2.3.181 Problems 18001 to 18100

Table 2.935: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18001	1100	\begin{align*} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	3.078
18002	744	\begin{align*} y^{\prime }&=\sqrt {x +y+1} \\ \end{align*}	✓	✓	✓	✓	3.079
18003	2323	\begin{align*} y^{\prime }&=\frac {2 t}{y+t^{2} y} \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.079
18004	12105	\begin{align*} y^{\prime }&=\frac {y \left (x +y\right )}{x \left (x +y+y^{3}+y^{4}\right )} \\ \end{align*}	✓	✓	✓	✗	3.079
18005	25426	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{\frac {201 t}{100}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.079
18006	8724	\begin{align*} y^{\prime }&=\frac {2 y-x +5}{2 x -y-4} \\ \end{align*}	✓	✓	✓	✓	3.080
18007	21728	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{4}\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	3.080
18008	2980	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y&=0 \\ y \left (0\right ) &= -6 \\ \end{align*}	✓	✓	✓	✓	3.082
18009	9818	\begin{align*} 16 {y^{\prime }}^{2} x +8 y y^{\prime }+y^{6}&=0 \\ \end{align*}	✓	✓	✓	✓	3.082
18010	6408	\begin{align*} x^{4} y^{\prime \prime }&=-4 y^{2}+x^{2} y^{\prime } \left (x +y^{\prime }\right ) \\ \end{align*}	✗	✓	✓	✗	3.084
18011	4620	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (x \right )-\cos \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.085
18012	19955	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }&=3 x y^{2}-x^{2} \\ \end{align*}	✓	✓	✓	✗	3.085
18013	26279	\begin{align*} \left (x^{2}+2 x -1\right ) y^{\prime }-\left (x +1\right ) y&=x -1 \\ \end{align*}	✓	✓	✓	✓	3.085
18014	27285	\begin{align*} \left (2 x^{2} y \ln \left (y\right )-x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.086
18015	1111	\begin{align*} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.088
18016	45	\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.089
18017	8887	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.090
18018	13355	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b \\ \end{align*}	✓	✗	✗	✗	3.090
18019	2076	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.091
18020	6419	\begin{align*} 2 f \left (x \right )^{2} y^{\prime \prime }&=2 f \left (x \right )^{2} y^{3}+f \left (x \right ) y^{2} f^{\prime }\left (x \right )+f \left (x \right ) \left (-2 f \left (x \right ) y+3 f^{\prime }\left (x \right )\right ) y^{\prime }+y \left (-2 f \left (x \right )^{3}-2 {f^{\prime }\left (x \right )}^{2}+f \left (x \right ) f^{\prime \prime }\left (x \right )\right ) \\ \end{align*}	✗	✓	✗	✗	3.091
18021	14142	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.091
18022	1616	\begin{align*} y^{\prime }&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✗	✗	✗	✗	3.092
18023	1798	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )-x \left (x +2\right ) y+x +2&=0 \\ \end{align*}	✓	✓	✓	✓	3.093
18024	12947	\begin{align*} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.093
18025	9201	\begin{align*} x^{2} y^{\prime }-2 y&=3 x^{2} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.094
18026	1099	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✓	3.095
18027	2077	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.095
18028	19342	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.095
18029	19723	\begin{align*} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	3.095
18030	22578	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.095
18031	2098	\begin{align*} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.096
18032	4865	\begin{align*} x^{2} y^{\prime }&=a +b x +c \,x^{2}+y x \\ \end{align*}	✓	✓	✓	✓	3.096
18033	6028	\begin{align*} \left (a \left (a +1\right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.096
18034	19126	\begin{align*} {y^{\prime }}^{2}+2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.096
18035	7035	\begin{align*} 3 x y^{2} y^{\prime }+y^{3}-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.097
18036	8317	\begin{align*} y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.097
18037	9322	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.098
18038	4108	\begin{align*} x y^{\prime }+2 y&=\left (3 x +2\right ) {\mathrm e}^{3 x} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.099
18039	10160	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✓	3.099
18040	19180	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	3.100
18041	9722	\begin{align*} \left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.101
18042	25607	\begin{align*} -y+y^{\prime }&={\mathrm e}^{t} \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.101
18043	25682	\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.102
18044	18800	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.105
18045	17615	\begin{align*} 2 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.106
18046	8260	\begin{align*} x y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.107
18047	3592	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.108
18048	4629	\begin{align*} y^{\prime }&=\sec \left (x \right )-y \cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.108
18049	8427	\begin{align*} y^{\prime }&=2 y+x^{2}+5 \\ \end{align*}	✓	✓	✓	✓	3.108
18050	15540	\begin{align*} y^{\prime }&=x^{3}+y^{3} \\ \end{align*}	✗	✗	✗	✗	3.108
18051	17616	\begin{align*} 2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.108
18052	24919	\begin{align*} y^{\prime }&=-{\mathrm e}^{y}-1 \\ \end{align*}	✓	✓	✓	✓	3.108
18053	4911	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\tan \left (x \right )-2 y x \\ \end{align*}	✓	✓	✓	✓	3.109
18054	5935	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=\left (1-x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.109
18055	16250	\begin{align*} y y^{\prime }&=\sin \left (x \right ) \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	3.109
18056	22342	\begin{align*} y^{\prime }+y x&=x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.109
18057	19728	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	3.110
18058	23930	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.110
18059	4619	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (x \right )+\cos \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.112
18060	8426	\begin{align*} y x +x^{2} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	3.112
18061	19353	\begin{align*} \left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.112
18062	8802	\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	3.113
18063	160	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	3.114
18064	19957	\begin{align*} \left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	3.114
18065	11636	\begin{align*} \left (\ln \left (y\right )+x \right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	3.115
18066	16365	\begin{align*} y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.115
18067	5758	\begin{align*} y^{\prime \prime }&=\left (1+2 \tan \left (x \right )^{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	3.116
18068	17186	\begin{align*} y^{\prime }-3 y&=27 t^{2} \\ \end{align*}	✓	✓	✓	✓	3.116
18069	27011	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 7 \\ y^{\prime }\left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	3.116
18070	8440	\begin{align*} r^{\prime }+r \sec \left (t \right )&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.117
18071	2095	\begin{align*} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.118
18072	21380	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.118
18073	7465	\begin{align*} \frac {1}{x}+2 x y^{2}+\left (2 x^{2} y-\cos \left (y\right )\right ) y^{\prime }&=0 \\ y \left (1\right ) &= \pi \\ \end{align*}	✓	✓	✓	✗	3.119
18074	22503	\begin{align*} y&=x y^{\prime }-\tan \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	3.120
18075	2069	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.122
18076	2094	\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.122
18077	8047	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	3.122
18078	10437	\begin{align*} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✗	3.122
18079	27346	\begin{align*} y^{\prime }&=\sqrt {\sin \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	3.123
18080	1705	\begin{align*} x^{3} y^{4}+2 x +\left (x^{4} y^{3}+3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.124
18081	9790	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	3.124
18082	7387	\begin{align*} x^{\prime }&=3 x t^{2} \\ \end{align*}	✓	✓	✓	✓	3.125
18083	21561	\begin{align*} {y^{\prime }}^{2}-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.125
18084	4968	\begin{align*} x^{3} y^{\prime }&=3-x^{2}+x^{2} y \\ \end{align*}	✓	✓	✓	✓	3.126
18085	6183	\begin{align*} 2 a^{2} y-2 a^{2} x y^{\prime }+\left (-a^{2} x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.126
18086	25480	\begin{align*} y^{\prime }&=y \left (1-\ln \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✓	3.126
18087	26860	\begin{align*} 3 y^{\prime }&=\frac {4 x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.126
18088	21972	\begin{align*} y^{\prime }&=y \sin \left (x \right )+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	3.127
18089	56	\begin{align*} \left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	3.128
18090	2481	\begin{align*} y^{\prime }-2 y t&=t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.128
18091	20686	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\ \end{align*}	✓	✓	✓	✓	3.128
18092	24389	\begin{align*} \left (2 x -1\right ) y+2 \left (x^{2}+y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.128
18093	8466	\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=10 \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.129
18094	1802	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+y x +x^{2}-\frac {1}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	3.131
18095	7332	\begin{align*} x^{2} y^{\prime }-y x&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	3.132
18096	21125	\begin{align*} x^{\prime \prime }-x&=0 \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.132
18097	22339	\begin{align*} y^{\prime }&=3 x +2 y \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.132
18098	7935	\begin{align*} x y^{\prime }&=2 y+{\mathrm e}^{x} x^{3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.133
18099	20194	\begin{align*} -y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	3.133
18100	1226	\begin{align*} y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \\ \end{align*}	✓	✓	✓	✗	3.134