2.3.161 Problems 16001 to 16100

Table 2.853: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16001	16102	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.736
16002	8173	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.737
16003	8782	\begin{align*} {\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.737
16004	14316	\begin{align*} x^{\prime \prime }-2 x^{\prime }&=4 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.737
16005	16308	\begin{align*} y^{\prime }+3 y&=\frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	3.737
16006	19231	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.738
16007	7971	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.739
16008	724	\begin{align*} y^{\prime } x&=3 y+x^{4} \cos \left (x \right ) \\ y \left (2 \pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.740
16009	5884	\begin{align*} \left (-x^{2}+4 a +2\right ) y+4 y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.740
16010	16107	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 t +{\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.740
16011	5803	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.741
16012	11667	\begin{align*} {y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	3.743
16013	12009	\begin{align*} y^{\prime }&=\frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )} \\ \end{align*}	✓	✓	✓	✗	3.743
16014	17419	\begin{align*} y^{\prime \prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.743
16015	19326	\begin{align*} -y+y^{\prime } x&=\left (1+y^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.745
16016	4785	\begin{align*} y^{\prime } x&=x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.747
16017	18321	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	3.747
16018	1280	\begin{align*} 9 y^{\prime \prime }+9 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.748
16019	12345	\begin{align*} b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.748
16020	12541	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (a \,x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.748
16021	21862	\begin{align*} 2 x +y y^{\prime } \left (4 {y^{\prime }}^{2}+6\right )&=0 \\ \end{align*}	✓	✓	✗	✗	3.748
16022	11863	\begin{align*} y^{\prime }&=F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x} \\ \end{align*}	✓	✓	✓	✗	3.749
16023	4104	\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.750
16024	16958	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.750
16025	18154	\begin{align*} y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{4 x} x \\ \end{align*}	✓	✓	✓	✓	3.750
16026	20840	\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.751
16027	1193	\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.753
16028	12329	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.753
16029	23141	\begin{align*} y y^{\prime }&=y+x^{2} \\ \end{align*}	✗	✗	✗	✗	3.755
16030	3008	\begin{align*} 2 y x -2 x y^{3}+x^{3}+\left (x^{2}+y^{2}-3 y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.756
16031	2495	\begin{align*} \sqrt {1+y^{2}}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	3.757
16032	19752	\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.757
16033	5852	\begin{align*} 2 y-\cot \left (2 x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.758
16034	24271	\begin{align*} x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.759
16035	7083	\begin{align*} y^{\prime \prime }+y^{\prime }&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	3.760
16036	24715	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 x^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.760
16037	10392	\begin{align*} y^{\prime \prime }+y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	3.761
16038	4854	\begin{align*} 2 y^{\prime } x&=\left (1+x -6 y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	3.763
16039	11568	\begin{align*} 2 y x +x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.763
16040	16200	\begin{align*} x^{2} y^{\prime }+x y^{2}&=x \\ \end{align*}	✓	✓	✓	✓	3.763
16041	19302	\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.763
16042	21154	\begin{align*} x^{\prime \prime }+4 x^{\prime }+x&=k \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.763
16043	1546	\begin{align*} y^{\prime }+\frac {k y}{x}&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.765
16044	4409	\begin{align*} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	3.765
16045	18333	\begin{align*} y^{\prime \prime } x +\left (2 x -1\right ) y^{\prime }&=-4 x^{2} \\ \end{align*}	✓	✓	✓	✗	3.765
16046	703	\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\ y \left (4\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	3.766
16047	20653	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=x^{3}+3 x \\ \end{align*}	✓	✓	✓	✗	3.766
16048	4422	\begin{align*} x^{2} \left (-y+y^{\prime } x \right )&=y \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	3.767
16049	16969	\begin{align*} x^{\prime \prime }+x&=t \cos \left (t \right )-\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.768
16050	23897	\begin{align*} y+6 x y^{3}-4 y^{4}-\left (2 x +4 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.768
16051	19463	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.769
16052	7072	\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.770
16053	20544	\begin{align*} y^{3} y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	3.770
16054	1581	\begin{align*} \left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	3.771
16055	11473	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.771
16056	18485	\begin{align*} y^{\prime }&=\left (1-12 x \right ) y^{2} \\ y \left (0\right ) &= -{\frac {1}{8}} \\ \end{align*}	✓	✓	✓	✓	3.771
16057	22522	\begin{align*} r^{2} \sin \left (t \right )&=\left (2 r \cos \left (t \right )+10\right ) r^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.771
16058	19404	\begin{align*} x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.772
16059	22790	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=24 x +24 \\ \end{align*}	✓	✓	✓	✓	3.772
16060	23322	\begin{align*} 2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.773
16061	7447	\begin{align*} x^{{10}/{3}}-2 y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.774
16062	18878	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.775
16063	24956	\begin{align*} {\mathrm e}^{t} y^{\prime }&=y^{3}-y \\ \end{align*}	✓	✓	✓	✓	3.775
16064	11329	\begin{align*} y^{\prime }+a y \left (-x +y\right )-1&=0 \\ \end{align*}	✓	✓	✓	✗	3.776
16065	13729	\begin{align*} y^{\prime \prime } x +a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.776
16066	17930	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	3.776
16067	22485	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.776
16068	53	\begin{align*} y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.779
16069	10319	\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	3.779
16070	23895	\begin{align*} x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.779
16071	13451	\begin{align*} y^{\prime }&=f \left (x \right )+x f \left (x \right ) y+y^{2} \\ \end{align*}	✓	✓	✓	✗	3.780
16072	14231	\begin{align*} T^{\prime }&=2 a t \left (T^{2}-a^{2}\right ) \\ T \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.780
16073	23030	\begin{align*} z^{\prime \prime }+6 z^{\prime }+9 z&=0 \\ \end{align*}	✓	✓	✓	✓	3.780
16074	15413	\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.781
16075	17804	\begin{align*} x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= {\frac {1}{3}} \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.781
16076	20173	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	3.782
16077	12331	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.783
16078	14137	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 \sin \left (x \right ) y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	3.783
16079	18496	\begin{align*} x^{2} y^{\prime }&=y-y x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.783
16080	24262	\begin{align*} y^{\prime }&=x^{3}-2 y x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.783
16081	5281	\begin{align*} \left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.784
16082	4915	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=-1-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.785
16083	5997	\begin{align*} \left (a^{2} x^{2}+2\right ) y-2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.785
16084	195	\begin{align*} {\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.787
16085	13789	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (a^{2} x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.787
16086	17657	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.787
16087	22319	\begin{align*} y^{\prime }&=\frac {-x +3}{y+5} \\ \end{align*}	✓	✓	✓	✓	3.787
16088	13387	\begin{align*} \left (\cos \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \cos \left (\mu x \right ) y-d^{2}+c d \cos \left (\mu x \right ) \\ \end{align*}	✓	✓	✓	✗	3.788
16089	22360	\begin{align*} y^{\prime }&=-\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.788
16090	2984	\begin{align*} \sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t}&=0 \\ \end{align*}	✓	✓	✓	✓	3.789
16091	20331	\begin{align*} y^{\prime \prime }+3 y^{\prime }-54 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.789
16092	3683	\begin{align*} y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	3.791
16093	16375	\begin{align*} y^{2} {\mathrm e}^{x y^{2}}-2 x +2 x y \,{\mathrm e}^{x y^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.791
16094	21011	\begin{align*} t x^{\prime }+x&=2 t^{2} \\ \end{align*}	✓	✓	✓	✓	3.792
16095	4238	\begin{align*} \left (x +y-1\right ) y^{\prime }&=x -y+1 \\ \end{align*}	✓	✓	✓	✓	3.794
16096	8691	\begin{align*} \left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.794
16097	3980	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=\delta \left (-2+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.795
16098	3386	\begin{align*} x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.796
16099	7818	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.796
16100	13735	\begin{align*} y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.796