6.318 |
|
|
\[ {}{y^{\prime }}^{2} = {\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right ) \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.48 |
|
|
\[ {}2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.306 |
|
|
\[ {}2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.204 |
|
|
\[ {}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 x y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
7.216 |
|
|
\[ {}2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right ) = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.972 |
|
|
\[ {}3 {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.305 |
|
|
\[ {}3 {y^{\prime }}^{2}+4 x y^{\prime }+x^{2}-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.894 |
|
|
\[ {}4 {y^{\prime }}^{2} = 9 x \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.227 |
|
|
\[ {}4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
11.534 |
|
|
\[ {}4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y} = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.481 |
|
|
\[ {}5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.383 |
|
|
\[ {}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.349 |
|
|
\[ {}9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
82.548 |
|
|
\[ {}x {y^{\prime }}^{2} = a \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.234 |
|
|
\[ {}x {y^{\prime }}^{2} = -x^{2}+a \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.574 |
|
|
\[ {}x {y^{\prime }}^{2} = y \] |
dAlembert, first_order_nonlinear_p_but_separable |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.632 |
|
|
\[ {}x {y^{\prime }}^{2}+x -2 y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.435 |
|
|
\[ {}x {y^{\prime }}^{2}+y^{\prime } = y \] |
dAlembert |
[_rational, _dAlembert] |
✓ |
✓ |
0.362 |
|
|
\[ {}x {y^{\prime }}^{2}+2 y^{\prime }-y = 0 \] |
dAlembert |
[_rational, _dAlembert] |
✓ |
✓ |
0.366 |
|
|
\[ {}x {y^{\prime }}^{2}-2 y^{\prime }-y = 0 \] |
dAlembert |
[_rational, _dAlembert] |
✓ |
✓ |
0.329 |
|
|
\[ {}x {y^{\prime }}^{2}+4 y^{\prime }-2 y = 0 \] |
dAlembert |
[_rational, _dAlembert] |
✓ |
✓ |
0.349 |
|
|
\[ {}x {y^{\prime }}^{2}+x y^{\prime }-y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.375 |
|
|
\[ {}x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.241 |
|
|
\[ {}x {y^{\prime }}^{2}+y y^{\prime }+a = 0 \] |
dAlembert |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
0.438 |
|
|
\[ {}x {y^{\prime }}^{2}-y y^{\prime }+a = 0 \] |
clairaut |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.263 |
|
|
\[ {}x {y^{\prime }}^{2}-y y^{\prime }+x a = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.434 |
|
|
\[ {}x {y^{\prime }}^{2}+y y^{\prime }+x^{3} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
8.079 |
|
|
\[ {}x {y^{\prime }}^{2}-y y^{\prime }+a y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.448 |
|
|
\[ {}x {y^{\prime }}^{2}+y y^{\prime }-y^{4} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.631 |
|
|
\[ {}x {y^{\prime }}^{2}+\left (-y+a \right ) y^{\prime }+b = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.294 |
|
|
\[ {}x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.258 |
|
|
\[ {}x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.279 |
|
|
|
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