2.3.118 Problems 11701 to 11800

Table 2.767: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
11701	4766	\begin{align*} y^{\prime } x +2+\left (-x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.815
11702	5953	\begin{align*} x^{2} y^{\prime \prime }&=b x +a \\ \end{align*}	✓	✓	✓	✓	1.815
11703	16425	\begin{align*} y y^{\prime \prime }+2 {y^{\prime }}^{2}&=3 y y^{\prime } \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= {\frac {3}{4}} \\ \end{align*}	✓	✓	✓	✗	1.815
11704	23166	\begin{align*} y^{\prime }+\frac {y}{x}&=-2 x y^{2} \\ \end{align*}	✓	✓	✓	✓	1.815
11705	12284	\begin{align*} y^{\prime \prime }+y-a \cos \left (b x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.816
11706	22482	\begin{align*} x^{2} y^{\prime \prime }&=x^{2}+1 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.816
11707	1216	\begin{align*} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.817
11708	2407	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\sqrt {1+t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.817
11709	19585	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.817
11710	21400	\begin{align*} y^{\prime }+\tan \left (\theta \right ) y&=\cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	1.817
11711	13773	\begin{align*} x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-n \left (n +1\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.818
11712	20203	\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.818
11713	9193	\begin{align*} x^{2} y^{\prime }+y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.819
11714	315	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.820
11715	7189	\begin{align*} 4 \left (1-x \right ) x y^{\prime \prime }-4 y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.820
11716	1128	\begin{align*} -\frac {3 y}{2}+y^{\prime }&=2 \,{\mathrm e}^{t}+3 t \\ \end{align*}	✓	✓	✓	✓	1.821
11717	7606	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.821
11718	15504	\begin{align*} {y^{\prime }}^{2}-9 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.821
11719	2496	\begin{align*} y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.822
11720	4904	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.822
11721	2064	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.823
11722	8651	\begin{align*} 4 y^{\prime \prime }+24 y^{\prime }+37 y&=17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.823
11723	21027	\begin{align*} x^{\prime }+x&=a t \\ \end{align*}	✓	✓	✓	✓	1.823
11724	14174	\begin{align*} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✗	✓	1.824
11725	20125	\begin{align*} y^{\prime \prime }&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.825
11726	17406	\begin{align*} y^{\prime \prime }+y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.826
11727	4220	\begin{align*} y^{\prime }&=\frac {4 x y}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	1.827
11728	15875	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	1.827
11729	16587	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=8 x^{2}-3 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	1.827
11730	21383	\begin{align*} 3 x^{2}+4 y x +\left (2 x^{2}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.827
11731	25702	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	1.827
11732	4099	\begin{align*} y^{\prime }+y&=x^{2}+2 \\ \end{align*}	✓	✓	✓	✓	1.828
11733	8819	\begin{align*} {y^{\prime }}^{2}&=a^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.828
11734	13730	\begin{align*} y^{\prime \prime } x +a x y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	1.828
11735	20954	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	1.828
11736	8465	\begin{align*} x^{2} y^{\prime }-y&=x^{3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.829
11737	15876	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✗	✓	1.830
11738	22585	\begin{align*} y^{\prime } x +2 y-\cos \left (x \right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	1.831
11739	383	\begin{align*} x^{\prime \prime }+9 x&=10 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.832
11740	1112	\begin{align*} 2 y+y^{\prime } t&=t^{2}-t +1 \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.832
11741	4221	\begin{align*} y^{\prime }&=\frac {2 y}{x^{2}-1} \\ \end{align*}	✓	✓	✓	✓	1.832
11742	20692	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.832
11743	12846	\begin{align*} y^{\prime \prime }+6 a^{10} y^{11}-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.833
11744	13871	\begin{align*} x^{4} y^{\prime \prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	1.833
11745	16135	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=13 \operatorname {Heaviside}\left (t -4\right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.833
11746	22207	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.833
11747	2459	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t -\left (1+t \right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.834
11748	16338	\begin{align*} y^{\prime }&=x^{2}-2 y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	1.834
11749	21580	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.834
11750	100	\begin{align*} \frac {1+2 x y}{x^{\prime }}&=y^{2}+1 \\ \end{align*}	✓	✓	✓	✓	1.835
11751	2543	\begin{align*} y^{\prime \prime }+y^{\prime } t +y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.835
11752	24727	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	1.835
11753	7317	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.836
11754	8221	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.836
11755	11282	\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 x \left (x -1\right )}\right ) y \\ \end{align*}	✓	✓	✓	✓	1.836
11756	17593	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=\sec \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.836
11757	839	\begin{align*} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.837
11758	6986	\begin{align*} y^{\prime }&=x^{3}+\frac {2 y}{x}-\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	1.837
11759	20273	\begin{align*} y^{\prime }+3 x^{2} y&=x^{5} {\mathrm e}^{x^{3}} \\ \end{align*}	✓	✓	✓	✓	1.838
11760	4076	\begin{align*} 5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.839
11761	4641	\begin{align*} y^{\prime }&=\sec \left (x \right )-\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	1.839
11762	25622	\begin{align*} y^{\prime \prime }&=t \\ \end{align*}	✓	✓	✓	✓	1.839
11763	13843	\begin{align*} x^{3} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.840
11764	15877	\begin{align*} w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\ \end{align*}	✓	✓	✓	✓	1.840
11765	22452	\begin{align*} i^{\prime }+3 i&={\mathrm e}^{-2 t} \\ i \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.840
11766	1139	\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.841
11767	6388	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+2 y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.841
11768	8896	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.841
11769	19417	\begin{align*} x^{2} y^{\prime }-y^{2}&=2 y x \\ \end{align*}	✓	✓	✓	✓	1.841
11770	9055	\begin{align*} y^{\prime } x&=y+x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	1.842
11771	19518	\begin{align*} y^{\prime \prime }+y&=\cot \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.842
11772	20953	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	1.843
11773	4903	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-x^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.844
11774	21285	\begin{align*} x^{\prime }-x&=\operatorname {Heaviside}\left (t -a \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.844
11775	30	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.845
11776	4919	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=n \left (1-2 y x +y^{2}\right ) \\ \end{align*}	✗	✓	✓	✗	1.845
11777	5219	\begin{align*} \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	1.845
11778	14038	\begin{align*} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.845
11779	87	\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.846
11780	9624	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.846
11781	11822	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{3}+b x \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+y^{\prime }+b x&=0 \\ \end{align*}	✓	✓	✓	✓	1.846
11782	16588	\begin{align*} y^{\prime \prime }-9 y&=36 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	1.846
11783	14903	\begin{align*} y^{\prime }+2 \cot \left (x \right ) y&=5 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.847
11784	54	\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	1.848
11785	6535	\begin{align*} \left (1-2 y\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.848
11786	1179	\begin{align*} y^{\prime }&=y \left (3-t y\right ) \\ \end{align*}	✓	✓	✓	✓	1.849
11787	3955	\begin{align*} y^{\prime }+2 y&=2 \operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.849
11788	6490	\begin{align*} 4 y y^{\prime \prime }&=a y+b y^{2}+c y^{3}+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.849
11789	4894	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-1&=y x \\ \end{align*}	✓	✓	✓	✓	1.851
11790	20268	\begin{align*} y-x \sin \left (x^{2}\right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.851
11791	21334	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.851
11792	179	\begin{align*} x^{3}+3 y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.852
11793	1258	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.852
11794	6026	\begin{align*} a \left (1+a \right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.852
11795	15874	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (3\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	1.852
11796	18123	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=4 y^{2} \\ \end{align*}	✓	✓	✓	✗	1.852
11797	23184	\begin{align*} y \,{\mathrm e}^{y x}+\left (x \,{\mathrm e}^{y x}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.852
11798	25449	\begin{align*} -2 y+y^{\prime }&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.852
11799	14056	\begin{align*} x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\ \end{align*}	✓	✓	✗	✗	1.853
11800	21379	\begin{align*} 3 x \left (y x -2\right )+\left (x^{3}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.854