Problems 5901 to 6000

Table 2.121: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

5901	$(x^{2} + y^{2} + 1) y^{'} + 2 x y + x^{2} + 3 = 0$	[_exact, _rational]	✓	✓	✓	✗

5902	$y^{'} \cos (x) + y + (1 + \sin (x)) \cos (x) = 0$	[_linear]	✓	✓	✓	✓

5903	$y^{2} + 12 x^{2} y + (2 x y + 4 x^{3}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓

5904	$(x^{2} - y) y^{'} + x = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓	✓	✓

5905	$(x^{2} - y) y^{'} - 4 x y = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

5906	$x y^{'} y + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

5907	$2 x y^{'} y + 3 x^{2} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

5908	$(2 x y^{3} - x^{4}) y^{'} + 2 x^{3} y - y^{4} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5909	${(x y - 1)}^{2} x y^{'} + (1 + x^{2} y^{2}) y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

5910	$(x^{2} + y^{2}) y^{'} + 2 x (2 x + y) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✗

5911	$3 x y^{2} y^{'} + y^{3} - 2 x = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	✓	✓	✓	✓

5912	$2 y^{3} y^{'} + x y^{2} - x^{3} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

5913	$(2 x y^{3} + x y + x^{2}) y^{'} - x y + y^{2} = 0$	[_rational]	✓	✓	✓	✗

5914	$(2 y^{3} + y) y^{'} - 2 x^{3} - x = 0$	[_separable]	✓	✓	✓	✓

5915	$y^{'} - e^{x - y} + e^{x} = 0$	[_separable]	✓	✓	✓	✓

5916	$y^{''} + 2 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5917	$y^{''} - 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5918	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5919	$6 y^{''} - 11 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5920	$y^{''} + 2 y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5921	$y^{'''} + y^{''} - 10 y^{'} - 6 y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

5922	$y^{''''} - y^{'''} - 4 y^{''} + 4 y^{'} = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5923	$y^{''''} + 4 y^{'''} + y^{''} - 4 y^{'} - 2 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5924	$y^{''''} - a^{2} y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5925	$y^{''} - 2 k y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5926	$y^{''} + 4 k y^{'} - 12 k^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5927	$y^{''''} = 0$	[[_high_order, _quadrature]]	✓	✓	✓	✓

5928	$y^{''} + 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5929	$3 y^{'''} + 5 y^{''} + y^{'} - y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

5930	$y^{'''} - 6 y^{''} + 12 y^{'} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

5931	$y^{''} - 2 a y^{'} + a^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5932	$y^{''''} + 3 y^{'''} = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5933	$y^{''''} - 2 y^{''} = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5934	$y^{''''} + 2 y^{'''} - 11 y^{''} - 12 y^{'} + 36 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5935	$36 y^{''''} - 37 y^{''} + 4 y^{'} + 5 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5936	$y^{''''} - 8 y^{''} + 36 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5937	$y^{''} - 2 y^{'} + 5 y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5938	$y^{''} - y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5939	$y^{''''} + 5 y^{''} + 6 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5940	$y^{''} - 4 y^{'} + 20 y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5941	$y^{''''} + 4 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5942	$y^{'''} + 8 y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

5943	$y^{''''} + 4 y^{''} = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5944	$y^{(5)} + 2 y^{'''} + y^{'} = 0$	[[_high_order, _missing_x]]	✓	✓	✓	✓

5945	$y^{''} = 0$ i.c.	[[_2nd_order, _quadrature]]	✓	✓	✓	✓

5946	$y^{''} + 4 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5947	$y^{''} - 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5948	$y^{''} - 4 y^{'} + 20 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5949	$3 y^{'''} + 5 y^{''} + y^{'} - y = 0$ i.c.	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

5950	$y^{''} + 3 y^{'} + 2 y = 4$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

5951	$y^{''} + 3 y^{'} + 2 y = 12 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

5952	$y^{''} + 3 y^{'} + 2 y = e^{i x}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

5953	$y^{''} + 3 y^{'} + 2 y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5954	$y^{''} + 3 y^{'} + 2 y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5955	$y^{''} + 3 y^{'} + 2 y = 8 + 6 e^{x} + 2 \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5956	$y^{''} + y^{'} + y = x^{2}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

5957	$y^{''} - 2 y^{'} - 8 y = 9 x e^{x} + 10 e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5958	$y^{''} - 3 y^{'} = 2 e^{2 x} \sin (x)$	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

5959	$y^{''} + y^{'} = x^{2} + 2 x$	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

5960	$y^{''} + y^{'} = x + \sin (2 x)$	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

5961	$y^{''} + y = 4 x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5962	$y^{''} + 4 y = x \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5963	$y^{''} + 2 y^{'} + y = x^{2} e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5964	$y^{''} + 3 y^{'} + 2 y = e^{- 2 x} + x^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5965	$y^{''} - 3 y^{'} + 2 y = x e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5966	$y^{''} + y^{'} - 6 y = x + e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

5967	$y^{''} + y = \sin (x) + e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5968	$y^{''} + y = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5969	$y^{''} + y = \sin (2 x) \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5970	$y^{''} - 5 y^{'} - 6 y = e^{3 x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

5971	$y^{''} - y^{'} - 2 y = 5 \sin (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5972	$y^{''} + 9 y = 8 \cos (x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5973	$y^{''} - 5 y^{'} + 6 y = e^{x} (2 x - 3)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5974	$y^{''} - 3 y^{'} + 2 y = e^{- x}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

5975	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5976	$y^{''} + y = \cot (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5977	$y^{''} + y = \sec {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5978	$y^{''} - y = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5979	$y^{''} + y = \sin {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5980	$y^{''} + 3 y^{'} + 2 y = 12 e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

5981	$y^{''} + 2 y^{'} + y = x^{2} e^{- x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5982	$y^{''} + y = 4 x \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5983	$y^{''} + 2 y^{'} + y = e^{- x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5984	$y^{''} + y = \csc (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5985	$y^{''} + y = \tan {(x)}^{2}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5986	$y^{''} + 2 y^{'} + y = \frac{e^{- x}}{x}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5987	$y^{''} + y = \sec (x) \csc (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5988	$y^{''} - 2 y^{'} + y = e^{x} \ln (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5989	$y^{''} - 3 y^{'} + 2 y = \cos (e^{- x})$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5990	$x^{2} y^{''} - y^{'} x + y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

5991	$y^{''} - \frac{2 y^{'}}{x} + \frac{2 y}{x^{2}} = x \ln (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5992	$x^{2} y^{''} + y^{'} x - 4 y = x^{3}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

5993	$x^{2} y^{''} + y^{'} x - y = x^{2} e^{- x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5994	$2 x^{2} y^{''} + 3 y^{'} x - y = \frac{1}{x}$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	✓	✓	✓

5995	$y^{''} = 2 y y^{'}$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓	✓	✗

5996	$y^{3} y^{''} = k$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✓

5997	$y y^{''} = {y^{'}}^{2} - 1$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓	✓	✗

5998	$x^{2} y^{''} + y^{'} x = 1$	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

5999	$x y^{''} - y^{'} = x^{2}$	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

6000	$(1 + y) y^{''} = 3 {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓	✓	✗

2.2.60 Problems 5901 to 6000