Problems 18601 to 18700

Table 2.375: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

18601	$y^{''} + y = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.757

18602	$y^{'''} + y^{''} - 4 y^{'} - 4 y = x$	[[_3rd_order, _with_linear_symmetries]]	✓	0.138

18603	$y^{''} + y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.662

18604	$y^{'''} - y^{''} + y^{'} - y = \cos (x)$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	0.701

18605	$y^{'''} - 3 y^{''} + 3 y^{'} - y = e^{x}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.152

18606	$y^{''''} - y = x^{4}$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.150

18607	$e y^{''} = \frac{P (\frac{L}{2} - x)}{2}$	[[_2nd_order, _quadrature]]	✓	1.037

18608	$e y^{''} = \frac{w (\frac{L^{2}}{4} - x^{2})}{2}$	[[_2nd_order, _quadrature]]	✓	1.047

18609	$e y^{''} = - \frac{(w L + P) x}{2} - \frac{w x^{2}}{2}$	[[_2nd_order, _quadrature]]	✓	1.069

18610	$e y^{''} = - P (L - x)$	[[_2nd_order, _quadrature]]	✓	1.056

18611	$e y^{''} = - P L + (w L + P) x - \frac{w (L^{2} + x^{2})}{2}$	[[_2nd_order, _quadrature]]	✓	1.174

18612	$e y^{''} = P (- y + a)$	[[_2nd_order, _missing_x]]	✓	3.091

18613	$x^{3} y^{'''} + 7 x^{2} y^{''} + 8 y^{'} x = \ln {(x)}^{2}$	[[_3rd_order, _missing_y]]	✓	0.354

18614	$x^{2} y^{''} + 3 y^{'} x - 8 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.991

18615	$x^{3} y^{'''} - 3 x^{2} y^{''} + 6 y^{'} x - 6 y = x^{3}$	[[_3rd_order, _with_linear_symmetries]]	✓	0.284

18616	$x^{3} y^{'''} + 2 x^{2} y^{''} - 4 y^{'} x + 4 y = \ln (x)$	[[_3rd_order, _with_linear_symmetries]]	✓	0.271

18617	$x^{3} y^{'''} + 4 x^{2} y^{''} + y^{'} x - y = 0$	[[_3rd_order, _exact, _linear, _homogeneous]]	✓	0.148

18618	$x y^{''} + 2 y^{'} = 2 x$	[[_2nd_order, _missing_y]]	✓	0.797

18619	$x^{2} y^{''} - y^{'} x + y = \ln (x)$	[[_2nd_order, _with_linear_symmetries]]	✓	1.488

18620	$(x^{2} - 1) y^{''} + 4 y^{'} x + 2 y = 2 x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.028

18621	$(x^{2} + 1) y^{''} + 4 y^{'} x + 2 y = x$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	0.915

18622	$y^{''} - \cot (x) y^{'} + y \csc {(x)}^{2} = \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.067

18623	$(x^{2} - x) y^{''} + (3 x - 2) y^{'} + y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.978

18624	$(3 x^{2} + x) y^{''} + 2 (1 + 6 x) y^{'} + 6 y = \sin (x)$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	1.398

18625	$(x^{3} + x^{2} - 3 x + 1) y^{'''} + (9 x^{2} + 6 x - 9) y^{''} + (18 x + 6) y^{'} + 6 y = x^{3}$	[[_3rd_order, _fully, _exact, _linear]]	✓	1.200

18626	$x^{2} y^{'''} + 5 x y^{''} + 4 y^{'} = - \frac{1}{x^{2}}$	[[_3rd_order, _missing_y]]	✓	0.271

18627	$y^{''} = \cos (x)$	[[_2nd_order, _quadrature]]	✓	0.878

18628	$x^{2} y^{''} = \ln (x)$	[[_2nd_order, _quadrature]]	✓	0.513

18629	$y^{''} = - a^{2} y$	[[_2nd_order, _missing_x]]	✓	1.424

18630	$y^{''} = \frac{1}{y^{2}}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	77.857

18631	$y y^{''} - {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.491

18632	$y y^{''} - {y^{'}}^{2} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.571

18633	$(x^{2} + 1) y^{''} - 1 - {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.709

18634	$x y^{''} + 3 y^{'} = 3 x$	[[_2nd_order, _missing_y]]	✓	1.036

18635	$x = y^{''} + y^{'}$	[[_2nd_order, _missing_y]]	✓	0.988

18636	$x = {y^{'}}^{2} + y$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	0.770

18637	$y = y^{'} x - {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.484

18638	$V^{''} + \frac{2 V^{'}}{r} = 0$	[[_2nd_order, _missing_y]]	✓	0.535

18639	$V^{''} + \frac{V^{'}}{r} = 0$	[[_2nd_order, _missing_y]]	✓	0.660

18640	$[\begin{matrix} z^{'} + 7 y - 3 z = 0 \\ 7 y^{'} + 63 y - 36 z = 0 \end{matrix}]$	system_of_ODEs	✓	0.374

18641	$[\begin{matrix} z^{'} + 2 y^{'} + 3 y = 0 \\ y^{'} + 3 y - 2 z = 0 \end{matrix}]$	system_of_ODEs	✓	0.405

18642	$[\begin{matrix} y^{'} + 3 y + z = 0 \\ z^{'} + 3 y + 5 z = 0 \end{matrix}]$	system_of_ODEs	✓	0.313

18643	$[\begin{matrix} y^{'} + 3 y + 2 z = 0 \\ z^{'} + 2 y - 4 z = 0 \end{matrix}]$	system_of_ODEs	✓	0.545

18644	$[\begin{matrix} y^{'} - 3 y - 2 z = 0 \\ z^{'} + y - 2 z = 0 \end{matrix}]$	system_of_ODEs	✓	0.671

18645	$[\begin{matrix} y^{'} + z^{'} + 6 y = 0 \\ z^{'} + 5 y + z = 0 \end{matrix}]$	system_of_ODEs	✓	0.464

18646	$[\begin{matrix} z^{'} + y^{'} + 5 y - 3 z = x + e^{x} \\ y^{'} + 2 y - z = e^{x} \end{matrix}]$	system_of_ODEs	✓	0.918

18647	$[\begin{matrix} z^{'} + y + 3 z = e^{x} \\ y^{'} + 3 y + 4 z = e^{2 x} \end{matrix}]$	system_of_ODEs	✓	0.931

18648	$[\begin{matrix} z^{'} - 3 y + 2 z = e^{x} \\ y^{'} + 2 y - z = e^{3 x} \end{matrix}]$	system_of_ODEs	✓	1.231

18649	$[\begin{matrix} z^{'} + 5 y - 2 z = x \\ y^{'} + 4 y + z = x \end{matrix}]$	system_of_ODEs	✓	2.058

18650	$[\begin{matrix} z^{'} + 7 y - 9 z = e^{x} \\ y^{'} - y - 3 z = e^{2 x} \end{matrix}]$	system_of_ODEs	✓	1.717

18651	$[\begin{matrix} y^{'} - 2 y - 2 z = e^{3 x} \\ z^{'} + 5 y - 2 z = e^{4 x} \end{matrix}]$	system_of_ODEs	✓	1.178

18652	${y^{'}}^{2} + y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.507

18653	$y^{''} - \frac{2 y^{'}}{x} + \frac{2 y}{x^{2}} = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.157

18654	$v^{''} + \frac{2 v^{'}}{r} = 0$	[[_2nd_order, _missing_y]]	✓	0.526

18655	$y^{''} - k^{2} y = 0$	[[_2nd_order, _missing_x]]	✓	1.646

18656	$(1 - x) y^{'} - 1 - y = 0$	[_separable]	✓	1.574

18657	$y^{'} + \sqrt{\frac{1 - y^{2}}{- x^{2} + 1}} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	33.732

18658	$y - y^{'} x = a (y^{'} + y^{2})$	[_separable]	✓	1.604

18659	$3 e^{x} \tan (y) + (1 - e^{x}) \sec {(y)}^{2} y^{'} = 0$	[_separable]	✓	3.296

18660	$x^{2} + y^{2} - 2 x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	7.760

18661	$y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	6.819

18662	$x^{2} y - (x^{3} + y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	142.574

18663	$(3 x + 4 y) y^{'} + y - 2 x = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	88.821

18664	$3 y - 7 x + 7 + (7 y - 3 x + 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.176

18665	$(y - 3 x + 3) y^{'} = 2 y - x - 4$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	88.627

18666	$x^{2} - 4 x y - 2 y^{2} + (y^{2} - 4 x y - 2 x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	4.351

18667	$x + y y^{'} + \frac{y^{'} x - y}{x^{2} + y^{2}} = 0$	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓	1.526

18668	$a^{2} - 2 x y - y^{2} - {(x + y)}^{2} y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	1.554

18669	$2 a x + b y + g + (2 c y + b x + e) y^{'} = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.551

18670	$(2 x^{2} y + 4 x^{3} - 12 x y^{2} + 3 y^{2} - x e^{y} + e^{2 x}) y^{'} + 12 x^{2} y + 2 x y^{2} + 4 x^{3} - 4 y^{3} + 2 e^{2 x} y - e^{y} = 0$	[_exact]	✓	3.029

18671	$y - y^{'} x + \ln (x) = 0$	[_linear]	✓	0.949

18672	$(x y + 1) y - x (1 - x y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.898

18673	$a (y^{'} x + 2 y) = x y^{'} y$	[_separable]	✓	2.292

18674	$x^{4} e^{x} - 2 m x y^{2} + 2 m x^{2} y y^{'} = 0$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓	2.589

18675	$y (e^{x} + 2 x y) - e^{x} y^{'} = 0$	[_Bernoulli]	✓	2.289

18676	$x^{2} y - 2 x y^{2} - (x^{3} - 3 x^{2} y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.739

18677	$y (x y + 2 x^{2} y^{2}) + x (x y - x^{2} y^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.979

18678	$2 y y^{'} + 2 x + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.240

18679	$x^{2} + y^{2} - x^{2} y y^{'} = 0$	[_rational, _Bernoulli]	✓	1.889

18680	$3 x^{2} y^{4} + 2 x y + (2 x^{3} y^{3} - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	4.904

18681	$y^{4} + 2 y + (x y^{3} + 2 y^{4} - 4 x) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.293

18682	$y^{3} - 2 x^{2} y + (2 x y^{2} - x^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	46.452

18683	$2 x^{2} y - 3 y^{4} + (3 x^{3} + 2 x y^{3}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	4.543

18684	$y^{2} + 2 x^{2} y + (2 x^{3} - x y) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.321

18685	$y^{'} x - a y = x + 1$	[_linear]	✓	2.171

18686	$y^{'} + y = e^{- x}$	[[_linear, ‘class A‘]]	✓	0.911

18687	$\cos {(x)}^{2} y^{'} + y = \tan (x)$	[_linear]	✓	4.159

18688	$(x + 1) y^{'} - n y = e^{x} {(x + 1)}^{n + 1}$	[_linear]	✓	1.734

18689	$(x^{2} + 1) y^{'} + 2 x y = 4 x^{2}$	[_linear]	✓	1.194

18690	$y^{'} + \frac{y}{x} = y^{6} x^{2}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.280

18691	$1 + y^{2} = (\arctan (y) - x) y^{'}$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	8.149

18692	$y^{'} + \frac{2 y}{x} = 3 x^{2} y^{1 / 3}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	6.424

18693	$y^{'} + \frac{x y}{- x^{2} + 1} = x \sqrt{y}$	[_rational, _Bernoulli]	✓	2.586

18694	$3 x (- x^{2} + 1) y^{2} y^{'} + (2 x^{2} - 1) y^{3} = a x^{3}$	[_rational, _Bernoulli]	✓	2.482

18695	${(x + y)}^{2} y^{'} = a^{2}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	12.497

18696	$y^{'} x - y = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.200

18697	$y^{'} x - y = x \sqrt{x^{2} + y^{2}}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.533

18698	$\sec {(x)}^{2} \tan (y) + \sec {(y)}^{2} \tan (x) y^{'} = 0$	[_separable]	✓	39.977

18699	$y^{2} + x y^{2} + (x^{2} - x^{2} y) y^{'} = 0$	[_separable]	✓	1.906

18700	$y^{'} + \frac{(- 2 x + 1) y}{x^{2}} = 1$	[_linear]	✓	1.590

2.2.187 Problems 18601 to 18700