2.3.165 Problems 16401 to 16500

Table 2.879: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16401	16692	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	2.549
16402	25474	\begin{align*} y^{\prime }&=a y-b y^{n} \\ \end{align*}	✓	✓	✓	✗	2.549
16403	2308	\begin{align*} t y+y^{\prime }&=1+t \\ y \left (\frac {3}{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.550
16404	13744	\begin{align*} y^{\prime \prime } x +\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (c -1\right ) \left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.550
16405	18084	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.551
16406	924	\begin{align*} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }&=5 x-y-t^{2} \\ \end{align*}	✓	✓	✓	✓	2.552
16407	24936	\begin{align*} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.552
16408	8432	\begin{align*} x^{2} y^{\prime }+x \left (2+x \right ) y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.553
16409	20006	\begin{align*} \left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.553
16410	25182	\begin{align*} y^{\prime \prime }+y^{\prime } t +\left (t^{2}+1\right )^{2} y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	2.553
16411	22035	\begin{align*} -y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.554
16412	25457	\begin{align*} y^{\prime }&=y-t^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.555
16413	8260	\begin{align*} y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	2.556
16414	19614	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.556
16415	11569	\begin{align*} \left (x^{2}+y^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.557
16416	25001	\begin{align*} 2 t y+y^{\prime }&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.557
16417	3632	\begin{align*} y^{\prime }+y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	2.558
16418	22440	\begin{align*} y^{3}+2 \,{\mathrm e}^{x} y+\left ({\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.558
16419	22739	\begin{align*} y^{\prime \prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	2.558
16420	26215	\begin{align*} {\mathrm e}^{-y} \left (1+y^{\prime }\right )&=1 \\ \end{align*}	✓	✓	✓	✓	2.558
16421	17140	\begin{align*} -y+y^{\prime }&=2 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.559
16422	19908	\begin{align*} a^{2}-2 y x -y^{2}-\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.559
16423	22171	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	2.560
16424	8547	\begin{align*} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.561
16425	8733	\begin{align*} y^{\prime }&=\frac {x -2 y+5}{-4-2 x +y} \\ \end{align*}	✓	✓	✓	✓	2.561
16426	13748	\begin{align*} y^{\prime \prime } x +\left (a \,x^{2}+b \right ) x y^{\prime }+\left (3 a \,x^{2}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.562
16427	19789	\begin{align*} y^{\prime }+\frac {y}{x}&=-x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	2.562
16428	25440	\begin{align*} y^{\prime }-4 y&=\cos \left (3 t \right )+\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.562
16429	772	\begin{align*} x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.563
16430	1001	\begin{align*} x_{1}^{\prime }&=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\ x_{2}^{\prime }&=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\ x_{3}^{\prime }&=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\ x_{4}^{\prime }&=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \\ \end{align*}	✓	✓	✓	✓	2.563
16431	1559	\begin{align*} y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.563
16432	7687	\begin{align*} y^{\prime \prime } x +\frac {y^{\prime }}{2}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.563
16433	8882	\begin{align*} x^{2} y^{\prime }+2 y x&=1 \\ \end{align*}	✓	✓	✓	✓	2.563
16434	15366	\begin{align*} \left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.563
16435	23912	\begin{align*} y^{\prime }-\frac {y}{-x^{2}+1}&=3 \\ \end{align*}	✓	✓	✓	✓	2.563
16436	8451	\begin{align*} y^{\prime }+4 y x&=x^{3} {\mathrm e}^{x^{2}} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.564
16437	26388	\begin{align*} y^{\prime }&=\frac {1}{2 x -y^{2}} \\ \end{align*}	✓	✓	✓	✗	2.564
16438	4124	\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.565
16439	11871	\begin{align*} y^{\prime }&=\frac {x +F \left (-\left (x -y\right ) \left (x +y\right )\right )}{y} \\ \end{align*}	✓	✓	✓	✗	2.566
16440	12453	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	2.567
16441	12629	\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	2.568
16442	22008	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ \end{align*}	✓	✓	✓	✓	2.568
16443	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*}	✓	✓	✓	✗	2.569
16444	3447	\begin{align*} y^{\prime }&=2 y \\ y \left (\ln \left (3\right )\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.570
16445	11860	\begin{align*} y^{\prime }&=F \left (\frac {y}{a +x}\right ) \\ \end{align*}	✓	✓	✓	✗	2.571
16446	17401	\begin{align*} y^{\prime \prime }+100 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.572
16447	2834	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.573
16448	19396	\begin{align*} y^{\prime }&=1+3 \tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.573
16449	1099	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✓	2.576
16450	11690	\begin{align*} 3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	2.576
16451	14064	\begin{align*} x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	2.578
16452	18873	\begin{align*} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=2 \left (t -1\right )^{2} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✗	2.578
16453	2489	\begin{align*} y^{\prime }&=\left (1+t \right ) \left (1+y\right ) \\ \end{align*}	✓	✓	✓	✓	2.579
16454	16143	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=\delta \left (t -1\right )-3 \delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.579
16455	19800	\begin{align*} 3 y^{2} y^{\prime }+y^{3}&=x -1 \\ \end{align*}	✓	✓	✓	✓	2.579
16456	22995	\begin{align*} y^{\prime }+\frac {y \ln \left (x \right )}{x}&=2 \\ \end{align*}	✓	✓	✓	✓	2.579
16457	8546	\begin{align*} y^{\prime \prime } x -y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.580
16458	15586	\begin{align*} y^{\prime }&=y^{2}-2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	2.580
16459	68	\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\ y \left (4\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	2.581
16460	20023	\begin{align*} x {y^{\prime }}^{2}-\left (x -a \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.582
16461	20957	\begin{align*} y^{\prime }&=y-\mu y^{2} \\ \end{align*}	✓	✓	✓	✓	2.582
16462	22950	\begin{align*} y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.582
16463	5384	\begin{align*} {y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	2.583
16464	7566	\begin{align*} {y^{\prime }}^{3} x -y {y^{\prime }}^{2}+2&=0 \\ \end{align*}	✓	✓	✓	✗	2.584
16465	12449	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x -5 y-\ln \left (x \right ) x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.584
16466	23183	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	2.584
16467	26407	\begin{align*} y^{\prime }-1&={\mathrm e}^{x +2 y} \\ \end{align*}	✓	✓	✓	✓	2.585
16468	3227	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=1-x \\ \end{align*}	✓	✓	✓	✓	2.586
16469	14224	\begin{align*} \left (1+t \right ) x^{\prime }+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.586
16470	23154	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.586
16471	758	\begin{align*} \left ({\mathrm e}^{y}+x \right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \\ \end{align*}	✓	✓	✓	✓	2.587
16472	25672	\begin{align*} 2 y^{\prime } x -y&=2 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	2.587
16473	2459	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t -\left (1+t \right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	2.589
16474	22062	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.589
16475	16145	\begin{align*} y^{\prime \prime }+y^{\prime }+5 y&=\operatorname {Heaviside}\left (-2+t \right ) \sin \left (-8+4 t \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.590
16476	18291	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.590
16477	21435	\begin{align*} y^{\prime }&={\mathrm e}^{x}+y \\ \end{align*}	✓	✓	✓	✓	2.592
16478	24799	\begin{align*} 4 y^{3} {y^{\prime }}^{2}+4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	2.592
16479	5033	\begin{align*} \left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.593
16480	696	\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.594
16481	2359	\begin{align*} y^{\prime }&=t \left (1+y\right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.594
16482	8217	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\ x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	2.594
16483	5874	\begin{align*} b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.595
16484	10326	\begin{align*} y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \\ \end{align*}	✓	✓	✓	✓	2.595
16485	17228	\begin{align*} 2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.595
16486	1712	\begin{align*} -y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.596
16487	6868	\begin{align*} y^{\prime } x -a y+y^{2}&=x^{-2 a} \\ \end{align*}	✓	✓	✓	✗	2.596
16488	8452	\begin{align*} \left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.596
16489	11704	\begin{align*} x {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.597
16490	9224	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*}	✓	✓	✓	✓	2.598
16491	17670	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.598
16492	25712	\begin{align*} \left (y^{3}+1\right ) y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.598
16493	19253	\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.599
16494	25753	\begin{align*} y^{\prime }+\sin \left (x \right ) y&=x \\ \end{align*}	✓	✓	✓	✓	2.599
16495	18929	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right . \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.600
16496	8951	\begin{align*} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.601
16497	18376	\begin{align*} y^{\prime \prime } x +\sin \left (x \right ) y&=x \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*} Series expansion around \(x=\pi \).	✓	✓	✓	✗	2.602
16498	8427	\begin{align*} y^{\prime }&=2 y+x^{2}+5 \\ \end{align*}	✓	✓	✓	✓	2.603
16499	3311	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.604
16500	12342	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.604