2.3.155 Problems 15401 to 15500

Table 2.883: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15401	1745	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.899
15402	6107	\begin{align*} -y-3 x y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.899
15403	18330	\begin{align*} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.899
15404	24821	\begin{align*} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✗	✗	1.899
15405	1837	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=-2 x^{2} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.901
15406	6495	\begin{align*} y y^{\prime }+{y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.901
15407	25319	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=\delta \left (-3+t \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.901
15408	6100	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	1.902
15409	11390	\begin{align*} x y^{\prime }+y-x \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.902
15410	7698	\begin{align*} x y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.904
15411	8187	\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.905
15412	18025	\begin{align*} y^{2} \left (1+{y^{\prime }}^{2}\right )-4 y y^{\prime }-4 x&=0 \\ \end{align*}	✓	✓	✓	✗	1.905
15413	19891	\begin{align*} y^{\prime }-2 y-2 z&={\mathrm e}^{3 x} \\ z^{\prime }+5 y-2 z&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	1.905
15414	22743	\begin{align*} y^{\prime \prime }+y^{\prime }&=4 x^{3}-2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.906
15415	26298	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x^{2} y^{2}+y x \\ \end{align*}	✓	✓	✓	✓	1.906
15416	510	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.907
15417	15107	\begin{align*} x y^{\prime \prime }&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	1.907
15418	7959	\begin{align*} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	1.908
15419	9822	\begin{align*} {y^{\prime }}^{2} x^{2}-\left (1+2 y x \right ) y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.908
15420	12531	\begin{align*} 2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.908
15421	24153	\begin{align*} 2 x^{2}+y x -2 y^{2}-\left (x^{2}-4 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.911
15422	6136	\begin{align*} -2 \left (-3 x +1\right ) y-x \left (1-4 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.912
15423	6855	\begin{align*} 2 y x +\left (y^{2}-2 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.913
15424	12104	\begin{align*} y^{\prime }&=\frac {x \left ({\mathrm e}^{-2 x^{2}} x^{4}-4 x^{2} {\mathrm e}^{-x^{2}} y-4 x^{2} {\mathrm e}^{-x^{2}}+4 y^{2}+4 \,{\mathrm e}^{-x^{2}}\right )}{4} \\ \end{align*}	✓	✓	✓	✓	1.913
15425	15906	\begin{align*} -2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.913
15426	11357	\begin{align*} y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b}&=0 \\ \end{align*}	✗	✗	✗	✗	1.914
15427	13696	\begin{align*} y^{\prime \prime }+\left (a \,x^{2}+2 b \right ) y^{\prime }+\left (a b \,x^{2}-a x +b^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.914
15428	14188	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.914
15429	18006	\begin{align*} x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=a \\ \end{align*}	✓	✓	✓	✓	1.914
15430	24799	\begin{align*} 4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	1.914
15431	24721	\begin{align*} y^{\prime \prime }+y&=3 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.915
15432	2475	\begin{align*} t^{2} y+y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.917
15433	20726	\begin{align*} y-2 x y^{\prime }+a y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.917
15434	6135	\begin{align*} 2 \left (5+x \right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.918
15435	6188	\begin{align*} -y+x y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.918
15436	8300	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	1.918
15437	13245	\begin{align*} x y^{\prime }&=a \,x^{n} y^{2}+b y+c \,x^{m} \\ \end{align*}	✓	✓	✓	✗	1.919
15438	17158	\begin{align*} y^{\prime }-x&=y \\ \end{align*}	✓	✓	✓	✓	1.919
15439	20158	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.919
15440	1235	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \\ \end{align*}	✓	✓	✓	✓	1.920
15441	3643	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \\ \end{align*}	✓	✓	✓	✗	1.921
15442	10009	\begin{align*} y&=x y^{\prime }+{y^{\prime }}^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	1.921
15443	16267	\begin{align*} 2 y+y^{\prime }&=20 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	1.921
15444	24928	\begin{align*} y^{\prime }&=3 y+12 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.921
15445	26542	\begin{align*} y^{\prime \prime }+9 y-9&=0 \\ \end{align*}	✓	✓	✓	✓	1.921
15446	14862	\begin{align*} x^{\prime }&=a x+b y \\ y^{\prime }&=c x+d y \\ \end{align*}	✓	✓	✓	✓	1.922
15447	20452	\begin{align*} {y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✗	✓	1.922
15448	23396	\begin{align*} y^{\prime \prime }-\frac {5 y^{\prime }}{x}+\frac {5 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	1.922
15449	17187	\begin{align*} -y+y^{\prime }&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.923
15450	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.	✓	✓	✓	✓	1.923
15451	25405	\begin{align*} y^{\prime }+9 y&=90 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.923
15452	8889	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.924
15453	18020	\begin{align*} x&=\frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.924
15454	22627	\begin{align*} y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✗	1.924
15455	16470	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*}	✓	✓	✓	✓	1.925
15456	22789	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.925
15457	1244	\begin{align*} y^{\prime }&=\frac {x}{x^{2}+y+y^{3}} \\ \end{align*}	✓	✓	✓	✓	1.926
15458	1552	\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {7}{x^{2}}+3 \\ \end{align*}	✓	✓	✓	✓	1.926
15459	14411	\begin{align*} x^{\prime }&=3 x+2 y+3 \\ y^{\prime }&=7 x+5 y+2 t \\ \end{align*}	✓	✓	✓	✓	1.926
15460	26666	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=2 \cos \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.926
15461	21017	\begin{align*} x^{\prime }-2 x&=3 t \\ \end{align*}	✓	✓	✓	✓	1.927
15462	791	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y&=1 \\ \end{align*}	✓	✓	✓	✓	1.928
15463	10457	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.928
15464	20590	\begin{align*} y^{\prime \prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.928
15465	5423	\begin{align*} {y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y&=0 \\ \end{align*}	✓	✓	✓	✓	1.929
15466	8171	\begin{align*} p^{\prime }&=p \left (1-p\right ) \\ \end{align*}	✓	✓	✓	✓	1.929
15467	12629	\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	1.929
15468	745	\begin{align*} y^{\prime }&=\left (4 x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.930
15469	11305	\begin{align*} y^{\prime }+a y-b \sin \left (c x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.930
15470	27309	\begin{align*} x^{2}+y^{2}+x +y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.930
15471	5625	\begin{align*} {y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.931
15472	10433	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.931
15473	21018	\begin{align*} x^{\prime }+3 x&=-2 t \\ \end{align*}	✓	✓	✓	✓	1.931
15474	2473	\begin{align*} \frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \\ \end{align*}	✓	✓	✓	✓	1.932
15475	3727	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=\frac {F_{0} \cos \left (\omega t \right )}{m} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.932
15476	14314	\begin{align*} x^{\prime \prime }-b x^{\prime }+x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.932
15477	14693	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=x^{3} \\ \end{align*}	✓	✓	✓	✗	1.932
15478	15286	\begin{align*} x^{\prime }&=3 x-2 y+3 z \\ y^{\prime }&=x-y+2 z+2 \,{\mathrm e}^{-t} \\ z^{\prime }&=-2 x+2 y-2 z \\ \end{align*}	✓	✓	✓	✓	1.932
15479	22286	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.932
15480	6035	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=x^{3} \\ \end{align*}	✓	✓	✓	✗	1.935
15481	6095	\begin{align*} 6 y-2 y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.935
15482	6203	\begin{align*} 4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.935
15483	2302	\begin{align*} t^{2} y+y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.937
15484	12836	\begin{align*} y^{\prime \prime }-6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.937
15485	22864	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=2 x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.937
15486	23453	\begin{align*} \left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.937
15487	22751	\begin{align*} y^{\prime \prime }+y&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.938
15488	21662	\begin{align*} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.939
15489	17356	\begin{align*} 3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= {\frac {17}{3}} \\ \end{align*}	✓	✓	✓	✓	1.940
15490	23113	\begin{align*} y^{\prime }-2 y&={\mathrm e}^{x} \left (1-x \right ) \\ \end{align*}	✓	✓	✓	✓	1.940
15491	24351	\begin{align*} x -y+2+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.940
15492	754	\begin{align*} 3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.941
15493	25314	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.941
15494	2809	\begin{align*} x^{\prime }&=-x \left (1-x\right ) \\ \end{align*}	✓	✓	✓	✓	1.943
15495	15794	\begin{align*} y^{\prime }&=\sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.943
15496	6179	\begin{align*} -\left (5+4 x \right ) y+32 x y^{\prime }+16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.944
15497	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.	✓	✓	✓	✗	1.944
15498	2553	\begin{align*} t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y&=0 \\ \end{align*}	✓	✓	✓	✓	1.945
15499	14945	\begin{align*} x^{\prime \prime }+\omega ^{2} x&=\cos \left (\alpha t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.945
15500	20037	\begin{align*} y^{\prime \prime }-m^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.945