Problems 601 to 698

Table 2.31: Problems not solved by Maple


#	ODE	Mathematica	Maple

11104	$y^{''} + 2 k e^{x μ} y^{'} + (a e^{2 λ x} + b e^{λ x} + k^{2} e^{2 x μ} + k μ e^{x μ} + c) y = 0$	✓	✗

11109	$y^{''} + (a + b e^{2 λ x}) y^{'} + λ (a - λ - b e^{2 λ x}) y = 0$	✓	✗

11111	$y^{''} + (2 e^{λ x} a - λ) y^{'} + (a^{2} e^{2 λ x} + c e^{x μ}) y = 0$	✓	✗

11116	$y^{''} + (2 e^{λ x} a - λ) y^{'} + (a^{2} e^{2 λ x} + b e^{2 x μ} + c e^{x μ} + k) y = 0$	✓	✗

11117	$y^{''} + (2 e^{λ x} a + b - λ) y^{'} + (a^{2} e^{2 λ x} + a b e^{λ x} + c e^{2 x μ} + d e^{x μ} + k) y = 0$	✓	✗

11118	$y^{''} + (e^{λ x} a + b e^{x μ}) y^{'} + a e^{λ x} (b e^{x μ} + λ) y = 0$	✗	✗

11121	$y^{''} + (e^{λ x} a + b e^{x μ} + c) y^{'} + (a b e^{x (λ + μ)} + e^{λ x} a c + b μ e^{x μ}) y = 0$	✗	✗

11198	$x^{3} y^{4} + x^{2} y^{3} + x y^{2} + y + (x^{4} y^{3} - x^{3} y^{2} - x^{3} y + x) y^{'} = 0$	✗	✗

11224	${(x - y^{'} - y)}^{2} = x^{2} (2 x y - x^{2} y^{'})$	✗	✗

11230	$(- y + x y^{'}) (y y^{'} + x) = a^{2} y^{'}$	✓	✗

11329	$x^{2} (- x^{3} + 1) y^{''} - x^{3} y^{'} - 2 y = 0$	✗	✗

11404	${x^{'}}^{2} + t x = \sqrt{t + 1}$	✗	✗

11415	$\cos (θ) v^{'} + v = 3$	✗	✗

11518	$x^{'} + 4 x = \cos (2 t) Heaviside (2 π - t)$	✓	✗

11589	$y^{''} + y = 0$	✗	✗

11590	$y^{''} + y = 0$	✗	✗

11599	$3 x^{2} y + 2 - (x^{3} + y) y^{'} = 0$	✗	✗

11604	$\frac{2 y^{\frac{3}{2}} + 1}{x^{\frac{1}{3}}} + (3 \sqrt{x} \sqrt{y} - 1) y^{'} = 0$	✗	✗

11904	$(x^{4} - 2 x^{3} + x^{2}) y^{''} + 2 (- 1 + x) y^{'} + x^{2} y = 0$	✓	✗

11905	$(x^{5} + x^{4} - 6 x^{3}) y^{''} + x^{2} y^{'} + (- 2 + x) y = 0$	✓	✗

11994	$x^{'} = - x (k^{2} + x^{2})$	✓	✗

11995	$y^{'} + \frac{y}{x} = x^{2}$	✗	✗

12050	$(t \cos (t) - \sin (t)) x^{''} - x^{'} t \sin (t) - x \sin (t) = 0$	✗	✗

12134	$y^{'} = x y^{3} + x^{2}$	✗	✗

12214	$y^{'} = \sin (x y)$	✗	✗

12218	$y^{'} = t \ln (y^{2 t}) + t^{2}$	✓	✗

12220	$y^{'} = \ln (x y)$	✗	✗

12226	$y^{''} + y y^{''''} = 1$	✗	✗

12238	$y^{'''} + x y^{''} - y^{2} = \sin (x)$	✗	✗

12239	${y^{'}}^{2} + x y {y^{'}}^{2} = \ln (x)$	✗	✗

12240	$\sin (y^{''}) + y y^{''''} = 1$	✗	✗

12241	$\sinh (x) {y^{'}}^{2} + y^{''} = x y$	✗	✗

12243	${y^{'''}}^{2} + \sqrt{y} = \sin (x)$	✗	✗

12248	$(x - 3) y^{''} + \ln (x) y = x^{2}$	✗	✗

12251	$x y^{''} + 2 x^{2} y^{'} + y \sin (x) = \sinh (x)$	✗	✗

12252	$\sin (x) y^{''} + x y^{'} + 7 y = 1$	✗	✗

12264	$\ln (x^{2} + 1) y^{''} + \frac{4 x y^{'}}{x^{2} + 1} + \frac{(- x^{2} + 1) y}{{(x^{2} + 1)}^{2}} = 0$	✗	✗

12269	$x y^{''} + (6 x y^{2} + 1) y^{'} + 2 y^{3} + 1 = 0$	✗	✗

12281	$y^{''} + \frac{(- 1 + x) y^{'}}{x} + \frac{y}{x^{3}} = \frac{e^{- \frac{1}{x}}}{x^{3}}$	✗	✗

12352	$t^{2} y^{''} - 6 t y^{'} + \sin (2 t) y = \ln (t)$	✗	✗

12354	$y^{''} + t y^{'} - y \ln (t) = \cos (2 t)$	✗	✗

12406	$x^{3} y^{''} + x^{2} y^{'} + y = 0$	✓	✗

12407	$x^{2} y^{''} + y^{'} - 2 y = 0$	✓	✗

12412	$x y^{''} + {(1 + x)}^{2} y = 0$	✗	✗

12421	$x y (1 - {y^{'}}^{2}) = (x^{2} - y^{2} - a^{2}) y^{'}$	✓	✗

12570	$x^{''} + x^{'} + x - x^{3} = 0$	✗	✗

12571	$x^{''} + x^{'} + x + x^{3} = 0$	✗	✗

12614	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$	✗	✗

12631	$y^{'} = x^{3} + y^{3}$	✗	✗

12636	$y^{'} = \frac{1}{\sqrt{15 - x^{2} - y^{2}}}$	✗	✗

12749	$(x^{2} - 4) y^{''} + \ln (x) y = x e^{x}$	✗	✗

12827	$[y_{1}^{'} (x) = \sin (x) y_{1} (x) + \sqrt{x} y_{2} (x) + \ln (x), y_{2}^{'} (x) = \tan (x) y_{1} (x) - e^{x} y_{2} (x) + 1]$	✗	✗

12828	$[y_{1}^{'} (x) = \sin (x) y_{1} (x) + \sqrt{x} y_{2} (x) + \ln (x), y_{2}^{'} (x) = \tan (x) y_{1} (x) - e^{x} y_{2} (x) + 1]$	✗	✗

12829	$[y_{1}^{'} (x) = e^{- x} y_{1} (x) - \sqrt{1 + x} y_{2} (x) + x^{2}, y_{2}^{'} (x) = \frac{y_{1} (x)}{{(- 2 + x)}^{2}}]$	✗	✗

12830	$[y_{1}^{'} (x) = e^{- x} y_{1} (x) - \sqrt{1 + x} y_{2} (x) + x^{2}, y_{2}^{'} (x) = \frac{y_{1} (x)}{{(- 2 + x)}^{2}}]$	✗	✗

12842	$[y_{1}^{'} (x) = 2 x y_{1} (x) - x^{2} y_{2} (x) + 4 x, y_{2}^{'} (x) = e^{x} y_{1} (x) + 3 e^{- x} y_{2} (x) - \cos (3 x)]$	✗	✗

12938	$y^{'} = 2 y^{3} + t^{2}$	✗	✗

13034	$y^{'} = (y - 3) (\sin (y) \sin (t) + \cos (t) + 1)$	✗	✗

13057	$y^{'} = (y - 1) (y - 2) (y - e^{\frac{t}{2}})$	✗	✗

13250	$y^{2} y^{''} = 8 x^{2}$	✗	✗

13289	$\sin (x + y) - y y^{'} = 0$	✗	✗

13348	$y^{2} y^{'} + 3 x^{2} y = \sin (x)$	✗	✗

13529	$y^{''} + x^{2} y^{'} + 4 y = y^{3}$	✗	✗

13535	$y y^{'''} + 6 y^{''} + 3 y^{'} = y$	✗	✗

13559	$x^{3} y^{'''} - 4 y^{''} + 10 y^{'} - 12 y = 0$	✗	✗

13569	$x^{2} y^{''} - 4 x y^{'} + 6 y = 0$	✗	✗

13570	$x y^{''} - y^{'} + 4 x^{3} y = 0$	✗	✗

14043	$[x^{'} (t) = x (t) y (t) - 6 y (t), y^{'} (t) = x (t) - y (t) - 5]$	✗	✗

14050	$x {y^{''}}^{2} + 2 y = 2 x$	✗	✗

14051	$x^{''} + 2 \sin (x) = \sin (2 t)$	✗	✗

14101	$4 x (x^{2} + y^{2}) - 5 y + 4 y (x^{2} + y^{2} - 5 x) y^{'} = 0$	✗	✗

14121	$y^{''} + 4 y = t$	✗	✗

14126	$y^{'} + t^{2} = \frac{1}{y^{2}}$	✗	✗

14133	$y^{'} = \sin (y) - \cos (t)$	✗	✗

14296	$e^{2 t} - y - (e^{y} - t) y^{'} = 0$	✗	✗

14313	$1 - y^{2} \cos (t y) + (t y \cos (t y) + \sin (t y)) y^{'} = 0$	✗	✗

14323	$e^{y} - 2 t y + (t e^{y} - t^{2}) y^{'} = 0$	✗	✗

14327	$\frac{1}{t^{2} + 1} - y^{2} - 2 t y y^{'} = 0$	✗	✗

14328	$\frac{2 t}{t^{2} + 1} + y + (e^{y} + t) y^{'} = 0$	✗	✗

14440	$y^{'} = x + y^{\frac{1}{3}}$	✗	✗

14441	$y^{'} = \sin (x^{2} y)$	✗	✗

14472	$y^{''} + b (t) y^{'} + c (t) y = 0$	✗	✗

14473	$y^{''} + b (t) y^{'} + c (t) y = 0$	✗	✗

14626	$e^{- 2 t} (y y^{''} - {y^{'}}^{2}) - 2 t (t + 1) y = 0$	✗	✗

14633	$4 t^{2} y^{''} + 4 t y^{'} + (16 t^{2} - 1) y = 16 t^{\frac{3}{2}}$	✗	✗

14803	$x (1 + x) y^{''} + \frac{y^{'}}{x^{2}} + 5 y = 0$	✓	✗

14870	$y^{''} - 8 y^{'} + 16 y = \frac{e^{4 t}}{t^{3}}$	✗	✗

14941	$y^{'} = \sin (y) - \cos (x)$	✗	✗

15001	$x^{3} y^{'} - \sin (y) = 1$	✗	✗

15059	$y^{'} - \tan (y) = \frac{e^{x}}{\cos (y)}$	✓	✗

15197	$y^{'''} = \sqrt{1 - {y^{''}}^{2}}$	✓	✗

15217	$y^{3} y^{''} = - 1$	✓	✗

15432	$4 x y^{''} + 2 y^{'} + y = 1$	✓	✗

15444	$x^{''} - 2 {x^{'}}^{2} + x^{'} - 2 x = 0$	✗	✗

15446	$x^{''} + e^{- x^{'}} - x = 0$	✗	✗

15449	$x^{''} - x^{'} + x - x^{2} = 0$	✗	✗

15453	$y^{''} + y = 0$	✗	✗

15524	$[x^{'} (t) = \cos {(x (t))}^{2} \cos {(y (t))}^{2} + \sin {(x (t))}^{2} \cos {(y (t))}^{2}, y^{'} (t) = - \frac{\sin (2 x (t)) \sin (2 y (t))}{2}]$	✗	✗

2.2.7 Problems 601 to 698