Problems 6201 to 6300

Table 2.127: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

6201	$x^{2} y^{''} + y^{'} x + y = 2 x$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6202	$x^{2} (2 - x) y^{''} + 2 y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

6203	$(x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

6204	$x y^{''} - 2 (x + 1) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

6205	$3 x y^{''} - 2 (3 x - 1) y^{'} + (3 x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

6206	$x^{2} y^{''} + (x + 1) y^{'} - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✗

6207	$x (x + 1) y^{''} - (x - 1) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

6208	$x^{2} y^{'} - x y = \frac{1}{x}$	[_linear]	✓	✓	✓	✓

6209	$x \ln (y) y^{'} - y \ln (x) = 0$	[_separable]	✓	✓	✓	✓

6210	$y^{'''} + 2 y^{''} + 2 y^{'} = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

6211	$r^{''} - 6 r^{'} + 9 r = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

6212	$2 x - y \sin (2 x) = (\sin {(x)}^{2} - 2 y) y^{'}$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✗

6213	$y^{''} + 2 y^{'} + 2 y = 10 e^{x} + 6 e^{- x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

6214	$3 x^{3} y^{2} y^{'} - x^{2} y^{3} = 1$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

6215	$x^{2} y^{''} - y^{'} x + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6216	$y^{'} - 2 y - y^{2} e^{3 x} = 0$	[[_1st_order, _with_linear_symmetries], _Bernoulli]	✓	✓	✓	✓

6217	$u (1 - v) + v^{2} (1 - u) u^{'} = 0$	[_separable]	✓	✓	✓	✓

6218	$y + 2 x - y^{'} x = 0$	[_linear]	✓	✓	✓	✓

6219	$x y^{''} + y^{'} = 4 x$	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

6220	$y^{''} + 4 y^{'} + 5 y = 26 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6221	$y^{''} + 4 y^{'} + 5 y = 2 e^{- 2 x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

6222	$y^{''} - 4 y^{'} + 4 y = 6 e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6223	$y^{''} - 5 y^{'} + 6 y = e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6224	$(2 x + y) y^{'} - x + 2 y = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

6225	$(x \cos (y) - e^{- \sin (y)}) y^{'} + 1 = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓

6226	$\sin {(x)}^{2} y^{'} + \sin {(x)}^{2} + (x + y) \sin (2 x) = 0$	[_linear]	✓	✓	✓	✓

6227	$y^{''} - 2 y^{'} + 5 y = 5 x + 4 e^{x} (1 + \sin (2 x))$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

6228	$y^{'} + x y = \frac{x}{y}$	[_separable]	✓	✓	✓	✓

6229	$y^{''''} - 2 y^{'''} + 13 y^{''} - 18 y^{'} + 36 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

6230	$\sin (θ) \cos (θ) r^{'} - \sin {(θ)}^{2} = r \cos {(θ)}^{2}$	[_linear]	✓	✓	✓	✓

6231	$x (y y^{''} + {y^{'}}^{2}) = y y^{'}$	[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓	✓	✗

6232	$3 x^{2} y + x^{3} y^{'} = 0$ i.c.	[_separable]	✓	✓	✓	✓

6233	$y^{'} x - y = x^{2}$ i.c.	[_linear]	✓	✓	✓	✓

6234	$y^{''} + y^{'} - 6 y = 6$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

6235	$y y^{''} + {y^{'}}^{2} + 4 = 0$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓	✓	✗

6236	$y^{'} x = x y + y$	[_separable]	✓	✓	✓	✗

6237	$y^{'} x = x y + y$	[_separable]	✓	✓	✓	✓

6238	$y^{'} = 3 x^{2} y$	[_separable]	✓	✓	✓	✓

6239	$y^{'} = 3 x^{2} y$	[_separable]	✓	✓	✓	✓

6240	$y^{'} x = y$	[_separable]	✓	✓	✓	✗

6241	$y^{'} x = y$	[_separable]	✓	✓	✓	✓

6242	$y^{''} = - 4 y$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

6243	$y^{''} = - 4 y$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

6244	$y^{''} = y$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

6245	$y^{''} = y$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

6246	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

6247	$y^{''} - 2 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

6248	$x^{2} y^{''} - 3 y^{'} x + 3 y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

6249	$x^{2} y^{''} - 3 y^{'} x + 3 y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

6250	$(x^{2} + 2 x) y^{''} - 2 (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6251	$(x^{2} + 2 x) y^{''} - 2 (x + 1) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

6252	$(x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6253	$(x^{2} + 1) y^{''} - 2 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

6254	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6255	$y^{''} - 4 y^{'} x + (4 x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

6256	$y^{'} - \sin (x + y) = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓

6257	$y^{'} = 4 y^{2} - 3 y + 1$	[_quadrature]	✓	✓	✓	✓

6258	$s^{'} = t \ln (s^{2 t}) + 8 t^{2}$	[‘y=_G(x,y’)‘]	✗	✗	✓	✗

6259	$y^{'} = \frac{y e^{x + y}}{x^{2} + 2}$	[_separable]	✓	✓	✓	✓

6260	$(x y^{2} + 3 y^{2}) y^{'} - 2 x = 0$	[_separable]	✓	✓	✓	✓

6261	$s^{2} + s^{'} = \frac{s + 1}{s t}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✗	✗	✗	✗

6262	$y^{'} x = \frac{1}{y^{3}}$	[_separable]	✓	✓	✓	✓

6263	$x^{'} = 3 x t^{2}$	[_separable]	✓	✓	✓	✓

6264	$x^{'} = \frac{t e^{- t - 2 x}}{x}$	[_separable]	✓	✓	✓	✓

6265	$y^{'} = \frac{x}{y^{2} \sqrt{x + 1}}$	[_separable]	✓	✓	✓	✓

6266	$x v^{'} = \frac{1 - 4 v^{2}}{3 v}$	[_separable]	✓	✓	✓	✓

6267	$y^{'} = \frac{\sec {(y)}^{2}}{x^{2} + 1}$	[_separable]	✓	✓	✓	✓

6268	$y^{'} = 3 x^{2} {(1 + y^{2})}^{3 / 2}$	[_separable]	✓	✓	✓	✓

6269	$x^{'} - x^{3} = x$	[_quadrature]	✓	✓	✓	✓

6270	$x + x y^{2} + e^{x^{2}} y y^{'} = 0$	[_separable]	✓	✓	✓	✓

6271	$\frac{y^{'}}{y} + y e^{\cos (x)} \sin (x) = 0$	[_separable]	✓	✓	✓	✓

6272	$y^{'} = (1 + y^{2}) \tan (x)$ i.c.	[_separable]	✓	✓	✓	✓

6273	$y^{'} = x^{3} (1 - y)$ i.c.	[_separable]	✓	✓	✓	✓

6274	$\frac{y^{'}}{2} = \sqrt{1 + y} \cos (x)$ i.c.	[_separable]	✓	✓	✓	✗

6275	$x^{2} y^{'} = \frac{4 x^{2} - x - 2}{(x + 1) (1 + y)}$ i.c.	[_separable]	✓	✓	✓	✓

6276	$\frac{y^{'}}{θ} = \frac{y \sin (θ)}{y^{2} + 1}$ i.c.	[_separable]	✓	✓	✓	✗

6277	$x^{2} + 2 y y^{'} = 0$ i.c.	[_separable]	✓	✓	✓	✓

6278	$y^{'} = 2 t \cos {(y)}^{2}$ i.c.	[_separable]	✓	✓	✓	✓

6279	$y^{'} = 8 x^{3} e^{- 2 y}$ i.c.	[_separable]	✓	✓	✓	✓

6280	$y^{'} = x^{2} (1 + y)$ i.c.	[_separable]	✓	✓	✓	✓

6281	$\sqrt{y} + (x + 1) y^{'} = 0$ i.c.	[_separable]	✓	✓	✓	✗

6282	$y^{'} = e^{x^{2}}$ i.c.	[_quadrature]	✓	✓	✓	✓

6283	$y^{'} = \frac{e^{x^{2}}}{y^{2}}$ i.c.	[_separable]	✓	✓	✓	✓

6284	$y^{'} = \sqrt{1 + \sin (x)} (1 + y^{2})$ i.c.	[_separable]	✓	✓	✓	✓

6285	$y^{'} = 2 y - 2 t y$ i.c.	[_separable]	✓	✓	✓	✓

6286	$y^{'} = y^{1 / 3}$	[_quadrature]	✓	✓	✓	✓

6287	$y^{'} = y^{1 / 3}$ i.c.	[_quadrature]	✓	✓	✓	✓

6288	$y^{'} = (x - 3) {(1 + y)}^{2 / 3}$	[_separable]	✓	✓	✓	✓

6289	$y^{'} = x y^{3}$	[_separable]	✓	✓	✓	✓

6290	$y^{'} = x y^{3}$ i.c.	[_separable]	✓	✓	✓	✓

6291	$y^{'} = x y^{3}$ i.c.	[_separable]	✓	✓	✓	✓

6292	$y^{'} = x y^{3}$ i.c.	[_separable]	✓	✓	✓	✓

6293	$y^{'} = y^{2} - 3 y + 2$ i.c.	[_quadrature]	✓	✓	✓	✓

6294	$x^{2} y^{'} + \sin (x) - y = 0$	[_linear]	✓	✓	✓	✓

6295	$x^{'} + t x = e^{x}$	[‘y=_G(x,y’)‘]	✗	✗	✗	✗

6296	$(t^{2} + 1) y^{'} = t y - y$	[_separable]	✓	✓	✓	✓

6297	$3 t = e^{t} y^{'} + \ln (t) y$	[_linear]	✓	✓	✓	✓

6298	$x x^{'} + x t^{2} = \sin (t)$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✗	✗	✗	✗

6299	$3 r = r^{'} - θ^{3}$	[[_linear, ‘class A‘]]	✓	✓	✓	✓

6300	$y^{'} - y - e^{3 x} = 0$	[[_linear, ‘class A‘]]	✓	✓	✓	✓

2.2.63 Problems 6201 to 6300