higher order missing y

Table 2.511: higher order missing y


#	ODE	CAS classiﬁcation	Solved?

4414	$y^{'''} = 2 (y^{''} - 1) \cot (x)$	[[_3rd_order, _missing_y]]	✓

6780	$(2 x^{3} - 1) y^{'''} - 6 x^{2} y^{''} + 6 x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

7526	$3 {y^{''}}^{2} - y^{'} y^{'''} - y^{''} {y^{'}}^{2} = 0$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

7532	$y^{(5)} - \frac{y^{''''}}{t} = 0$	[[_high_order, _missing_y]]	✓

7553	$a y^{''} y^{'''} = \sqrt{1 + {y^{''}}^{2}}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓

11457	$x^{2} y^{'''} - x y^{''} + (x^{2} + 1) y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

11477	$x^{3} y^{'''} + 3 x^{2} y^{''} + (- a^{2} + 1) x y^{'} = 0$	[[_3rd_order, _missing_y]]	✓

11487	$4 x^{4} y^{'''} - 4 x^{3} y^{''} + 4 x^{2} y^{'} - 1 = 0$	[[_3rd_order, _missing_y]]	✓

11762	$y^{'''} - a^{2} ({y^{'}}^{5} + 2 {y^{'}}^{3} + y^{'}) = 0$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓

11771	$2 y^{'} y^{'''} - 3 {y^{'}}^{2} = 0$	[[_3rd_order, _missing_x]]	✓

11772	$(1 + {y^{'}}^{2}) y^{'''} - 3 y^{'} {y^{''}}^{2} = 0$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

11773	$(1 + {y^{'}}^{2}) y^{'''} - (3 y^{'} + a) {y^{''}}^{2} = 0$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

11774	$y^{''} y^{'''} - a \sqrt{b^{2} {y^{''}}^{2} + 1} = 0$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓

11776	$3 y^{''} y^{''''} - 5 {y^{'''}}^{2} = 0$	[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	✓

12910	${(x y^{'''} - y^{''})}^{2} = {y^{'''}}^{2} + 1$	[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]	✓

13832	${y^{'''}}^{2} + {y^{''}}^{2} = 1$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓

13860	$6 y^{''} y^{''''} - 5 {y^{'''}}^{2} = 0$	[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	✓

14079	$y^{'''} + \frac{3 y^{''}}{x} = 0$	[[_3rd_order, _missing_y]]	✓

14156	$y^{'''} = {y^{''}}^{2}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

14157	$y^{'} y^{'''} - 3 {y^{''}}^{2} = 0$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

14402	$x y^{'''} + x y^{'} = 4$ i.c.	[[_3rd_order, _missing_y]]	✓

15147	$y^{'''} = 2 \sqrt{y^{''}}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓

16357	$t^{2} \ln (t) y^{'''} - t y^{''} + y^{'} = 1$	[[_3rd_order, _missing_y]]	✓

16358	$(t^{2} + t) y^{'''} + (- t^{2} + 2) y^{''} - (t + 2) y^{'} = - 2 - t$	[[_3rd_order, _missing_y]]	✓

16848	$y^{'''} = \sqrt{1 - {y^{''}}^{2}}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓

16859	$y^{'''} + {y^{''}}^{2} = 0$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

17891	${y^{'''}}^{2} + x^{2} = 1$	[[_3rd_order, _quadrature]]	✓

17893	$a^{3} y^{'''} y^{''} = \sqrt{1 + c^{2} {y^{''}}^{2}}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓

17894	$y^{'''} = \sqrt{1 + {y^{''}}^{2}}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓

17896	$y^{''} - x y^{'''} + {y^{'''}}^{3} = 0$	[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]	✓

17910	$5 {y^{'''}}^{2} - 3 y^{''} y^{''''} = 0$	[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	✓

18526	$y^{'''} + \frac{3 y^{''}}{x} = 0$	[[_3rd_order, _missing_y]]	✓

18885	$2 x y^{'''} y^{''} = {y^{''}}^{2} - a^{2}$	[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

18896	$y^{''} y^{'''} = 2$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

19292	$y^{'''} \csc {(x)}^{2} = 1$	[[_3rd_order, _quadrature]]	✓

19323	$y^{''} y^{'''} = 2$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

19353	$2 x y^{'''} y^{''} = {y^{''}}^{2} - a^{2}$	[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓

2.5.5 higher order missing y