Problems 16701 to 16800

Table 2.337: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

16701	$y^{'} \sin (x) + \cos (x) y = 1$	[_linear]	✓	✓	✓	✓

16702	$y^{'} \cos (x) - y \sin (x) = - \sin (2 x)$ i.c.	[_linear]	✓	✓	✓	✓

16703	$y^{'} + 2 x y = 2 x y^{2}$	[_separable]	✓	✓	✓	✓

16704	$3 x y^{2} y^{'} - 2 y^{3} = x^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

16705	$(x^{3} + e^{y}) y^{'} = 3 x^{2}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

16706	$y^{'} + 3 x y = y e^{x^{2}}$	[_separable]	✓	✓	✓	✓

16707	$y^{'} - 2 y e^{x} = 2 \sqrt{y e^{x}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	✓	✓	✗

16708	$2 \ln (x) y^{'} + \frac{y}{x} = \frac{\cos (x)}{y}$	[_Bernoulli]	✓	✓	✓	✓

16709	$2 y^{'} \sin (x) + \cos (x) y = y^{3} \sin {(x)}^{2}$	[_Bernoulli]	✓	✓	✓	✓

16710	$(x^{2} + y^{2} + 1) y^{'} + x y = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓

16711	$y^{'} - \cos (x) y = y^{2} \cos (x)$	[_separable]	✓	✓	✓	✓

16712	$y^{'} - \tan (y) = \frac{e^{x}}{\cos (y)}$	[‘y=_G(x,y’)‘]	✓	✓	✓	✓

16713	$y^{'} = y (e^{x} + \ln (y))$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	✓	✓	✓

16714	$y^{'} \cos (y) + \sin (y) = x + 1$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✓

16715	$y y^{'} + 1 = (x - 1) e^{- \frac{y^{2}}{2}}$	[‘y=_G(x,y’)‘]	✗	✓	✓	✗

16716	$y^{'} + \sin (2 y) x = 2 x e^{- x^{2}} \cos {(y)}^{2}$	[‘y=_G(x,y’)‘]	✗	✓	✓	✗

16717	$x (2 x^{2} + y^{2}) + y (x^{2} + 2 y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✓

16718	$3 x^{2} + 6 x y^{2} + (6 x^{2} y + 4 y^{3}) y^{'} = 0$	[_exact, _rational]	✓	✓	✓	✗

16719	$\frac{x}{\sqrt{x^{2} + y^{2}}} + \frac{1}{x} + \frac{1}{y} + (\frac{y}{\sqrt{x^{2} + y^{2}}} + \frac{1}{y} - \frac{x}{y^{2}}) y^{'} = 0$	[_exact]	✓	✓	✗	✗

16720	$3 x^{2} \tan (y) - \frac{2 y^{3}}{x^{3}} + (x^{3} \sec {(y)}^{2} + 4 y^{3} + \frac{3 y^{2}}{x^{2}}) y^{'} = 0$	[_exact]	✓	✓	✗	✗

16721	$2 x + \frac{x^{2} + y^{2}}{x^{2} y} = \frac{(x^{2} + y^{2}) y^{'}}{x y^{2}}$	[[_homogeneous, ‘class D‘], _exact, _rational]	✓	✓	✓	✗

16722	$\frac{\sin (2 x)}{y} + x + (y - \frac{\sin {(x)}^{2}}{y^{2}}) y^{'} = 0$	[_exact]	✓	✓	✓	✗

16723	$3 x^{2} - 2 x - y + (2 y - x + 3 y^{2}) y^{'} = 0$	[_exact, _rational]	✓	✓	✓	✗

16724	$\frac{x y}{\sqrt{x^{2} + 1}} + 2 x y - \frac{y}{x} + (\sqrt{x^{2} + 1} + x^{2} - \ln (x)) y^{'} = 0$	[_separable]	✓	✓	✓	✓

16725	$\sin (y) + y \sin (x) + \frac{1}{x} + (x \cos (y) - \cos (x) + \frac{1}{y}) y^{'} = 0$	[_exact]	✓	✓	✓	✗

16726	$\frac{y + \sin (x) \cos {(x y)}^{2}}{\cos {(x y)}^{2}} + (\frac{x}{\cos {(x y)}^{2}} + \sin (y)) y^{'} = 0$	[_exact]	✓	✓	✗	✗

16727	$\frac{2 x}{y^{3}} + \frac{(y^{2} - 3 x^{2}) y^{'}}{y^{4}} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✗

16728	$y (a^{2} + x^{2} + y^{2}) y^{'} + x (x^{2} + y^{2} - a^{2}) = 0$	[_exact, _rational]	✓	✓	✓	✗

16729	$3 x^{2} y + y^{3} + (x^{3} + 3 x y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✗

16730	$1 - x^{2} y + x^{2} (y - x) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓

16731	$x^{2} + y - y^{'} x = 0$	[_linear]	✓	✓	✓	✓

16732	$x + y^{2} - 2 x y^{'} y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

16733	$2 x^{2} y + 2 y + 5 + (2 x^{3} + 2 x) y^{'} = 0$	[_linear]	✓	✓	✓	✓

16734	$x^{4} \ln (x) - 2 x y^{3} + 3 x^{2} y^{2} y^{'} = 0$	[_Bernoulli]	✓	✓	✓	✓

16735	$x + \sin (x) + \sin (y) + y^{'} \cos (y) = 0$	[‘y=_G(x,y’)‘]	✓	✓	✓	✓

16736	$2 x y^{2} - 3 y^{3} + (7 - 3 x y^{2}) y^{'} = 0$	[_rational]	✓	✓	✓	✓

16737	$3 y^{2} - x + (2 y^{3} - 6 x y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

16738	$x^{2} + y^{2} + 1 - 2 x y^{'} y = 0$	[_rational, _Bernoulli]	✓	✓	✓	✓

16739	$x - x y + (y + x^{2}) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

16740	$4 {y^{'}}^{2} - 9 x = 0$	[_quadrature]	✓	✓	✓	✓

16741	${y^{'}}^{2} - 2 y y^{'} = y^{2} (- 1 + e^{2 x})$	[_separable]	✓	✓	✓	✓

16742	${y^{'}}^{2} - 2 y^{'} x - 8 x^{2} = 0$	[_quadrature]	✓	✓	✓	✓

16743	$x^{2} {y^{'}}^{2} + 3 x y^{'} y + 2 y^{2} = 0$	[_separable]	✓	✓	✓	✓

16744	${y^{'}}^{2} - (2 x + y) y^{'} + x^{2} + x y = 0$	[_quadrature]	✓	✓	✓	✓

16745	${y^{'}}^{3} + (x + 2) e^{y} = 0$	[[_1st_order, _with_exponential_symmetries]]	✓	✓	✓	✗

16746	${y^{'}}^{3} = y {y^{'}}^{2} - x^{2} y^{'} + x^{2} y$	[_quadrature]	✓	✓	✓	✓

16747	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

16748	${y^{'}}^{2} - 4 y^{'} x + 2 y + 2 x^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

16749	$y = {y^{'}}^{2} e^{y^{'}}$	[_quadrature]	✓	✓	✓	✓

16750	$y^{'} = e^{\frac{y^{'}}{y}}$	[_quadrature]	✓	✓	✓	✗

16751	$x = \ln (y^{'}) + \sin (y^{'})$	[_quadrature]	✓	✓	✓	✗

16752	$x = {y^{'}}^{2} - 2 y^{'} + 2$	[_quadrature]	✓	✓	✓	✓

16753	$y = y^{'} \ln (y^{'})$	[_quadrature]	✓	✓	✓	✓

16754	$y = (y^{'} - 1) e^{y^{'}}$	[_quadrature]	✓	✓	✓	✓

16755	$x {y^{'}}^{2} = e^{\frac{1}{y^{'}}}$	[_quadrature]	✓	✓	✓	✗

16756	$x {({y^{'}}^{2} + 1)}^{3 / 2} = a$	[_quadrature]	✓	✓	✓	✓

16757	$y^{2 / 5} + {y^{'}}^{2 / 5} = a^{2 / 5}$	[_quadrature]	✓	✓	✓	✓

16758	$x = \sin (y^{'}) + y^{'}$	[_quadrature]	✓	✓	✓	✗

16759	$y = y^{'} (1 + y^{'} \cos (y^{'}))$	[_quadrature]	✓	✓	✓	✗

16760	$y = \arcsin (y^{'}) + \ln ({y^{'}}^{2} + 1)$	[_quadrature]	✓	✓	✓	✗

16761	$y = 2 y^{'} x + \ln (y^{'})$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

16762	$y = x (y^{'} + 1) + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

16763	$y = 2 y^{'} x + \sin (y^{'})$	[_dAlembert]	✓	✓	✓	✗

16764	$y = x {y^{'}}^{2} - \frac{1}{y^{'}}$	[_dAlembert]	✓	✓	✓	✗

16765	$y = \frac{3 y^{'} x}{2} + e^{y^{'}}$	[_dAlembert]	✓	✓	✓	✗

16766	$y = y^{'} x + \frac{a}{{y^{'}}^{2}}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	✓	✓	✗

16767	$y = y^{'} x + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	✓	✓	✓

16768	$x {y^{'}}^{2} - y y^{'} - y^{'} + 1 = 0$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	✓	✓	✗

16769	$y = y^{'} x + a \sqrt{{y^{'}}^{2} + 1}$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	✓	✓	✗

16770	$x = \frac{y}{y^{'}} + \frac{1}{{y^{'}}^{2}}$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	✓	✓	✗

16771	$e^{- x} y^{'} + y^{2} - 2 y e^{x} = 1 - e^{2 x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓	✓	✓

16772	$y^{'} + y^{2} - 2 y \sin (x) + \sin {(x)}^{2} - \cos (x) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓	✓	✓

16773	$y^{'} x - y^{2} + (2 x + 1) y = x^{2} + 2 x$	[[_1st_order, _with_linear_symmetries], _rational, _Riccati]	✓	✓	✓	✓

16774	$x^{2} y^{'} = 1 + x y + x^{2} y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	✓	✓	✓

16775	$y^{2} ({y^{'}}^{2} + 1) - 4 y y^{'} - 4 x = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

16776	${y^{'}}^{2} - 4 y = 0$	[_quadrature]	✓	✓	✓	✓

16777	${y^{'}}^{3} - 4 x y^{'} y + 8 y^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

16778	${y^{'}}^{2} - y^{2} = 0$	[_quadrature]	✓	✓	✓	✓

16779	$y^{'} = y^{2 / 3} + a$	[_quadrature]	✓	✓	✓	✓

16780	${(y^{'} x + y)}^{2} + 3 x^{5} (y^{'} x - 2 y) = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

16781	$y {(y - 2 y^{'} x)}^{2} = 2 y^{'}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

16782	$8 {y^{'}}^{3} - 12 {y^{'}}^{2} = 27 y - 27 x$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✗	✗

16783	${(y^{'} - 1)}^{2} = y^{2}$	[_quadrature]	✓	✓	✓	✓

16784	$y = {y^{'}}^{2} - y^{'} x + x$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

16785	${(y^{'} x + y)}^{2} = y^{2} y^{'}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

16786	$y^{2} {y^{'}}^{2} + y^{2} = 1$	[_quadrature]	✓	✓	✓	✓

16787	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

16788	$3 x {y^{'}}^{2} - 6 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

16789	$y = y^{'} x + \sqrt{a^{2} {y^{'}}^{2} + b^{2}}$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	✓	✓	✗

16790	$y^{'} = {(x - y)}^{2} + 1$	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓

16791	$x \sin (x) y^{'} + (\sin (x) - x \cos (x)) y = \sin (x) \cos (x) - x$	[_linear]	✓	✓	✓	✓

16792	$y^{'} + \cos (x) y = y^{n} \sin (2 x)$	[_Bernoulli]	✓	✓	✓	✓

16793	$x^{3} - 3 x y^{2} + (y^{3} - 3 x^{2} y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✓

16794	$5 x y - 4 y^{2} - 6 x^{2} + (y^{2} - 8 x y + \frac{5 x^{2}}{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✗

16795	$3 x y^{2} - x^{2} + (3 x^{2} y - 6 y^{2} - 1) y^{'} = 0$	[_exact, _rational]	✓	✓	✓	✗

16796	$y - x y^{2} \ln (x) + y^{'} x = 0$	[_Bernoulli]	✓	✓	✓	✓

16797	$2 x y e^{x^{2}} - x \sin (x) + e^{x^{2}} y^{'} = 0$	[_linear]	✓	✓	✓	✓

16798	$y^{'} = \frac{1}{2 x - y^{2}}$	[[_1st_order, _with_exponential_symmetries]]	✓	✓	✓	✗

16799	$x^{2} + y^{'} x = 3 x + y^{'}$	[_quadrature]	✓	✓	✓	✓

16800	$x y^{'} y - y^{2} = x^{4}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	✓	✓	✓

2.2.168 Problems 16701 to 16800