2.3.52 Problems 5101 to 5200

Table 2.653: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5101	21287	\begin{align*} x^{\prime }-x&=k \delta \left (t \right ) \\ x \left (0\right ) &= a \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.401
5102	22880	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.401
5103	23645	\begin{align*} y^{\prime \prime \prime }-y&=-1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.401
5104	23786	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.401
5105	25113	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.401
5106	25132	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=16 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.401
5107	25138	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&=10 t \,{\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.401
5108	5395	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.402
5109	7235	\begin{align*} \left ({\mathrm e}^{x}+1\right ) y^{\prime }+2 \,{\mathrm e}^{x} y&=\left ({\mathrm e}^{x}+1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.402
5110	7240	\begin{align*} x^{\prime }&=\cos \left (y \right )-x \tan \left (y \right ) \\ \end{align*}	✓	✓	✓	✓	0.402
5111	8498	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.402
5112	8573	\begin{align*} y^{\prime \prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.402
5113	9606	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.402
5114	10350	\begin{align*} y^{\prime } x +y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.402
5115	10460	\begin{align*} x^{\prime }&=3 x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.402
5116	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*}	✓	✓	✓	✗	0.402
5117	14385	\begin{align*} x^{\prime }&=-2 x-y \\ y^{\prime }&=-4 y \\ \end{align*}	✓	✓	✓	✓	0.402
5118	15010	\begin{align*} x^{\prime }&=-6 x+2 y \\ y^{\prime }&=-2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.402
5119	16820	\begin{align*} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.402
5120	22272	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=9 x+y \\ \end{align*}	✓	✓	✓	✓	0.402
5121	22732	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.402
5122	23004	\begin{align*} 8 y^{\prime \prime }-10 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.402
5123	24053	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.402
5124	1	\begin{align*} y^{\prime }&=2 x +1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.403
5125	629	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.403
5126	974	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.403
5127	2151	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \\ \end{align*}	✓	✓	✓	✓	0.403
5128	2425	\begin{align*} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t +y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.403
5129	3936	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.403
5130	6939	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.403
5131	7757	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.403
5132	7887	\begin{align*} x \sqrt {x^{2}+y^{2}}-y+\left (y \sqrt {x^{2}+y^{2}}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.403
5133	7993	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-2 x^{2}+2 x +2 \\ \end{align*}	✓	✓	✓	✓	0.403
5134	8031	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.403
5135	10726	\begin{align*} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.403
5136	19686	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.403
5137	23588	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.403
5138	25131	\begin{align*} y^{\prime \prime }-4 y&={\mathrm e}^{-6 t} \\ \end{align*}	✓	✓	✓	✓	0.403
5139	471	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.404
5140	973	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.404
5141	1089	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.404
5142	2294	\begin{align*} y^{\prime }+{\mathrm e}^{t^{2}} y&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.404
5143	3570	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.404
5144	7200	\begin{align*} u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.404
5145	8902	\begin{align*} y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.404
5146	10252	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2} \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.404
5147	14146	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.404
5148	14975	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.404
5149	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*}	✓	✓	✓	✓	0.404
5150	22823	\begin{align*} y^{\prime }&=2 x -y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.404
5151	24512	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.404
5152	25333	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } t -4 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.404
5153	26550	\begin{align*} y^{\prime \prime }-2 k y^{\prime }+k^{2} y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.404
5154	26579	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.404
5155	374	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.405
5156	1335	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.405
5157	1336	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}	✓	✓	✓	✓	0.405
5158	1369	\begin{align*} \left (-x^{2}+3\right ) y^{\prime \prime }-3 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.405
5159	5906	\begin{align*} b x y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.405
5160	6304	\begin{align*} y^{\prime \prime }&=a +y x +2 y^{3} \\ \end{align*}	✗	✗	✗	✗	0.405
5161	7718	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.405
5162	9450	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.405
5163	9455	\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&={\mathrm e}^{2 t} t \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.405
5164	10255	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.405
5165	12413	\begin{align*} x^{2} y^{\prime \prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.405
5166	12760	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-6 x^{3} \left (x -1\right ) \ln \left (x \right )+x^{3} \left (8+x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.405
5167	14580	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.405
5168	15220	\begin{align*} y+2 y^{\prime }&={\mathrm e}^{-\frac {t}{2}} \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.405
5169	15392	\begin{align*} y&=y y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.405
5170	16413	\begin{align*} \left (y-3\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.405
5171	16842	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.405
5172	16939	\begin{align*} x^{\prime }&=-2 y \\ y^{\prime }&=8 x \\ \end{align*}	✓	✓	✓	✓	0.405
5173	22082	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.405
5174	23258	\begin{align*} y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.405
5175	26414	\begin{align*} y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.405
5176	1403	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.406
5177	2420	\begin{align*} y^{\prime \prime }-2 y^{\prime } t +\lambda y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.406
5178	8636	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3} \\ y \left (\frac {3}{2}\right ) &= 4 \\ y^{\prime }\left (\frac {3}{2}\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.406
5179	9259	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.406
5180	10345	\begin{align*} y^{\prime }+\left (a t +b t \right ) y&=0 \\ y \left (-3\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.406
5181	10986	\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.406
5182	16615	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-200 \\ \end{align*}	✓	✓	✓	✓	0.406
5183	17622	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.406
5184	18133	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.406
5185	8892	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.407
5186	11069	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.407
5187	15081	\begin{align*} y^{\prime \prime }+4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.407
5188	19689	\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.407
5189	1929	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5190	2414	\begin{align*} \left (t^{2}+2\right ) y^{\prime \prime }-y^{\prime } t -3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.408
5191	2784	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{2} \\ x_{3}^{\prime }&=3 x_{3}+{\mathrm e}^{2 t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.408
5192	6014	\begin{align*} \left (x^{2}+6\right ) y+4 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5193	6961	\begin{align*} 2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5194	8485	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5195	8494	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5196	10495	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5197	12294	\begin{align*} y^{\prime \prime }-c \,x^{a} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.408
5198	13156	\(\left [\begin {array}{ccc} 3 & 6 & -2 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.408
5199	14716	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.408
5200	15470	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.408