Problems 7801 to 7900

Table 2.159: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

7801	$(x + 1) (x^{2} + 1) y^{'} = 2 x^{2} + x$ i.c.	[_quadrature]	✓	✓	✓	✓

7802	$y^{'} = 1 + 2 x y$	[_linear]	✓	✓	✓	✓

7803	$y^{''} - 5 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

7804	$y^{'} = \frac{2 x y^{2}}{1 - x^{2} y}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓

7805	$2 y^{'''} + y^{''} - 5 y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

7806	$x^{5} y^{'} + y^{5} = 0$	[_separable]	✓	✓	✓	✓

7807	$y^{'} = 4 x y$	[_separable]	✓	✓	✓	✓

7808	$y^{'} + y \tan (x) = 0$	[_separable]	✓	✓	✓	✓

7809	$1 + y^{2} + (x^{2} + 1) y^{'} = 0$	[_separable]	✓	✓	✓	✓

7810	$y \ln (y) - y^{'} x = 0$	[_separable]	✓	✓	✓	✓

7811	$y^{'} x = (- 4 x^{2} + 1) \tan (y)$	[_separable]	✓	✓	✓	✓

7812	$y^{'} \sin (y) = x^{2}$	[_separable]	✓	✓	✓	✓

7813	$y^{'} - y \tan (x) = 0$	[_separable]	✓	✓	✓	✓

7814	$x y^{'} y = - 1 + y$	[_separable]	✓	✓	✓	✓

7815	$x y^{2} - x^{2} y^{'} = 0$	[_separable]	✓	✓	✓	✓

7816	$y y^{'} = x + 1$ i.c.	[_separable]	✓	✓	✓	✓

7817	$x^{2} y^{'} = y$ i.c.	[_separable]	✓	✓	✓	✓

7818	$\frac{y^{'}}{x^{2} + 1} = \frac{x}{y}$ i.c.	[_separable]	✓	✓	✓	✓

7819	$y^{2} y^{'} = x + 2$ i.c.	[_separable]	✓	✓	✓	✓

7820	$y^{'} = x^{2} y^{2}$ i.c.	[_separable]	✓	✓	✓	✓

7821	$(1 + y) y^{'} = - x^{2} + 1$ i.c.	[_separable]	✓	✓	✓	✓

7822	$\frac{y^{''}}{y^{'}} = x^{2}$	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

7823	$y^{'} y^{''} = x (x + 1)$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]	✓	✓	✓	✓

7824	$y^{'} - x y = 0$	[_separable]	✓	✓	✓	✓

7825	$y^{'} + x y = x$	[_separable]	✓	✓	✓	✓

7826	$y^{'} + y = \frac{1}{e^{2 x} + 1}$	[_linear]	✓	✓	✓	✓

7827	$y^{'} + y = 2 x e^{- x} + x^{2}$	[[_linear, ‘class A‘]]	✓	✓	✓	✓

7828	$2 y - x^{3} = y^{'} x$	[_linear]	✓	✓	✓	✓

7829	$y^{'} + 2 x y = 0$	[_separable]	✓	✓	✓	✓

7830	$y^{'} x - 3 y = x^{4}$	[_linear]	✓	✓	✓	✓

7831	$(x^{2} + 1) y^{'} + 2 x y = \cot (x)$	[_linear]	✓	✓	✓	✓

7832	$y^{'} + \cot (x) y = 2 x \csc (x)$	[_linear]	✓	✓	✓	✓

7833	$y - x + x y \cot (x) + y^{'} x = 0$	[_linear]	✓	✓	✓	✓

7834	$y^{'} - x y = 0$ i.c.	[_separable]	✓	✓	✓	✓

7835	$y^{'} - 2 x y = 6 x e^{x^{2}}$ i.c.	[_linear]	✓	✓	✓	✓

7836	$x \ln (x) y^{'} + y = 3 x^{3}$ i.c.	[_linear]	✗	✗	✗	✓

7837	$y^{'} - \frac{y}{x} = x^{2}$ i.c.	[_linear]	✓	✓	✓	✓

7838	$y^{'} + 4 y = e^{- x}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

7839	$x y + x^{2} y^{'} = 2 x$ i.c.	[_separable]	✓	✓	✓	✓

7840	$y^{'} x + y = x^{4} y^{3}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

7841	$x y^{2} y^{'} + y^{3} = x \cos (x)$	[_Bernoulli]	✓	✓	✓	✓

7842	$y^{'} x + y = x y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

7843	$y^{'} + x y = x y^{4}$	[_separable]	✓	✓	✓	✗

7844	$(e^{y} - 2 x y) y^{'} = y^{2}$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓

7845	$y - y^{'} x = y^{'} y^{2} e^{y}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

7846	$y^{'} x + 2 = x^{3} (- 1 + y) y^{'}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓	✓	✓

7847	$y^{'} x = 2 x^{2} y + y \ln (x)$	[_separable]	✓	✓	✓	✓

7848	$y^{'} \sin (2 x) = 2 y + 2 \cos (x)$	[_linear]	✓	✓	✓	✗

7849	$(x + \frac{2}{y}) y^{'} + y = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓

7850	$\sin (x) \tan (y) + 1 + \cos (x) \sec {(y)}^{2} y^{'} = 0$	[‘y=_G(x,y’)‘]	✓	✗	✓	✗

7851	$y - x^{3} + (y^{3} + x) y^{'} = 0$	[_exact, _rational]	✓	✓	✓	✗

7852	$2 y^{2} - 4 x + 5 = (4 - 2 y + 4 x y) y^{'}$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✗	✗	✗	✗

7853	$y + y \cos (x y) + (x + x \cos (x y)) y^{'} = 0$	[_separable]	✓	✓	✓	✓

7854	$\cos (x) \cos {(y)}^{2} + 2 \sin (x) \sin (y) \cos (y) y^{'} = 0$	[_separable]	✓	✓	✓	✓

7855	$(\sin (x) \sin (y) - x e^{y}) y^{'} = e^{y} + \cos (x) \cos (y)$	[_exact]	✓	✓	✓	✗

7856	$- \frac{\sin (\frac{x}{y})}{y} + \frac{x \sin (\frac{x}{y}) y^{'}}{y^{2}} = 0$	[_separable]	✓	✓	✓	✓

7857	$1 + y + (1 - x) y^{'} = 0$	[_separable]	✓	✓	✓	✓

7858	$2 x y^{3} + \cos (x) y + (3 x^{2} y^{2} + \sin (x)) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓	✓	✗

7859	$\frac{y}{1 - x^{2} y^{2}} + \frac{x y^{'}}{1 - x^{2} y^{2}} = 1$	[_exact, _rational, _Riccati]	✓	✓	✓	✓

7860	$2 x y^{4} + \sin (y) + (4 x^{2} y^{3} + x \cos (y)) y^{'} = 0$	[_exact]	✓	✓	✓	✗

7861	$\frac{y^{'} x + y}{1 - x^{2} y^{2}} + x = 0$	[_exact, _rational, _Riccati]	✓	✓	✓	✓

7862	$2 x (1 + \sqrt{x^{2} - y}) = \sqrt{x^{2} - y} y^{'}$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✓

7863	$\ln (y) x + x y + (y \ln (x) + x y) y^{'} = 0$	[_separable]	✓	✓	✓	✓

7864	$e^{y^{2}} - \csc (y) \csc {(x)}^{2} + (2 x y e^{y^{2}} - \csc (y) \cot (y) \cot (x)) y^{'} = 0$	[_exact]	✓	✓	✓	✗

7865	$1 + y^{2} \sin (2 x) - 2 y \cos {(x)}^{2} y^{'} = 0$	[_exact, _Bernoulli]	✓	✓	✓	✓

7866	$\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} + \frac{y y^{'}}{{(x^{2} + y^{2})}^{3 / 2}} = 0$	[_separable]	✓	✓	✓	✓

7867	$3 x^{2} (1 + \ln (y)) + (\frac{x^{3}}{y} - 2 y) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓

7868	$\frac{y - y^{'} x}{{(x + y)}^{2}} + y^{'} = 1$	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓	✓	✓	✗

7869	$\frac{4 y^{2} - 2 x^{2}}{4 x y^{2} - x^{3}} + \frac{(8 y^{2} - x^{2}) y^{'}}{4 y^{3} - x^{2} y} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✓

7870	$x^{2} - 2 y^{2} + x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

7871	$x^{2} y^{'} - 3 x y - 2 y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

7872	$x^{2} y^{'} = 3 (x^{2} + y^{2}) \arctan (\frac{y}{x}) + x y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

7873	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) + x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

7874	$y^{'} x = y + 2 e^{- \frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

7875	$x - y - (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

7876	$y^{'} x = 2 x - 6 y$	[_linear]	✓	✓	✓	✓

7877	$y^{'} x = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

7878	$x^{2} y^{'} = y^{2} + 2 x y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

7879	$x^{3} + y^{3} - x y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

7880	$y^{'} = \frac{x + y + 4}{x - y - 6}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

7881	$y^{'} = \frac{x + y + 4}{x + y - 6}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

7882	$2 x - 2 y + (- 1 + y) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

7883	$y^{'} = \frac{x + y - 1}{x + 4 y + 2}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✗

7884	$2 x + 3 y - 1 - 4 (x + 1) y^{'} = 0$	[_linear]	✓	✓	✓	✓

7885	$y^{'} = \frac{1 - x y^{2}}{2 x^{2} y}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

7886	$y^{'} = \frac{2 + 3 x y^{2}}{4 x^{2} y}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

7887	$y^{'} = \frac{y - x y^{2}}{x + x^{2} y}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓

7888	$y^{'} = \sin (\frac{y}{x}) - \cos (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✗

7889	$e^{\frac{x}{y}} - \frac{y y^{'}}{x} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

7890	$y^{'} = \frac{x^{2} - x y}{y^{2} \cos (\frac{x}{y})}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✗

7891	$y^{'} = \frac{y \tan (\frac{y}{x})}{x}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

7892	$(3 x^{2} - y^{2}) y^{'} - 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

7893	$x y - 1 + (x^{2} - x y) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✗

7894	$y^{'} x + y + 3 x^{3} y^{4} y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

7895	$e^{x} + (e^{x} \cot (y) + 2 \csc (y) y) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓

7896	$(x + 2) \sin (y) + x \cos (y) y^{'} = 0$	[_separable]	✓	✓	✓	✓

7897	$y + (x - 2 x^{2} y^{3}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

7898	$x + 3 y^{2} + 2 x y^{'} y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

7899	$y + (2 x - e^{y} y) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓

7900	$y \ln (y) - 2 x y + (x + y) y^{'} = 0$	[‘y=_G(x,y’)‘]	✓	✓	✓	✗

2.2.79 Problems 7801 to 7900