2.3.165 Problems 16401 to 16500

Table 2.861: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16401	1712	\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.579
16402	4957	\begin{align*} 2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.579
16403	9083	\begin{align*} y^{\prime }&=4 y x \\ \end{align*}	✓	✓	✓	✓	1.579
16404	14266	\begin{align*} x^{\prime }+p \left (t \right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	1.579
16405	15478	\begin{align*} x^{\prime \prime }+x+x^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	1.579
16406	15909	\begin{align*} -2 y+y^{\prime }&=7 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.579
16407	17145	\begin{align*} y^{\prime } x +y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.579
16408	19860	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=2 x \\ \end{align*}	✓	✓	✓	✗	1.579
16409	67	\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.580
16410	14135	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.580
16411	16902	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.580
16412	22444	\begin{align*} 3 x^{2}+y+3 x^{3} y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.580
16413	22563	\begin{align*} i^{\prime }+3 i&=10 \sin \left (t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.580
16414	19861	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=x \\ \end{align*}	✓	✓	✓	✗	1.581
16415	2089	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.582
16416	9769	\begin{align*} 2 a y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.582
16417	17639	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=8 \\ \end{align*}	✓	✓	✓	✓	1.582
16418	4968	\begin{align*} x^{3} y^{\prime }&=3-x^{2}+x^{2} y \\ \end{align*}	✓	✓	✓	✓	1.583
16419	5543	\begin{align*} y {y^{\prime }}^{2}&=a^{2} x \\ \end{align*}	✓	✓	✓	✓	1.583
16420	23194	\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.583
16421	17520	\begin{align*} y^{\prime \prime }+9 y&=\frac {\csc \left (3 t \right )}{2} \\ y \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.584
16422	18619	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=x \\ \end{align*}	✓	✓	✓	✓	1.584
16423	1177	\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ \end{align*}	✓	✓	✓	✓	1.585
16424	12332	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-\left (x +1\right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.585
16425	16757	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	1.585
16426	17468	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.585
16427	20269	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=2 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.585
16428	3776	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.586
16429	13927	\begin{align*} y^{\prime \prime }+a \left (\lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.586
16430	16340	\begin{align*} x y^{2}-6+x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.586
16431	24825	\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.587
16432	4985	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=x -\left (5 x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✓	1.588
16433	15253	\begin{align*} y^{\prime \prime \prime \prime }-16 y&=32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.588
16434	15947	\begin{align*} y^{\prime }&=3 y+{\mathrm e}^{7 t} \\ \end{align*}	✓	✓	✓	✓	1.588
16435	800	\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	1.589
16436	3217	\begin{align*} y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \sin \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	1.589
16437	4626	\begin{align*} y^{\prime }&=1-\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	1.589
16438	8251	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	1.589
16439	15958	\begin{align*} y^{\prime }+5 y&=3 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.589
16440	12938	\begin{align*} y y^{\prime \prime }+a {y^{\prime }}^{2}+y^{3} b&=0 \\ \end{align*}	✓	✓	✓	✗	1.590
16441	5839	\begin{align*} a \left (1+k \right ) x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✗	✗	1.591
16442	3540	\begin{align*} y^{\prime }-\frac {y}{x}&=2 \ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	1.592
16443	9345	\begin{align*} y^{\prime \prime }&=-3 y \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.592
16444	14441	\begin{align*} 2 y x +1+\left (x^{2}+4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.592
16445	4190	\begin{align*} y^{\prime }-y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	1.593
16446	4711	\begin{align*} y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.593
16447	9660	\begin{align*} x^{\prime }&=4 x+2 y+{\mathrm e}^{t} \\ y^{\prime }&=-x+3 y-{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.594
16448	1590	\begin{align*} y^{\prime }+\frac {\left (1+y\right ) \left (y-1\right ) \left (y-2\right )}{x +1}&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.595
16449	9011	\begin{align*} y^{\prime }&=y^{2} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	1.595
16450	12303	\begin{align*} y^{\prime \prime }+\left (a \cos \left (x \right )^{2}+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.595
16451	16372	\begin{align*} 2 y+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.597
16452	1352	\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y&=t \\ \end{align*}	✓	✓	✓	✓	1.598
16453	5975	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.598
16454	21998	\begin{align*} \frac {1}{x}-\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	1.598
16455	2091	\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.599
16456	4220	\begin{align*} y^{\prime }&=\frac {4 x y}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	1.599
16457	20772	\begin{align*} y^{\prime \prime }&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.599
16458	23757	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\pi \right ) &= 2 \\ \end{align*}	✗	✗	✗	✗	1.599
16459	24987	\begin{align*} t \left (t +1\right ) y^{\prime }&=2+y \\ \end{align*}	✓	✓	✓	✓	1.599
16460	1799	\begin{align*} y^{\prime }+y^{2}+4 y x +4 x^{2}+2&=0 \\ \end{align*}	✓	✓	✓	✓	1.601
16461	16697	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✗	1.601
16462	18502	\begin{align*} y^{\prime }&=\frac {2 x^{2}}{2 y^{2}-6} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.601
16463	20495	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	1.601
16464	20721	\begin{align*} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.601
16465	22978	\begin{align*} y^{\prime }-2 y x&=3 x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.601
16466	684	\begin{align*} y^{\prime }&=2 x \sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.602
16467	1208	\begin{align*} y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.602
16468	15402	\begin{align*} y^{\prime \prime }&=\frac {a}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	1.602
16469	16328	\begin{align*} 2 x \left (1+y\right )-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.602
16470	17481	\begin{align*} y^{\prime \prime }+4 y&=1 \\ \end{align*}	✓	✓	✓	✓	1.602
16471	3526	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\ y \left (0\right ) &= 2 a \\ \end{align*}	✓	✓	✓	✓	1.603
16472	4221	\begin{align*} y^{\prime }&=\frac {2 y}{x^{2}-1} \\ \end{align*}	✓	✓	✓	✓	1.603
16473	6133	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.604
16474	24943	\begin{align*} y^{\prime }&=\frac {t y}{1+y} \\ \end{align*}	✓	✓	✓	✓	1.604
16475	3531	\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.605
16476	4907	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.605
16477	13804	\begin{align*} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a b \,x^{n}+a c \,x^{n -1}+b^{2} x^{2}+2 b x c +c^{2}-c \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.605
16478	15155	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +7 y&=1 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	1.605
16479	1229	\begin{align*} y^{\prime }+y&=\frac {1}{{\mathrm e}^{x}+1} \\ \end{align*}	✓	✓	✓	✓	1.606
16480	8313	\begin{align*} y^{\prime }&=\frac {x^{2}}{5}+y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.606
16481	9050	\begin{align*} y^{\prime } y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.606
16482	24853	\begin{align*} {y^{\prime }}^{4}+y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✗	✗	1.606
16483	461	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.607
16484	5218	\begin{align*} \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.607
16485	14152	\begin{align*} \left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.607
16486	19972	\begin{align*} \left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.607
16487	2073	\begin{align*} x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (14+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.608
16488	16592	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=10 x +12 \\ y \left (1\right ) &= 6 \\ y^{\prime }\left (1\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	1.608
16489	24253	\begin{align*} 2 y&=\left (x^{2}-1\right ) \left (1-y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	1.608
16490	3523	\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+32 \\ \end{align*}	✓	✓	✓	✗	1.609
16491	9336	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {2}{x} \\ \end{align*}	✓	✓	✓	✓	1.609
16492	14260	\begin{align*} y^{\prime }+a y&=\sqrt {t +1} \\ \end{align*}	✓	✓	✓	✓	1.609
16493	15241	\begin{align*} y^{\prime \prime }+4 \pi ^{2} y&=3 \delta \left (t -\frac {1}{3}\right )-\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.609
16494	16964	\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.609
16495	20583	\begin{align*} x {y^{\prime }}^{2}+x y y^{\prime \prime }&=3 y^{\prime } y \\ \end{align*}	✓	✓	✓	✗	1.609
16496	10072	\begin{align*} y^{\prime }&=2 y \left (x \sqrt {y}-1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.610
16497	25438	\begin{align*} y^{\prime }&=-y-\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.610
16498	5226	\begin{align*} \left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.611
16499	14931	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.611
16500	4194	\begin{align*} y^{\prime }+y \ln \left (x \right )&=x^{-x} \\ \end{align*}	✓	✓	✓	✓	1.612