2.3.112 Problems 11101 to 11200

Table 2.755: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
11101	18956	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.590
11102	21670	\begin{align*} y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.590
11103	716	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.591
11104	7608	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y \left (\pi \right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.591
11105	1244	\begin{align*} y^{\prime }&=\frac {x}{x^{2}+y+y^{3}} \\ \end{align*}	✓	✓	✓	✓	1.592
11106	2481	\begin{align*} y^{\prime }-2 t y&=t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.592
11107	3447	\begin{align*} y^{\prime }&=2 y \\ y \left (\ln \left (3\right )\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.594
11108	194	\begin{align*} y^{\prime }&=x^{2}-2 y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	1.595
11109	1299	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.595
11110	10101	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	1.595
11111	12299	\begin{align*} y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.595
11112	16416	\begin{align*} y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	1.595
11113	2476	\begin{align*} t^{2} y+y^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	1.596
11114	8096	\begin{align*} x^{2} y^{\prime \prime }+4 \left (a +x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.596
11115	1150	\begin{align*} y^{\prime }&=\frac {3 x^{2}}{-4+3 y^{2}} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.597
11116	14413	\begin{align*} y^{\prime }+y&=x +1 \\ \end{align*}	✓	✓	✓	✓	1.597
11117	24437	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.597
11118	2483	\begin{align*} y+y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.598
11119	5358	\begin{align*} {y^{\prime }}^{2}+x^{2}&=4 y \\ \end{align*}	✓	✓	✓	✗	1.598
11120	15061	\begin{align*} \left (y^{2}-x \right ) y^{\prime }-y+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.598
11121	22340	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	1.598
11122	22474	\begin{align*} y^{\prime }&=\frac {x^{3}+2 y}{x^{3}+x} \\ \end{align*}	✓	✓	✓	✓	1.598
11123	1266	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.599
11124	2325	\begin{align*} y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.599
11125	6556	\begin{align*} y^{3} y^{\prime \prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	1.599
11126	7964	\begin{align*} y \left (3-4 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\ \end{align*}	✓	✓	✓	✓	1.599
11127	22499	\begin{align*} y^{\prime \prime }&=-\frac {4}{y^{3}} \\ y \left (2\right ) &= 4 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align*}	✓	✗	✓	✗	1.599
11128	7944	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.600
11129	245	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.602
11130	9755	\begin{align*} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✗	✗	1.602
11131	11319	\begin{align*} y^{\prime }-y^{2}-3 y+4&=0 \\ \end{align*}	✓	✓	✓	✓	1.602
11132	15120	\begin{align*} y^{\prime } x +y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	1.602
11133	22344	\begin{align*} y^{\prime }&=\frac {1}{x^{2}-y^{2}} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	1.602
11134	5549	\begin{align*} y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.603
11135	22003	\begin{align*} x^{2}+1+\frac {y^{\prime }}{y}&=0 \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.603
11136	3488	\begin{align*} f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.604
11137	4656	\begin{align*} y^{\prime }&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.604
11138	6424	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=a^{2} \\ \end{align*}	✓	✓	✓	✗	1.604
11139	7138	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x&=1 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.604
11140	10743	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.604
11141	24772	\begin{align*} 2 y^{\prime }+2 y+w^{\prime }-w&=x +1 \\ y^{\prime }+3 y+w^{\prime }+w&=4 x +14 \\ \end{align*}	✓	✓	✓	✓	1.604
11142	14782	\begin{align*} x^{\prime }+y^{\prime }-x+5 y&=t^{2} \\ x^{\prime }+2 y^{\prime }-2 x+4 y&=2 t +1 \\ \end{align*}	✓	✓	✓	✓	1.605
11143	20135	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	1.605
11144	834	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.607
11145	6960	\begin{align*} y-\left (x^{2}+y^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.607
11146	457	\begin{align*} y^{\prime \prime } x +\left (-x^{3}+x \right ) y^{\prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.609
11147	13682	\begin{align*} y^{\prime \prime }+a x y^{\prime }+b x y&=0 \\ \end{align*}	✗	✓	✓	✗	1.609
11148	22180	\begin{align*} {\mathrm e}^{x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.609
11149	3972	\begin{align*} y+y^{\prime }&=\delta \left (t -5\right ) \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.610
11150	3628	\begin{align*} y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.611
11151	15072	\begin{align*} y^{\prime \prime }+y&=\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.611
11152	18061	\begin{align*} 2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.611
11153	20411	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	1.611
11154	20542	\begin{align*} x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.611
11155	24826	\begin{align*} 5 {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	1.611
11156	8901	\begin{align*} y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.612
11157	17795	\begin{align*} t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime }&=1 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	1.612
11158	14644	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=9 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.613
11159	22503	\begin{align*} y&=y^{\prime } x -\tan \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	1.613
11160	15282	\begin{align*} x^{\prime }&=-14 x+39 y+78 \sinh \left (t \right ) \\ y^{\prime }&=-6 x+16 y+6 \cosh \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.614
11161	15440	\begin{align*} y^{\prime \prime }+2 h y^{\prime }+n^{2} y&=0 \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= c \\ \end{align*}	✓	✓	✓	✓	1.614
11162	7187	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.616
11163	1429	\begin{align*} x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.617
11164	2069	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.617
11165	6152	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.617
11166	8462	\begin{align*} y^{\prime }-2 y x&=1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.617
11167	1172	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.618
11168	5416	\begin{align*} {y^{\prime }}^{2}+\left (1+2 y\right ) y^{\prime }+y \left (-1+y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.618
11169	19261	\begin{align*} y^{\prime }&=\ln \left (x \right ) \\ y \left ({\mathrm e}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.618
11170	19488	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.619
11171	20372	\begin{align*} y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.619
11172	5056	\begin{align*} 1-y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	1.621
11173	7902	\begin{align*} y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.621
11174	18566	\begin{align*} y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.621
11175	20536	\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.621
11176	10102	\begin{align*} y^{\prime \prime }-4 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	1.622
11177	24729	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.622
11178	1283	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.623
11179	25436	\begin{align*} y^{\prime }&=a \left (t \right ) y+q \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.623
11180	12414	\begin{align*} a y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.624
11181	15615	\begin{align*} y^{\prime }&=y^{2} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.624
11182	19793	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	1.624
11183	22987	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\sec \left (x \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.624
11184	1240	\begin{align*} \left (1+t \right ) y+y^{\prime } t&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	1.625
11185	10789	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.625
11186	25457	\begin{align*} y^{\prime }&=y-t^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.625
11187	3588	\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.626
11188	5372	\begin{align*} {y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.626
11189	15054	\begin{align*} x^{2}-y+\left (y^{2} x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.626
11190	17882	\begin{align*} {\mathrm e}^{-y} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.626
11191	22550	\begin{align*} n^{\prime }&=-a n \\ n \left (0\right ) &= n_{0} \\ \end{align*}	✓	✓	✓	✓	1.626
11192	12535	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.627
11193	24943	\begin{align*} y^{\prime }&=\frac {t y}{1+y} \\ \end{align*}	✓	✓	✓	✓	1.627
11194	2400	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.628
11195	19614	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.628
11196	7556	\begin{align*} t +x+3+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.629
11197	19563	\begin{align*} y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	1.629
11198	25692	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.629
11199	5431	\begin{align*} {y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	1.630
11200	56	\begin{align*} \left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.631