2.3.165 Problems 16401 to 16500

Table 2.903: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16401	24278	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	1.889
16402	96	\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.890
16403	9779	\begin{align*} y^{\prime \prime }&=-{\mathrm e}^{-2 y} \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.890
16404	23347	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.890
16405	8470	\begin{align*} y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.891
16406	29	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.892
16407	692	\begin{align*} y^{\prime }&=1+x +y+y x \\ \end{align*}	✓	✓	✓	✓	1.892
16408	4208	\begin{align*} \sqrt {x^{2}+1}\, y^{\prime }+y&=2 x \\ \end{align*}	✓	✓	✓	✓	1.892
16409	10451	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.892
16410	11683	\begin{align*} {y^{\prime }}^{2}-y y^{\prime } x +y^{2} \ln \left (a y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.892
16411	21065	\begin{align*} 2 x^{2}+1&=\left (y^{5}-1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.892
16412	22022	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.892
16413	24938	\begin{align*} y^{\prime }&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.892
16414	3563	\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.893
16415	20844	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.893
16416	1172	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.894
16417	4265	\begin{align*} y^{\prime } x&=x^{5}+x^{3} y^{2}+y \\ \end{align*}	✓	✓	✓	✓	1.894
16418	4405	\begin{align*} y^{\prime }+\frac {y}{x}&={\mathrm e}^{y x} \\ \end{align*}	✓	✓	✓	✗	1.894
16419	720	\begin{align*} \left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.895
16420	4955	\begin{align*} x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.895
16421	15724	\begin{align*} y^{\prime }-3 y&=\delta \left (x -1\right )+2 \operatorname {Heaviside}\left (x -2\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.895
16422	4116	\begin{align*} \left (x +y^{2}\right ) y^{\prime }-x^{2}+y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.896
16423	8270	\begin{align*} y^{\prime }&=6 \sqrt {y}+5 x^{3} \\ y \left (-1\right ) &= 4 \\ \end{align*}	✗	✗	✗	✗	1.896
16424	12468	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.898
16425	24361	\begin{align*} 2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\ y \left (3\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.898
16426	20172	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	1.899
16427	14179	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.901
16428	21380	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.901
16429	4758	\begin{align*} y^{\prime } x&=x^{n} \ln \left (x \right )-y \\ \end{align*}	✓	✓	✓	✓	1.902
16430	11819	\begin{align*} {y^{\prime }}^{3} x -y {y^{\prime }}^{2}+a&=0 \\ \end{align*}	✓	✓	✓	✗	1.902
16431	17522	\begin{align*} y^{\prime \prime }-16 y&=16 t \,{\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.902
16432	16699	\begin{align*} \left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.903
16433	16737	\begin{align*} y^{\prime \prime }-5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.904
16434	4206	\begin{align*} y^{\prime }+\sin \left (x \right ) y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	1.905
16435	13300	\begin{align*} \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} {\mathrm e}^{\lambda x}+b \,\mu ^{2} {\mathrm e}^{\mu x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.905
16436	20729	\begin{align*} x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\ \end{align*}	✓	✓	✓	✓	1.905
16437	3632	\begin{align*} y^{\prime }+y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	1.906
16438	25424	\begin{align*} -y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.906
16439	2459	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t -\left (1+t \right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.907
16440	4341	\begin{align*} 2+y^{2}+2 x +2 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.907
16441	21334	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.908
16442	24337	\begin{align*} -y+y^{\prime } x&=x^{k} y \\ \end{align*}	✓	✓	✓	✓	1.908
16443	801	\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	1.909
16444	4621	\begin{align*} y^{\prime }&={\mathrm e}^{\sin \left (x \right )}+\cos \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	1.909
16445	5516	\begin{align*} x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.909
16446	217	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	1.910
16447	6048	\begin{align*} a y-2 x^{2} \tan \left (x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.910
16448	2948	\begin{align*} \left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	1.911
16449	18542	\begin{align*} \frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.911
16450	1113	\begin{align*} \frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.912
16451	1120	\begin{align*} -2 y+3 y^{\prime }&={\mathrm e}^{-\frac {\pi t}{2}} \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.912
16452	4287	\begin{align*} y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	1.912
16453	4904	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.912
16454	6545	\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }&=\left (1-3 y\right ) {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.912
16455	22772	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.912
16456	11329	\begin{align*} y^{\prime }+a y \left (-x +y\right )-1&=0 \\ \end{align*}	✓	✓	✓	✗	1.913
16457	21828	\begin{align*} y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.913
16458	24984	\begin{align*} y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.913
16459	27419	\begin{align*} x +y y^{\prime }&=y^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	1.913
16460	4939	\begin{align*} x \left (1-x \right ) y^{\prime }+2-3 y x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.914
16461	6499	\begin{align*} 2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.914
16462	11890	\begin{align*} y^{\prime }&=\frac {2 y+F \left (\frac {y}{x^{2}}\right ) x^{3}}{x} \\ \end{align*}	✓	✓	✓	✗	1.914
16463	15727	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=\cos \left (x \right )+2 \delta \left (x -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.915
16464	18536	\begin{align*} \frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.915
16465	20017	\begin{align*} y&=y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.915
16466	22144	\begin{align*} y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\ \end{align*}	✓	✓	✓	✓	1.915
16467	22394	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.915
16468	120	\begin{align*} y^{\prime }&=\sqrt {x +y+1} \\ \end{align*}	✓	✓	✓	✓	1.916
16469	8411	\begin{align*} x^{\prime }&=k \left (A -x\right )^{2} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.917
16470	9722	\begin{align*} \left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.917
16471	18087	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	1.917
16472	20661	\begin{align*} y^{\prime \prime }+\left (1-\frac {2}{x^{2}}\right ) y&=x^{2} \\ \end{align*}	✓	✓	✓	✗	1.917
16473	4631	\begin{align*} y^{\prime }+\csc \left (x \right )+2 \cot \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.918
16474	18539	\begin{align*} -y+y^{\prime }&=1+3 \sin \left (t \right ) \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	1.918
16475	18555	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.918
16476	21970	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.918
16477	22616	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -y&=1 \\ \end{align*}	✓	✓	✗	✓	1.918
16478	1265	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{4}} \\ \end{align*}	✓	✓	✓	✓	1.920
16479	4270	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.921
16480	5989	\begin{align*} -y+\left (a +x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.921
16481	17637	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=2 x \\ \end{align*}	✓	✓	✓	✓	1.921
16482	20096	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	1.921
16483	4194	\begin{align*} y^{\prime }+y \ln \left (x \right )&=x^{-x} \\ \end{align*}	✓	✓	✓	✓	1.922
16484	4627	\begin{align*} y^{\prime }&=x \csc \left (x \right )-\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	1.922
16485	14511	\begin{align*} a y^{\prime }+b y&=k \,{\mathrm e}^{-\lambda x} \\ \end{align*}	✓	✓	✓	✓	1.922
16486	25438	\begin{align*} y^{\prime }&=-y-\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.922
16487	4892	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-x^{2}+y \\ \end{align*}	✓	✓	✓	✓	1.923
16488	9745	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.923
16489	15870	\begin{align*} y^{\prime }&=\cos \left (y\right ) \\ y \left (0\right ) &= -\frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✗	1.923
16490	25449	\begin{align*} -2 y+y^{\prime }&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.923
16491	4612	\begin{align*} y^{\prime }&=a \cos \left (b x +c \right )+k y \\ \end{align*}	✓	✓	✓	✓	1.924
16492	6972	\begin{align*} 2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	1.924
16493	19779	\begin{align*} y^{\prime \prime }-2 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.924
16494	21053	\begin{align*} x^{\prime }&=\frac {-x+x^{2}}{2 x-1} \\ x \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.924
16495	23280	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.924
16496	12985	\begin{align*} 2 x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.925
16497	14224	\begin{align*} \left (1+t \right ) x^{\prime }+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.925
16498	15665	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.927
16499	21052	\begin{align*} x^{\prime }&=\frac {x^{2}+x}{2 x+1} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.927
16500	926	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=2 x_{3} \\ x_{3}^{\prime }&=3 x_{4} \\ x_{4}^{\prime }&=4 x_{1} \\ \end{align*}	✓	✓	✓	✓	1.928