Problems 9601 to 9700

Table 2.195: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

9601	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9602	$(x^{2} - 2 x) y^{''} + (- x^{2} + 2) y^{'} + (2 x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9603	$(2 x + 1) y^{''} - 2 y^{'} - (2 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9604	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9605	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9606	$x^{2} y^{''} + 2 x (x - 1) y^{'} + (x^{2} - 2 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9607	$x^{2} y^{''} - x (2 x - 1) y^{'} + (x^{2} - x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9608	$(- 2 x + 1) y^{''} + 2 y^{'} + (2 x - 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9609	$2 x y^{''} + (1 + 4 x) y^{'} + (2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9610	$x y^{''} - (2 x + 1) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9611	$4 x^{2} y^{''} - 4 x (x + 1) y^{'} + (2 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9612	$x y^{''} + (2 - 2 x) y^{'} + (x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9613	$x^{2} y^{''} - 2 y^{'} x + 2 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

9614	$x y^{''} - (2 x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9615	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9616	$x y^{''} - (1 + 4 x) y^{'} + (2 + 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9617	$4 x^{2} y^{''} - 4 y^{'} x + (- 16 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9618	$(2 x + 1) x y^{''} - 2 (2 x^{2} - 1) y^{'} - 4 (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9619	$(x^{2} - 2 x) y^{''} + (- x^{2} + 2) y^{'} + (2 x - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9620	$x y^{''} - (1 + 4 x) y^{'} + (2 + 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9621	$(3 x - 1) y^{''} - (3 x + 2) y^{'} - (6 x - 8) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9622	${(x + 1)}^{2} y^{''} - 2 (x + 1) y^{'} - (x^{2} + 2 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9623	$4 x^{2} y^{''} + (- 8 x^{2} + 4 x) y^{'} + (4 x^{2} - 4 x - 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9624	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9625	$(2 x + 1) y^{''} - 2 y^{'} - (2 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9626	$x y^{''} - (2 x + 2) y^{'} + (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9627	$x^{2} y^{''} - 2 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9628	$4 x^{2} y^{''} - 4 y^{'} x + (- 16 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9629	$4 x^{2} y^{''} - 4 y^{'} x + (4 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9630	$x^{2} y^{''} - 2 y^{'} x - (x^{2} - 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9631	$x^{2} y^{''} - 2 x (x + 1) y^{'} + (x^{2} + 2 x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9632	$x^{2} y^{''} - 2 x (x + 2) y^{'} + (x^{2} + 4 x + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9633	$x^{2} y^{''} - 4 y^{'} x + (x^{2} + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9634	$(x - 1) y^{''} - y^{'} x + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9635	$4 x^{2} y^{''} - 4 x (x + 1) y^{'} + (2 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9636	$(3 x - 1) y^{''} - (3 x + 2) y^{'} - (6 x - 8) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9637	$(x + 2) y^{''} + y^{'} x + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9638	$x^{2} (1 - x) y^{''} + x (x + 4) y^{'} + (2 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9639	$x^{2} (x + 1) y^{''} + x (2 x + 1) y^{'} - (6 x + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9640	$x^{2} (2 x^{2} + 1) y^{''} + x (2 x^{2} + 4) y^{'} + 2 (- x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9641	$x^{2} (x^{2} + 2) y^{''} + 2 x (x^{2} + 5) y^{'} + 2 (- x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9642	$(x^{2} + 1) y^{''} + 6 y^{'} x + 6 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9643	$(x^{2} + 1) y^{''} + 2 y^{'} x - 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9644	$(x^{2} + 1) y^{''} - 8 y^{'} x + 20 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9645	$(- x^{2} + 1) y^{''} - 8 y^{'} x - 12 y = 0$	[_Gegenbauer]	✓	✓	✓	✗

9646	$(2 x^{2} + 1) y^{''} + 7 y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9647	$(- x^{2} + 1) y^{''} - 5 y^{'} x - 4 y = 0$	[_Gegenbauer]	✓	✓	✓	✗

9648	$(x^{2} + 1) y^{''} - 10 y^{'} x + 28 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9649	$y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9650	$(2 x^{2} - 8 x + 11) y^{''} - 16 (x - 2) y^{'} + 36 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9651	$y^{''} + (x - 3) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9652	$(x^{2} - 8 x + 14) y^{''} - 8 (x - 4) y^{'} + 20 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9653	$(2 x^{2} + 4 x + 5) y^{''} - 20 (x + 1) y^{'} + 60 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9654	$(x^{3} + 1) y^{''} + 7 x^{2} y^{'} + 9 x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9655	$(2 x^{5} + 1) y^{''} + 14 x^{4} y^{'} + 10 x^{3} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✗	✓

9656	$y^{''} + x^{6} y^{'} + 7 x^{5} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9657	$(x^{8} + 1) y^{''} - 16 x^{7} y^{'} + 72 x^{6} y = 0$	[[_2nd_order, _with_linear_symmetries]]	✗	✓	✗	✗

9658	$y^{''} + x^{5} y^{'} + 6 y x^{4} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9659	$(3 x + 1) y^{''} + y^{'} x + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9660	$(3 x^{2} + x + 1) y^{''} + (2 + 15 x) y^{'} + 12 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9661	$(x + 2) y^{''} + (x + 1) y^{'} + 3 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9662	$(x + 4) y^{''} + (x + 2) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9663	$(2 x^{2} + 3 x) y^{''} + 10 (x + 1) y^{'} + 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9664	$x^{2} y^{''} - (6 - 7 x) y^{'} + 8 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9665	$(2 x^{2} + x + 1) y^{''} + (1 + 7 x) y^{'} + 2 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9666	$(3 + x) y^{''} + (2 x + 1) y^{'} - (2 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9667	$y^{''} + 3 y^{'} x + (2 x^{2} + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9668	$(2 + 4 x) y^{''} - 4 y^{'} - (6 + 4 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9669	$y^{''} - 3 y^{'} x + (2 x^{2} + 5) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9670	$2 y^{''} + 5 y^{'} x + (2 x^{2} + 4) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9671	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9672	$y^{''} + 4 y^{'} x + (4 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9673	$2 x^{2} (x^{2} + x + 1) y^{''} + x (11 x^{2} + 11 x + 9) y^{'} + (7 x^{2} + 10 x + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9674	$3 x^{2} y^{''} + 2 x (- 2 x^{2} + x + 1) y^{'} + (- 8 x^{2} + 2 x) y = 0$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✗

9675	$12 x^{2} (x + 1) y^{''} + x (3 x^{2} + 35 x + 11) y^{'} - (- 5 x^{2} - 10 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9676	$y^{''} + 3 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

9677	$18 x^{2} (x + 1) y^{''} + 3 x (x^{2} + 11 x + 5) y^{'} - (- 5 x^{2} - 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9678	$2 x^{2} y^{''} + x (2 x + 3) y^{'} - (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9679	$2 x^{2} y^{''} + x (5 + x) y^{'} - (2 - 3 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9680	$3 x^{2} y^{''} + x (x + 1) y^{'} - y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9681	$2 x^{2} y^{''} - y^{'} x + (- 2 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9682	$3 x^{2} y^{''} + x (x + 1) y^{'} - (3 x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9683	$2 (3 + x) x^{2} y^{''} + x (1 + 5 x) y^{'} + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9684	$x^{2} (x + 4) y^{''} - x (1 - 3 x) y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9685	$2 x^{2} y^{''} + 5 y^{'} x + (x + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

9686	$6 x^{2} y^{''} + x (10 - x) y^{'} - (x + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9687	$x^{2} (4 x + 3) y^{''} + x (11 + 4 x) y^{'} - (4 x + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9688	$2 x^{2} (3 x + 2) y^{''} + x (4 + 11 x) y^{'} - (1 - x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9689	$x^{2} (x + 2) y^{''} + 5 x (1 - x) y^{'} - (2 - 8 x) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9690	$8 x^{2} (- x^{2} + 1) y^{''} + 2 x (- 13 x^{2} + 1) y^{'} + (- 9 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9691	$x^{2} (x^{2} + 1) y^{''} - 2 x (- x^{2} + 2) y^{'} + 4 y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9692	$x (x^{2} + 3) y^{''} + (- x^{2} + 2) y^{'} - 8 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✗

9693	$4 x^{2} (- x^{2} + 1) y^{''} + x (- 19 x^{2} + 7) y^{'} - (14 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9694	$3 x^{2} (- x^{2} + 2) y^{''} + x (- 11 x^{2} + 1) y^{'} + (- 5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9695	$2 x^{2} (x^{2} + 2) y^{''} - x (- 7 x^{2} + 12) y^{'} + (3 x^{2} + 7) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9696	$2 x^{2} (x^{2} + 2) y^{''} + x (7 x^{2} + 4) y^{'} - (- 3 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9697	$2 x^{2} (2 x^{2} + 1) y^{''} + 5 x (6 x^{2} + 1) y^{'} - (- 40 x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9698	$x (x^{2} + 1) y^{''} + (7 x^{2} + 4) y^{'} + 8 x y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✗

9699	$2 x^{2} (x^{2} + 1) y^{''} + x (8 x^{2} + 3) y^{'} - (- 4 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

9700	$9 x^{2} y^{''} + 3 x (x^{2} + 3) y^{'} - (- 5 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

2.2.97 Problems 9601 to 9700