# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
\[ {}y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.174 |
|
\[ {}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.326 |
|
\[ {}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
22.196 |
|
\[ {}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.781 |
|
\[ {}y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.495 |
|
\[ {}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.971 |
|
\[ {}\left (-2 x +y\right ) {y^{\prime }}^{2}-2 \left (-1+x \right ) y^{\prime }+y-2 = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.936 |
|
\[ {}2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.817 |
|
\[ {}4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.879 |
|
\[ {}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.589 |
|
\[ {}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
1.192 |
|
\[ {}\left (a y+b \right ) \left (1+{y^{\prime }}^{2}\right )-c = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
6.11 |
|
\[ {}\left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0} = 0 \] |
dAlembert |
[_rational, _dAlembert] |
✓ |
✗ |
9.348 |
|
\[ {}\left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0 \] |
unknown |
[_rational] |
❇ |
N/A |
2.563 |
|
\[ {}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.627 |
|
\[ {}x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0 \] |
unknown |
[_rational] |
❇ |
N/A |
24.905 |
|
\[ {}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.207 |
|
\[ {}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 x y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
219.059 |
|
\[ {}a x y {y^{\prime }}^{2}-\left (a y^{2}+b \,x^{2}+c \right ) y^{\prime }+b x y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[_rational] |
✓ |
✓ |
100.549 |
|
\[ {}y^{2} {y^{\prime }}^{2}+y^{2}-a^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.729 |
|
\[ {}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
6.134 |
|
\[ {}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+y^{2}-4 x a +4 a^{2} = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
5.074 |
|
\[ {}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a y^{2}+b x +c = 0 \] |
unknown |
[_rational] |
✗ |
N/A |
5.374 |
|
\[ {}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2}+a = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
5.46 |
|
\[ {}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (1-a \right ) y^{2}+x^{2} a +\left (a -1\right ) b = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
7.128 |
|
\[ {}\left (y^{2}-a^{2}\right ) {y^{\prime }}^{2}+y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.174 |
|
\[ {}\left (y^{2}-2 x a +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
7.22 |
|
\[ {}\left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+\left (-a^{2}+1\right ) x^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.904 |
|
\[ {}\left (y^{2}+\left (1-a \right ) x^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (1-a \right ) y^{2}+x^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.012 |
|
\[ {}\left (y-x \right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
18.796 |
|
\[ {}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.49 |
|
\[ {}\left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.652 |
|
\[ {}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
10.343 |
|
\[ {}\left (-b +a \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }+a y^{2}-b \,x^{2}-a b = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
6.755 |
|
\[ {}\left (a y^{2}+b x +c \right ) {y^{\prime }}^{2}-b y y^{\prime }+d y^{2} = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
13.713 |
|
\[ {}\left (a y-b x \right )^{2} \left (a^{2} {y^{\prime }}^{2}+b^{2}\right )-c^{2} \left (a y^{\prime }+b \right )^{2} = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
30.862 |
|
\[ {}\left (\operatorname {b2} y+\operatorname {a2} x +\operatorname {c2} \right )^{2} {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {b0} y+\operatorname {a0} +\operatorname {c0} = 0 \] |
unknown |
[_rational] |
❇ |
N/A |
90.787 |
|
\[ {}x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y = 0 \] |
unknown |
[_rational] |
✗ |
N/A |
15.87 |
|
\[ {}x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0 \] |
separable, homogeneousTypeD2 |
[_separable] |
✓ |
✓ |
1.033 |
|
\[ {}x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (y-x \right ) y^{\prime }-y^{2} \left (x^{2} y-1\right ) = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
30.803 |
|
\[ {}\left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right ) = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
12.389 |
|
\[ {}\left (y^{4}+x^{2} y^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2} = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
8.423 |
|
\[ {}9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2} = 0 \] |
unknown |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
7.985 |
|
\[ {}x^{2} \left (y^{4} x^{2}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (-x^{2}+y^{2}\right ) y^{\prime }-y^{2} \left (x^{4} y^{2}-1\right ) = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
26.609 |
|
\[ {}\left (a^{2} \sqrt {x^{2}+y^{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a^{2} \sqrt {x^{2}+y^{2}}-y^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
22.525 |
|
\[ {}\left (a \left (x^{2}+y^{2}\right )^{\frac {3}{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (x^{2}+y^{2}\right )^{\frac {3}{2}}-y^{2} = 0 \] |
unknown |
[[_1st_order, _with_linear_symmetries]] |
✗ |
N/A |
39.219 |
|
\[ {}{y^{\prime }}^{2} \sin \left (y\right )+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4} = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
99.033 |
|
\[ {}{y^{\prime }}^{2} \left (a \cos \left (y\right )+b \right )-c \cos \left (y\right )+d = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
11.155 |
|
\[ {}f \left (x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.023 |
|
\[ {}\left (x^{2}+y^{2}\right ) f \left (\frac {x}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
6.807 |
|
\[ {}\left (x^{2}+y^{2}\right ) f \left (\frac {y}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
7.245 |
|
\[ {}{y^{\prime }}^{3}-\left (y-a \right )^{2} \left (y-b \right )^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.117 |
|
\[ {}{y^{\prime }}^{3}-f \left (x \right ) \left (a y^{2}+b y+c \right )^{2} = 0 \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.878 |
|
\[ {}{y^{\prime }}^{3}+y^{\prime }-y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.805 |
|
\[ {}{y^{\prime }}^{3}+x y^{\prime }-y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.293 |
|
\[ {}{y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.324 |
|
\[ {}{y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.045 |
|
\[ {}{y^{\prime }}^{3}-2 y y^{\prime }+y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.474 |
|
\[ {}{y^{\prime }}^{2}-a x y y^{\prime }+2 a y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
6.857 |
|
\[ {}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-y^{3} x^{3} = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.309 |
|
\[ {}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
15.946 |
|
\[ {}{y^{\prime }}^{3}+a {y^{\prime }}^{2}+b y+a b x = 0 \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
118.026 |
|
\[ {}{y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0 \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
163.223 |
|
\[ {}{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.626 |
|
\[ {}{y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+y^{4} x^{2}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6} = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
21.569 |
|
\[ {}a {y^{\prime }}^{3}+b {y^{\prime }}^{2}+c y^{\prime }-y-d = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
65.237 |
|
\[ {}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.572 |
|
\[ {}4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+3 y-x = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
10.048 |
|
\[ {}8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
19.878 |
|
\[ {}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{3}+b x \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+y^{\prime }+b x = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.499 |
|
\[ {}x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
179.494 |
|
\[ {}2 \left (x y^{\prime }+y\right )^{3}-y y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
17.451 |
|
\[ {}{y^{\prime }}^{3} \sin \left (x \right )-\left (y \sin \left (x \right )-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+y \sin \left (x \right ) = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.508 |
|
\[ {}2 y {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2 x y^{\prime }-x = 0 \] |
dAlembert, quadrature |
[_quadrature] |
✓ |
✓ |
0.523 |
|
\[ {}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
81.011 |
|
\[ {}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
81.368 |
|
\[ {}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
146.769 |
|
\[ {}x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
126.033 |
|
\[ {}{y^{\prime }}^{4}-\left (y-a \right )^{3} \left (y-b \right )^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
3.864 |
|
\[ {}{y^{\prime }}^{4}+3 \left (-1+x \right ) {y^{\prime }}^{2}-3 \left (2 y-1\right ) y^{\prime }+3 x = 0 \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
1.138 |
|
\[ {}{y^{\prime }}^{4}-4 y \left (x y^{\prime }-2 y\right )^{2} = 0 \] |
unknown |
[[_homogeneous, ‘class G‘]] |
✗ |
N/A |
1.073 |
|
\[ {}{y^{\prime }}^{6}-\left (y-a \right )^{4} \left (y-b \right )^{3} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
73.431 |
|
\[ {}x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
3.214 |
|
\[ {}{y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.43 |
|
\[ {}{y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1} = 0 \] |
separable, first_order_nonlinear_p_but_separable |
[_separable] |
✓ |
✓ |
40.158 |
|
\[ {}{y^{\prime }}^{n}-f \left (x \right ) g \left (y\right ) = 0 \] |
first_order_nonlinear_p_but_separable |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
0.72 |
|
\[ {}a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.252 |
|
\[ {}x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.272 |
|
\[ {}\sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
1.257 |
|
\[ {}\sqrt {1+{y^{\prime }}^{2}}+x {y^{\prime }}^{2}+y = 0 \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
210.911 |
|
\[ {}x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0 \] |
bernoulli, dAlembert, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
3.247 |
|
\[ {}a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.607 |
|
\[ {}y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-x a = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
180.667 |
|
\[ {}a y \sqrt {1+{y^{\prime }}^{2}}-2 x y y^{\prime }+y^{2}-x^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[_rational] |
✓ |
✓ |
19.386 |
|
\[ {}f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0 \] |
unknown |
[[_1st_order, _with_linear_symmetries]] |
✗ |
N/A |
6.225 |
|
\[ {}a \left ({y^{\prime }}^{3}+1\right )^{\frac {1}{3}}+b x y^{\prime }-y = 0 \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
4.359 |
|
\[ {}\ln \left (y^{\prime }\right )+x y^{\prime }+a y+b = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.369 |
|
\[ {}\ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right ) = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.636 |
|
\[ {}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0 \] |
separable, homogeneousTypeD2 |
[_separable] |
✓ |
✓ |
1.886 |
|
\[ {}\sin \left (y^{\prime }\right )+y^{\prime }-x = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.199 |
|
|
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