Problems 6601 to 6700

Table 2.135: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

6601	$\cos (y) + (1 + e^{- x}) \sin (y) y^{'} = 0$ i.c.	[_separable]	✓	✓	✓	✓

6602	$y^{2} + x y - y^{'} x = 0$ i.c.	[_rational, _Bernoulli]	✓	✓	✓	✓

6603	$y^{'} = - 2 {(2 x + 3 y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	✓	✓	✓

6604	$x - 2 \sin (y) + 3 + (2 x - 4 \sin (y) - 3) \cos (y) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	✓	✓	✓

6605	$x^{2} - y - y^{'} x = 0$	[_linear]	✓	✓	✓	✓

6606	$x^{2} + y^{2} + 2 x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓	✓	✓	✓

6607	$x + \cos (x) y + y^{'} \sin (x) = 0$	[_linear]	✓	✓	✓	✓

6608	$2 x + 3 y + 4 + (3 x + 4 y + 5) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

6609	$4 x^{3} y^{3} + \frac{1}{x} + (3 x^{4} y^{2} - \frac{1}{y}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	✓	✓	✓

6610	$2 u^{2} + 2 u v + (u^{2} + v^{2}) v^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	✓	✓	✗

6611	$x \sqrt{x^{2} + y^{2}} - y + (y \sqrt{x^{2} + y^{2}} - x) y^{'} = 0$	[_exact]	✓	✓	✓	✗

6612	$x + y + 1 - (3 - x + y) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

6613	$y^{2} - \frac{y}{(x + y) x} + 2 + (\frac{1}{x + y} + 2 (x + 1) y) y^{'} = 0$	[_exact, _rational]	✓	✓	✓	✗

6614	$2 x y e^{x^{2} y} + y^{2} e^{x y^{2}} + 1 + (x^{2} e^{x^{2} y} + 2 x y e^{x y^{2}} - 2 y) y^{'} = 0$	[_exact]	✓	✓	✓	✗

6615	$y (x - 2 y) - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

6616	$x y^{'} y + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

6617	$x^{2} + y^{2} + 2 x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓	✓	✓	✓

6618	$1 - \sqrt{a^{2} - x^{2}} y^{'} = 0$	[_quadrature]	✓	✓	✓	✓

6619	$x + y + 1 - (x - y - 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

6620	$x - x^{2} - y^{2} + y y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	✓	✓	✓

6621	$2 y - 3 x + y^{'} x = 0$	[_linear]	✓	✓	✓	✓

6622	$x - y^{2} + 2 x y^{'} y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

6623	$- y - 3 x^{2} (x^{2} + y^{2}) + y^{'} x = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	✓	✓	✓

6624	$y - \ln (x) - y^{'} x = 0$	[_linear]	✓	✓	✓	✓

6625	$3 x^{2} + y^{2} - 2 x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

6626	$x y - 2 y^{2} - (x^{2} - 3 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓

6627	$x + y - (x - y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✓

6628	$2 y - 3 x y^{2} - y^{'} x = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

6629	$y + x (x^{2} y - 1) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✗

6630	$y + x^{3} y + 2 x^{2} + (x + 4 x y^{4} + 8 y^{3}) y^{'} = 0$	[_rational]	✓	✓	✓	✗

6631	$- y - x^{2} e^{x} + y^{'} x = 0$	[_linear]	✓	✓	✓	✓

6632	$1 + y^{2} = (x^{2} + x) y^{'}$	[_separable]	✓	✓	✓	✓

6633	$2 y - x^{3} + y^{'} x = 0$	[_linear]	✓	✓	✓	✓

6634	$y + (- x + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

6635	$3 y^{3} - x y - (x^{2} + 6 x y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

6636	$3 x^{2} y^{2} + 4 (x^{3} y - 3) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✗

6637	$y (x + y) - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	✓	✓	✓

6638	$2 y + 3 x y^{2} + (x + 2 x^{2} y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓

6639	$y (y^{2} - 2 x^{2}) + x (2 y^{2} - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6640	$y^{'} x - y = 0$	[_separable]	✓	✓	✓	✓

6641	$y^{'} + y = 2 x + 2$	[[_linear, ‘class A‘]]	✓	✓	✓	✓

6642	$y^{'} - y = x y$	[_separable]	✓	✓	✓	✓

6643	$- 3 y - (x - 2) e^{x} + y^{'} x = 0$	[_linear]	✓	✓	✓	✓

6644	$i^{'} - 6 i = 10 \sin (2 t)$	[[_linear, ‘class A‘]]	✓	✓	✓	✓

6645	$y^{'} + y = y^{2} e^{x}$	[[_1st_order, _with_linear_symmetries], _Bernoulli]	✓	✓	✓	✓

6646	$y + (x y + x - 3 y) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓	✓	✓

6647	$(2 s - e^{2 t}) s^{'} = 2 s e^{2 t} - 2 \cos (2 t)$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓	✓	✗

6648	$y^{'} x + y - x^{3} y^{6} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

6649	$r^{'} + 2 r \cos (θ) + \sin (2 θ) = 0$	[_linear]	✓	✓	✓	✓

6650	$y (1 + y^{2}) = 2 (1 - 2 x y^{2}) y^{'}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓

6651	$y y^{'} - x y^{2} + x = 0$	[_separable]	✓	✓	✓	✓

6652	$(x - x \sqrt{x^{2} - y^{2}}) y^{'} - y = 0$	[‘y=_G(x,y’)‘]	✗	✓	✓	✗

6653	$2 x^{'} - \frac{x}{y} + x^{3} \cos (y) = 0$	[_Bernoulli]	✓	✓	✓	✓

6654	$y^{'} x = y (1 - x \tan (x)) + x^{2} \cos (x)$	[_linear]	✓	✓	✓	✓

6655	$2 + y^{2} - (x y + 2 y + y^{3}) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✓

6656	$1 + y^{2} = (\arctan (y) - x) y^{'}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✓

6657	$2 y^{5} x - y + 2 y^{'} x = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	✓	✓	✓

6658	$1 + \sin (y) = (2 y \cos (y) - x (\sec (y) + \tan (y))) y^{'}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	✓	✓	✗

6659	$y^{'} x = 2 y + x^{3} e^{x}$ i.c.	[_linear]	✓	✓	✓	✓

6660	$L i^{'} + R i = E \sin (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

6661	$x^{2} y^{'} \cos (y) = 2 x \sin (y) - 1$	[‘y=_G(x,y’)‘]	✓	✓	✓	✗

6662	$4 x^{2} y y^{'} = 3 x (3 y^{2} + 2) + 2 {(3 y^{2} + 2)}^{3}$	[_rational]	✗	✓	✓	✓

6663	$x y^{3} - y^{3} - x^{2} e^{x} + 3 x y^{2} y^{'} = 0$	[_Bernoulli]	✓	✓	✓	✓

6664	$y^{'} + (x + y) x = x^{3} {(x + y)}^{3} - 1$	[_Abel]	✓	✓	✓	✓

6665	$y + e^{y} - e^{- x} + (1 + e^{y}) y^{'} = 0$	[‘y=_G(x,y’)‘]	✓	✓	✓	✓

6666	$x^{2} {y^{'}}^{2} + x y^{'} y - 6 y^{2} = 0$	[_separable]	✓	✓	✓	✓

6667	$x {y^{'}}^{2} + (y - 1 - x^{2}) y^{'} - x (- 1 + y) = 0$	[_quadrature]	✓	✓	✓	✓

6668	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6669	$3 x^{4} {y^{'}}^{2} - y^{'} x - y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

6670	$8 y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

6671	$y^{2} {y^{'}}^{2} + 3 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

6672	${y^{'}}^{2} - y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	✓	✓	✓

6673	$16 y^{3} {y^{'}}^{2} - 4 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

6674	$x {y^{'}}^{5} - y {y^{'}}^{4} + (x^{2} + 1) {y^{'}}^{3} - 2 x y {y^{'}}^{2} + (x + y^{2}) y^{'} - y = 0$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	✓	✓	✗

6675	$x {y^{'}}^{2} - y y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

6676	$y = 2 y^{'} x + y^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

6677	${y^{'}}^{2} - y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

6678	$y = x (y^{'} + 1) + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

6679	$y = 2 y^{'} + \sqrt{{y^{'}}^{2} + 1}$	[_quadrature]	✓	✓	✓	✓

6680	$y {y^{'}}^{2} - y^{'} x + 3 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6681	$y = y^{'} x - 2 {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	✓	✓	✓

6682	$y^{2} {y^{'}}^{2} + 3 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

6683	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6684	$x {y^{'}}^{2} - 2 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6685	${(3 y - 1)}^{2} {y^{'}}^{2} = 4 y$	[_quadrature]	✓	✓	✓	✗

6686	$y = - y^{'} x + x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

6687	$2 y = {y^{'}}^{2} + 4 y^{'} x$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

6688	$y {(3 - 4 y)}^{2} {y^{'}}^{2} = 4 - 4 y$	[_quadrature]	✓	✓	✓	✓

6689	${y^{'}}^{3} - 4 x^{4} y^{'} + 8 x^{3} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

6690	$({y^{'}}^{2} + 1) {(x - y)}^{2} = {(y y^{'} + x)}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✗

6691	$y^{''} + y^{'} - 6 y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

6692	$y^{'''} - 6 y^{''} + 12 y^{'} - 8 y = 0$	[[_3rd_order, _missing_x]]	✓	✓	✓	✓

6693	$y^{''} - 3 y^{'} + 2 y = e^{5 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6694	$y^{''} + 9 y = x \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

6695	$x^{2} y^{''} - 3 y^{'} x + 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

6696	$x^{3} y^{'''} + y^{'} x - y = 3 x^{4}$	[[_3rd_order, _with_linear_symmetries]]	✓	✓	✓	✓

6697	$x y^{''} - y^{'} + 4 x^{3} y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

6698	$y^{''} + {y^{'}}^{2} + 1 = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	✓	✓	✓

6699	$y y^{''} + {y^{'}}^{2} = 2$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓	✓	✗

6700	$y y^{''} + {y^{'}}^{3} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	✓	✓	✗

2.2.67 Problems 6601 to 6700