Problems 8301 to 8400

Table 2.169: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	Maple	Mma	Sympy

8301	$4 x^{2} y^{''} + (16 x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8302	$x y^{''} + 3 y^{'} + x^{3} y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

8303	$9 x^{2} y^{''} + 9 y^{'} x + (x^{6} - 36) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8304	$y^{''} - x^{2} y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✗

8305	$x y^{''} + y^{'} - 7 x^{3} y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

8306	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

8307	$x^{2} y^{''} + 4 y^{'} x + (x^{2} + 2) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8308	$16 x^{2} y^{''} + 32 y^{'} x + (x^{4} - 12) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8309	$4 x^{2} y^{''} - 4 y^{'} x + (16 x^{2} + 3) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8310	$2 x y^{''} + y^{'} + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓	✓	✓

8311	$y^{''} - y^{'} x - y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

8312	$(x - 1) y^{''} + 3 y = 0$	[[_Emden, _Fowler]]	✓	✓	✓	✓

8313	$y^{''} - x^{2} y^{'} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8314	$x y^{''} - (x + 2) y^{'} + 2 y = 0$	[_Laguerre]	✓	✓	✓	✓

8315	$\cos (x) y^{''} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8316	$y^{''} + y^{'} x + 2 y = 0$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8317	$(x + 2) y^{''} + 3 y = 0$ i.c.	[[_Emden, _Fowler]]	✓	✓	✓	✓

8318	$(1 - 2 \sin (x)) y^{''} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8319	$y^{''} + y^{'} x + y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	✓	✓	✓

8320	$x y^{''} + (1 - \cos (x)) y^{'} + x^{2} y = 0$ i.c.	[[_Emden, _Fowler]]	✓	✓	✓	✓

8321	$(e^{x} - 1 - x) y^{''} + x y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

8322	$y^{''} + x^{2} y^{'} + 2 x y = 10 x^{3} - 2 x + 5$	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	✓	✓	✗

8323	$- y + y^{'} = 1$ i.c.	[_quadrature]	✓	✓	✓	✓

8324	$y + 2 y^{'} = 0$ i.c.	[_quadrature]	✓	✓	✓	✓

8325	$y^{'} + 6 y = e^{4 t}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

8326	$- y + y^{'} = 2 \cos (5 t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

8327	$y^{''} + 5 y^{'} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

8328	$y^{''} - 4 y^{'} = 6 e^{3 t} - 3 e^{- t}$ i.c.	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

8329	$y^{''} + y = \sqrt{2} \sin (\sqrt{2} t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8330	$y^{''} + 9 y = e^{t}$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8331	$2 y^{'''} + 3 y^{''} - 3 y^{'} - 2 y = e^{- t}$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8332	$y^{'''} + 2 y^{''} - y^{'} - 2 y = \sin (3 t)$ i.c.	[[_3rd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8333	$y + y^{'} = e^{- 3 t} \cos (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

8334	$y^{''} - 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

8335	$y^{'} + 4 y = e^{- 4 t}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

8336	$- y + y^{'} = 1 + e^{t} t$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

8337	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

8338	$y^{''} - 4 y^{'} + 4 y = t^{3} e^{2 t}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8339	$y^{''} - 6 y^{'} + 9 y = t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8340	$y^{''} - 4 y^{'} + 4 y = t^{3}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8341	$y^{''} - 6 y^{'} + 13 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

8342	$2 y^{''} + 20 y^{'} + 51 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

8343	$y^{''} - y = e^{t} \cos (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8344	$y^{''} - 2 y^{'} + 5 y = 1 + t$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓

8345	$y^{''} + 2 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

8346	$y^{''} + 8 y^{'} + 20 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

8347	$y + y^{'} = {\begin{array}{cc} 0 & 0 \leq t < 1 \\ 5 & 1 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✗

8348	$y + y^{'} = {\begin{array}{cc} 1 & 0 \leq t < 1 \\ - 1 & 1 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✗

8349	$y + y^{'} = {\begin{array}{cc} t & 0 \leq t < 1 \\ 0 & 1 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✗

8350	$y^{''} + 4 y = {\begin{array}{cc} 1 & 0 \leq t < 1 \\ 0 & 1 \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8351	$y^{''} + 4 y = Heaviside (t - 2 π) \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8352	$y^{''} - 5 y^{'} + 6 y = Heaviside (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8353	$y^{''} + y = {\begin{array}{cc} 0 & 0 \leq t < π \\ 1 & π \leq t < 2 π \\ 0 & 2 π \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8354	$y^{''} + 4 y^{'} + 3 y = 1 - Heaviside (t - 2) - Heaviside (t - 4) + Heaviside (t - 6)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8355	$y + y^{'} = t \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

8356	$- y + y^{'} = t e^{t} \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

8357	$y^{''} + 9 y = \cos (3 t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8358	$y^{''} + y = \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8359	$y^{''} + 16 y = {\begin{array}{cc} \cos (4 t) & 0 \leq t < π \\ 0 & π \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8360	$y^{''} + y = {\begin{array}{cc} 1 & 0 \leq t < \frac{π}{2} \\ \sin (t) & \frac{π}{2} \leq t \end{array}$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8361	$t y^{''} - y^{'} = 2 t^{2}$ i.c.	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

8362	$2 y^{''} + y^{'} t - 2 y = 10$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✗

8363	$y^{''} + y = \sin (t) + t \sin (t)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8364	$y^{'} - 3 y = δ (t - 2)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

8365	$y + y^{'} = δ (t - 1)$ i.c.	[[_linear, ‘class A‘]]	✓	✓	✓	✓

8366	$y^{''} + y = δ (t - 2 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8367	$y^{''} + 16 y = δ (t - 2 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8368	$y^{''} + y = δ (t - \frac{π}{2}) + δ (t - \frac{3 π}{2})$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8369	$y^{''} + y = δ (t - 2 π) + δ (t - 4 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8370	$y^{''} + 2 y^{'} = δ (t - 1)$ i.c.	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

8371	$y^{''} - 2 y^{'} = 1 + δ (t - 2)$ i.c.	[[_2nd_order, _missing_y]]	✓	✓	✓	✓

8372	$y^{''} + 4 y^{'} + 5 y = δ (t - 2 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8373	$y^{''} + 2 y^{'} + y = δ (t - 1)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8374	$y^{''} + 4 y^{'} + 13 y = δ (t - π) + δ (t - 3 π)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8375	$y^{''} - 7 y^{'} + 6 y = e^{t} + δ (t - 2) + δ (t - 4)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✗

8376	$y^{''} + 2 y^{'} + 10 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	✓	✓	✓

8377	$y^{''} + 2 y^{'} + 10 y = δ (t)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓

8378	$[\begin{matrix} x^{'} = 3 x - 5 y \\ y^{'} = 4 x + 8 y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8379	$[\begin{matrix} x^{'} = 4 x - 7 y \\ y^{'} = 5 x \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8380	$[\begin{matrix} x^{'} = - 3 x + 4 y - 9 z \\ y^{'} = 6 x - y \\ z^{'} = 10 x + 4 y + 3 z \end{matrix}]$	system_of_ODEs	✓	✓	✓	✗

8381	$[\begin{matrix} x^{'} = x - y \\ y^{'} = x + 2 z \\ z^{'} = - x + z \end{matrix}]$	system_of_ODEs	✓	✓	✓	✗

8382	$[\begin{matrix} x^{'} = x - y + z + t - 1 \\ y^{'} = 2 x + y - z - 3 t^{2} \\ z^{'} = x + y + z + t^{2} - t + 2 \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8383	$[\begin{matrix} x^{'} = - 3 x + 4 y + e^{- t} \sin (2 t) \\ y^{'} = 5 x + 9 z + 4 e^{- t} \cos (2 t) \\ z^{'} = y + 6 z - e^{- t} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✗

8384	$[\begin{matrix} x^{'} = 4 x + 2 y + e^{t} \\ y^{'} = - x + 3 y - e^{t} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8385	$[\begin{matrix} x^{'} = 7 x + 5 y - 9 z - 8 e^{- 2 t} \\ y^{'} = 4 x + y + z + 2 e^{5 t} \\ z^{'} = - 2 y + 3 z + e^{5 t} - 3 e^{- 2 t} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✗

8386	$[\begin{matrix} x^{'} = x - y + 2 z + e^{- t} - 3 t \\ y^{'} = 3 x - 4 y + z + 2 e^{- t} + t \\ z^{'} = - 2 x + 5 y + 6 z + 2 e^{- t} - t \end{matrix}]$	system_of_ODEs	✓	✗	✓	✗

8387	$[\begin{matrix} x^{'} = 3 x - 7 y + 4 \sin (t) + (t - 4) e^{4 t} \\ y^{'} = x + y + 8 \sin (t) + (2 t + 1) e^{4 t} \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8388	$[\begin{matrix} x^{'} = 3 x - 4 y \\ y^{'} = 4 x - 7 y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8389	$[\begin{matrix} x^{'} = - 2 x + 5 y \\ y^{'} = - 2 x + 4 y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8390	$[\begin{matrix} x^{'} = - x + \frac{y}{4} \\ y^{'} = x - y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8391	$[\begin{matrix} x^{'} = 2 x + y \\ y^{'} = - x \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8392	$[\begin{matrix} x^{'} = x + 2 y + z \\ y^{'} = 6 x - y \\ z^{'} = - x - 2 y - z \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8393	$[\begin{matrix} x^{'} = x + z \\ y^{'} = x + y \\ z^{'} = - 2 x - z \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8394	$[\begin{matrix} x^{'} = x + 2 y \\ y^{'} = 4 x + 3 y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8395	$[\begin{matrix} x^{'} = 2 x + 2 y \\ y^{'} = x + 3 y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8396	$[\begin{matrix} x^{'} = - 4 x + 2 y \\ y^{'} = - \frac{5 x}{2} + 2 y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8397	$[\begin{matrix} x^{'} = - \frac{5 x}{2} + 2 y \\ y^{'} = \frac{3 x}{4} - 2 y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8398	$[\begin{matrix} x^{'} = 10 x - 5 y \\ y^{'} = 8 x - 12 y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8399	$[\begin{matrix} x^{'} = - 6 x + 2 y \\ y^{'} = - 3 x + y \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

8400	$[\begin{matrix} x^{'} = x + y - z \\ y^{'} = 2 y \\ z^{'} = y - z \end{matrix}]$	system_of_ODEs	✓	✓	✓	✓

2.2.84 Problems 8301 to 8400