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	25232	\begin{align*} t^{2} y^{\prime \prime }-3 y^{\prime } t +13 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.997
16402	25823	\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right ) x^{2}}{\left (1+y\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	3.997
16403	4667	\begin{align*} y^{\prime }&=a +b y^{2} \\ \end{align*}	✓	✓	✓	✓	3.998
16404	15644	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.998
16405	17236	\begin{align*} -2 x -y \cos \left (y x \right )+\left (2 y-x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.998
16406	3534	\begin{align*} 2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	4.000
16407	4351	\begin{align*} y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.000
16408	4696	\begin{align*} y^{\prime }+y \left (1-x y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.000
16409	7466	\begin{align*} y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.000
16410	13650	\begin{align*} y^{\prime } x&=a y^{3}+3 a b \,x^{n} y^{2}-b n \,x^{n}-2 a \,b^{3} x^{3 n} \\ \end{align*}	✓	✓	✓	✗	4.000
16411	1246	\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}	✓	✓	✓	✓	4.003
16412	18757	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.003
16413	1562	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=\frac {2}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.004
16414	21101	\begin{align*} x&=t \left (1+x^{\prime }\right )+x^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.004
16415	141	\begin{align*} \cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.005
16416	4230	\begin{align*} y^{\prime } x&=2 y \left (-1+y\right ) \\ y \left (\frac {1}{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.005
16417	4329	\begin{align*} x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	4.005
16418	8973	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align*}	✗	✓	✓	✗	4.005
16419	11327	\begin{align*} y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1}&=0 \\ \end{align*}	✓	✓	✓	✗	4.005
16420	12037	\begin{align*} y^{\prime }&=\frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 y x +y^{2}} \\ \end{align*}	✓	✓	✓	✗	4.006
16421	1822	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (-\cos \left (x \right )+\sin \left (x \right )\right ) y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	4.007
16422	15749	\begin{align*} y_{1}^{\prime }&=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\ y_{2}^{\prime }&=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.007
16423	23976	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.007
16424	25004	\begin{align*} y^{\prime }&=\frac {4 t -3 y}{t -y} \\ \end{align*}	✓	✓	✓	✗	4.007
16425	10309	\begin{align*} {y^{\prime }}^{2}&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	4.009
16426	18131	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.009
16427	18360	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= {\mathrm e}^{\pi } \\ \end{align*}	✓	✓	✓	✓	4.010
16428	18516	\begin{align*} 2 t y+y^{\prime }&=16 t \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	4.010
16429	15839	\begin{align*} y^{\prime }&=t -y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.011
16430	8279	\begin{align*} y^{\prime } x +y&=\frac {1}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.012
16431	11780	\begin{align*} \left (y^{2}-2 a x +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.012
16432	12647	\begin{align*} y^{\prime \prime }&=-\frac {\left (-x^{2} \left (a^{2}-1\right )+2 \left (a +3\right ) b x -b^{2}\right ) y}{4 x^{2}} \\ \end{align*}	✗	✓	✓	✗	4.012
16433	795	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\ \end{align*}	✓	✓	✓	✓	4.013
16434	17315	\begin{align*} -\frac {1}{x^{5}}+\frac {1}{x^{3}}&=\left (2 y^{4}-6 y^{9}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.013
16435	20310	\begin{align*} y y^{\prime }+b y^{2}&=\cos \left (x \right ) a \\ \end{align*}	✓	✓	✓	✓	4.015
16436	5832	\begin{align*} \left (\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	4.018
16437	10160	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✓	4.018
16438	20967	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	4.018
16439	6979	\begin{align*} y^{\prime } x +x y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.019
16440	12873	\begin{align*} b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.019
16441	7021	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.020
16442	9252	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\ \end{align*}	✓	✓	✓	✓	4.022
16443	23846	\begin{align*} y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=1 \\ \end{align*}	✓	✓	✓	✗	4.022
16444	23913	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.022
16445	22409	\begin{align*} -y+y^{\prime } x&=\arctan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✗	4.023
16446	23315	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.023
16447	8400	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{\sqrt {x}}}{y} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	4.024
16448	2627	\begin{align*} t^{2} y^{\prime \prime }+5 y^{\prime } t -5 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.025
16449	13219	\begin{align*} x^{2} y^{\prime }&=y^{2} x^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right ) \\ \end{align*}	✓	✓	✓	✗	4.025
16450	8454	\begin{align*} y^{\prime }-\sin \left (x \right ) y&=2 \sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.026
16451	11441	\begin{align*} x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+a x +2&=0 \\ \end{align*}	✓	✓	✓	✗	4.027
16452	21996	\begin{align*} \cos \left (x \right ) x +\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.027
16453	1347	\begin{align*} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✗	4.028
16454	2516	\begin{align*} 2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.029
16455	16296	\begin{align*} y^{\prime }-\frac {y}{x}&=\frac {1}{y} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.029
16456	6447	\begin{align*} y y^{\prime \prime }&=-2 y^{2}+2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.030
16457	22000	\begin{align*} x +\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	4.031
16458	7251	\begin{align*} y x +\left (y^{2}-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.032
16459	25106	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.032
16460	3905	\begin{align*} x_{1}^{\prime }&=-16 x_{1}+30 x_{2}-18 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+8 x_{2}+16 x_{3} \\ x_{3}^{\prime }&=8 x_{1}-15 x_{2}+9 x_{3} \\ \end{align*}	✓	✓	✓	✓	4.033
16461	9348	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.033
16462	22972	\begin{align*} y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	4.033
16463	24755	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{2} \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.033
16464	17623	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.034
16465	9136	\begin{align*} 2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.036
16466	14128	\begin{align*} 4 y+y^{\prime \prime }&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.036
16467	24367	\begin{align*} y \left (1+2 x -y\right )+x \left (3 x -4 y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.037
16468	4617	\begin{align*} y^{\prime }&=x^{2} \left (a \,x^{3}+b y\right ) \\ \end{align*}	✓	✓	✓	✓	4.038
16469	24219	\begin{align*} x y \left (1+y^{2}\right )+\left (y^{2} x^{2}-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.038
16470	24260	\begin{align*} \left (a +x \right ) y^{\prime }&=b x +y \\ \end{align*}	✓	✓	✓	✓	4.038
16471	15399	\begin{align*} y^{\prime \prime }&=\frac {1}{2 y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	4.039
16472	22775	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	4.039
16473	2917	\begin{align*} 3 x^{2} y+x y^{2}+{\mathrm e}^{x}+\left (x^{3}+x^{2} y+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.040
16474	12456	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.040
16475	13449	\begin{align*} y^{\prime }&=y^{2}+f \left (x \right ) y-a^{2}-a f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	4.040
16476	19480	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.040
16477	20551	\begin{align*} y^{\prime \prime }+y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	4.040
16478	20635	\begin{align*} y^{\prime \prime }+\left (\tan \left (x \right )-1\right )^{2} y^{\prime }-n \left (n -1\right ) y \sec \left (x \right )^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	4.040
16479	5716	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.042
16480	12397	\begin{align*} 2 y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+a y&=0 \\ \end{align*}	✗	✓	✓	✗	4.042
16481	16316	\begin{align*} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.042
16482	1256	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.044
16483	5207	\begin{align*} \left (1+y\right ) y^{\prime } \sqrt {x^{2}+1}&=y^{3} \\ \end{align*}	✓	✓	✓	✓	4.045
16484	1688	\begin{align*} 3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.046
16485	6370	\begin{align*} 2 y^{\prime \prime }&=y \left (a -y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	4.046
16486	15926	\begin{align*} y^{\prime }-\frac {3 y}{t}&=2 t^{3} {\mathrm e}^{2 t} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.046
16487	3264	\begin{align*} y y^{\prime \prime }+1&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.047
16488	7144	\begin{align*} a y^{3} x +b y^{2}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.047
16489	11462	\begin{align*} 2 x^{2} y^{\prime }-2 y^{2}-y x +2 a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✗	4.047
16490	17859	\begin{align*} y^{\prime }&=-x^{2}+y \\ \end{align*}	✓	✓	✓	✓	4.047
16491	22107	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.049
16492	709	\begin{align*} 2 y^{\prime } x +y&=10 \sqrt {x} \\ y \left (2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.050
16493	6156	\begin{align*} -\left (a^{2}-x \right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.050
16494	1105	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	4.051
16495	8861	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.051
16496	20565	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.051
16497	13935	\begin{align*} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{3 \lambda x}+b \,{\mathrm e}^{2 \lambda x}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.053
16498	22431	\begin{align*} 3 x +2 y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.053
16499	7055	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.054
16500	20103	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	4.054