2.3.52 Problems 5101 to 5200

Table 2.635: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5101	10910	\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.270
5102	12608	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x^{3}}+\frac {2 y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.270
5103	14146	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.270
5104	14821	\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.270
5105	14995	\(\left [\begin {array}{cc} 2 & -3 \\ 3 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.270
5106	16460	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.270
5107	17863	\begin{align*} y^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	0.270
5108	19064	\begin{align*} y^{\prime }&=-x^{3} \\ \end{align*}	✓	✓	✓	✓	0.270
5109	22635	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.270
5110	23353	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	0.270
5111	23438	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.270
5112	24536	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.270
5113	24544	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=6 x +6 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.270
5114	1055	\begin{align*} y^{\prime \prime }+y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.271
5115	3193	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.271
5116	3503	\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.271
5117	3926	\begin{align*} x_{1}^{\prime }&=10 x_{1}-8 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.271
5118	4130	\begin{align*} y^{\prime \prime }+y&=x^{3}+x \\ \end{align*}	✓	✓	✓	✓	0.271
5119	7981	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.271
5120	9357	\begin{align*} y^{\prime }-y&=x^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.271
5121	10567	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.271
5122	12924	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.271
5123	14871	\begin{align*} x^{\prime }&=\sin \left (t \right )+\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.271
5124	16002	\begin{align*} x^{\prime }&=-4 x+y \\ y^{\prime }&=2 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.271
5125	18859	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.271
5126	19459	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.271
5127	20488	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=\ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.271
5128	22298	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.271
5129	22845	\begin{align*} y^{\prime \prime }+y x&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.271
5130	24651	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.271
5131	24662	\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{\frac {x}{2}}+12 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.271
5132	24696	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2}-3 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.271
5133	24706	\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{6} \\ \end{align*}	✓	✓	✓	✓	0.271
5134	25546	\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.271
5135	25817	\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.271
5136	4069	\begin{align*} \left (4 x^{2}+1\right ) y^{\prime \prime }-8 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.272
5137	4166	\begin{align*} y_{1}^{\prime }&=y_{1}+y_{2} \\ y_{2}^{\prime }&=3 y_{2}-y_{1} \\ \end{align*}	✓	✓	✓	✓	0.272
5138	8965	\begin{align*} y^{\prime \prime }+x^{3} y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.272
5139	10302	\begin{align*} x \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.272
5140	10380	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.272
5141	10669	\begin{align*} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.272
5142	10703	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.272
5143	14583	\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.272
5144	17596	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=-\frac {1}{t^{2}}-\frac {2}{t} \\ \end{align*}	✓	✓	✓	✓	0.272
5145	20421	\begin{align*} y&=y^{\prime } \left (-b +x \right )+\frac {a}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	0.272
5146	20512	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.272
5147	22617	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.272
5148	23706	\begin{align*} y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.272
5149	23848	\begin{align*} y^{\prime \prime }+y&=2 x -1 \\ \end{align*}	✓	✓	✓	✓	0.272
5150	24613	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.272
5151	24643	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.272
5152	25244	\begin{align*} -t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.272
5153	1377	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.273
5154	1765	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.273
5155	4129	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-2 x^{2}+2 x +2 \\ \end{align*}	✓	✓	✓	✓	0.273
5156	6550	\begin{align*} x y^{2} y^{\prime \prime }&=a \\ \end{align*}	✗	✓	✓	✗	0.273
5157	6871	\begin{align*} u^{\prime }+b u^{2}&=\frac {c}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	0.273
5158	7755	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=8 \\ \end{align*}	✓	✓	✓	✓	0.273
5159	7804	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=\frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.273
5160	8568	\begin{align*} y^{\prime } x -3 y&=k \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.273
5161	8895	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.273
5162	10263	\begin{align*} y^{\prime }&=a x \\ \end{align*}	✓	✓	✓	✓	0.273
5163	10460	\begin{align*} x^{\prime }&=3 x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.273
5164	10470	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
5165	10533	\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
5166	10568	\begin{align*} 2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
5167	10657	\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
5168	10708	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
5169	11142	\begin{align*} x^{4} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
5170	11180	\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
5171	13192	\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 2 & 0 \\ -1 & 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.273
5172	14376	\begin{align*} x^{\prime }&=-3 x \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.273
5173	14993	\(\left [\begin {array}{cc} 9 & 2 \\ 2 & 6 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.273
5174	16864	\begin{align*} y^{\prime }-{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.273
5175	17585	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.273
5176	18923	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.273
5177	19022	\begin{align*} x_{1}^{\prime }&=\frac {x_{1}}{2}-\frac {x_{2}}{4} \\ x_{2}^{\prime }&=x_{1}-\frac {x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.273
5178	21283	\begin{align*} x^{\prime \prime }-4 x^{\prime }+3 x&=1 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.273
5179	24579	\begin{align*} y^{\prime \prime }+9 y&=4 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.273
5180	24707	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.273
5181	25651	\begin{align*} u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \\ \end{align*}	✗	✗	✗	✗	0.273
5182	445	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ y \left (3\right ) &= 2 \\ y^{\prime }\left (3\right ) &= 0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.274
5183	2417	\begin{align*} y^{\prime \prime }+t^{2} y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.274
5184	3801	\begin{align*} y^{\prime \prime }-4 y&=5 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.274
5185	3855	\begin{align*} x_{1}^{\prime }&=-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.274
5186	5931	\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.274
5187	8338	\begin{align*} y^{\prime }&=\sin \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.274
5188	10675	\begin{align*} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.274
5189	10984	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.274
5190	14101	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.274
5191	14396	\begin{align*} x^{\prime }&=-3 x+y \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.274
5192	16003	\begin{align*} x^{\prime }&=-4 x+y \\ y^{\prime }&=2 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.274
5193	17992	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime } x -8 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.274
5194	18815	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=3 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.274
5195	20045	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.274
5196	22108	\begin{align*} 3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.274
5197	23507	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&={\mathrm e}^{2 x} \left (x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.274
5198	23767	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.274
5199	24690	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.274
5200	24695	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=4 \cos \left (x \right ) {\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.274