2.3.161 Problems 16001 to 16100

Table 2.895: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16001	1177	\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ \end{align*}	✓	✓	✓	✓	2.154
16002	24303	\begin{align*} x^{2}-2 y x -y^{2}-\left (x^{2}+2 y x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.154
16003	8683	\begin{align*} y^{\prime }-y&=2 x -3 \\ \end{align*}	✓	✓	✓	✓	2.156
16004	15804	\begin{align*} y^{\prime }&=\frac {1-y^{2}}{y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.156
16005	2839	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.158
16006	20740	\begin{align*} {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.158
16007	5711	\begin{align*} y^{\prime \prime }&=x +\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.159
16008	18924	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.159
16009	21435	\begin{align*} y^{\prime }&=y+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.159
16010	1110	\begin{align*} -y+y^{\prime }&=2 \,{\mathrm e}^{2 t} t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.160
16011	4526	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=\delta \left (t -2\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.160
16012	11425	\begin{align*} x y^{\prime }-y f \left (y x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.160
16013	15157	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	2.160
16014	1236	\begin{align*} y^{\prime }&=\frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}} \\ \end{align*}	✓	✓	✓	✗	2.161
16015	24839	\begin{align*} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.161
16016	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*}	✓	✓	✓	✓	2.162
16017	15301	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y&=x \\ \end{align*}	✓	✓	✓	✗	2.162
16018	26292	\begin{align*} x^{2} y^{\prime }+2 x^{3} y&=y^{2} \left (x^{3}+1\right ) \\ \end{align*}	✓	✓	✓	✓	2.162
16019	26338	\begin{align*} 2 x^{2} y+2 y+5+\left (2 x^{2}+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.162
16020	14137	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 y \sin \left (x \right )&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	2.164
16021	17164	\begin{align*} y+y^{\prime }&={\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.164
16022	25487	\begin{align*} y^{\prime }&=y^{2}-y^{4} \\ \end{align*}	✓	✓	✓	✓	2.164
16023	26164	\begin{align*} x -y+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.164
16024	26194	\begin{align*} y^{\prime }&=\frac {y+1}{x -1} \\ \end{align*}	✓	✓	✓	✓	2.164
16025	26672	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y&=4 \,{\mathrm e}^{x} \\ y \left (-\infty \right ) &= 0 \\ y^{\prime }\left (-1\right ) &= -{\mathrm e}^{-1} \\ \end{align*}	✓	✓	✓	✗	2.164
16026	1141	\begin{align*} y^{\prime }&=\frac {2 x}{y+x^{2} y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.165
16027	12644	\begin{align*} y^{\prime \prime }&=-\frac {b y}{x^{2} \left (x -a \right )^{2}}+c \\ \end{align*}	✓	✓	✓	✗	2.165
16028	1224	\begin{align*} y^{\prime }&=\frac {4 x^{3}+1}{y \left (2+3 y\right )} \\ \end{align*}	✓	✓	✓	✗	2.166
16029	1716	\begin{align*} y x +x +2 y+1+\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.166
16030	19152	\begin{align*} y^{2} \left (x^{2} y^{\prime \prime }-x y^{\prime }+y\right )&=x^{3} \\ \end{align*}	✗	✓	✓	✗	2.166
16031	5805	\begin{align*} y b^{2}+2 a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.167
16032	20514	\begin{align*} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.167
16033	902	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=72 x^{5} \\ \end{align*}	✓	✓	✓	✓	2.168
16034	7732	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=y x +1 \\ \end{align*}	✓	✓	✓	✓	2.168
16035	25418	\begin{align*} y^{\prime }&=2 y+\delta \left (-3+t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.169
16036	26233	\begin{align*} \ln \left (x \right )+y^{3}-3 x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.169
16037	16568	\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.170
16038	26291	\begin{align*} \left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.170
16039	1556	\begin{align*} y^{\prime }+y \tan \left (x \right )&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.171
16040	15949	\begin{align*} y^{\prime }&=-5 y+\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.171
16041	17115	\begin{align*} y^{\prime }&=\frac {y}{\ln \left (y\right )} \\ y \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	2.171
16042	20169	\begin{align*} y^{3} y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	2.171
16043	8790	\begin{align*} {y^{\prime }}^{2}-y^{2} a^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.172
16044	19687	\begin{align*} t^{2} x^{\prime \prime }-2 x^{\prime } t +2 x&=0 \\ \end{align*}	✓	✓	✓	✓	2.172
16045	20630	\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.172
16046	27331	\begin{align*} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.172
16047	24263	\begin{align*} L i^{\prime }+R i&=e \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.173
16048	8769	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y&=x +\frac {1}{x} \\ \end{align*}	✓	✓	✓	✗	2.174
16049	14316	\begin{align*} x^{\prime \prime }-2 x^{\prime }&=4 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.174
16050	15783	\begin{align*} y^{\prime }&=\frac {t}{y+t^{2} y} \\ \end{align*}	✓	✓	✓	✓	2.174
16051	18394	\begin{align*} x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.174
16052	21	\begin{align*} y^{\prime }&=y-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.175
16053	2308	\begin{align*} y t +y^{\prime }&=t +1 \\ y \left (\frac {3}{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.175
16054	5982	\begin{align*} -\left (p^{2}+x^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.175
16055	23912	\begin{align*} y^{\prime }-\frac {y}{-x^{2}+1}&=3 \\ \end{align*}	✓	✓	✓	✓	2.175
16056	15440	\begin{align*} y^{\prime \prime }+2 h y^{\prime }+n^{2} y&=0 \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= c \\ \end{align*}	✓	✓	✓	✓	2.176
16057	87	\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.177
16058	4740	\begin{align*} y^{\prime }&=f \left (a +b x +c y\right ) \\ \end{align*}	✓	✓	✓	✓	2.177
16059	7037	\begin{align*} \left (2 x y^{3}+y x +x^{2}\right ) y^{\prime }-y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.177
16060	27311	\begin{align*} x&=\left (x y^{\prime }+y\right ) \sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.177
16061	609	\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*}	✓	✓	✓	✓	2.178
16062	1551	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {{\mathrm e}^{-x^{2}}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.178
16063	16237	\begin{align*} y^{\prime }&=\tan \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.178
16064	19330	\begin{align*} x y^{\prime }&=y+x^{2}+9 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.178
16065	26895	\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.178
16066	27301	\begin{align*} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.178
16067	2961	\begin{align*} x^{\prime }+x&={\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	2.179
16068	10326	\begin{align*} y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \\ \end{align*}	✓	✓	✓	✓	2.180
16069	15025	\begin{align*} x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.180
16070	16700	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y&=\frac {10}{x} \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= -15 \\ \end{align*}	✓	✓	✓	✓	2.180
16071	20409	\begin{align*} \left (2 x -b \right ) y^{\prime }&=y-a y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.181
16072	12282	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.182
16073	7384	\begin{align*} \left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	2.183
16074	15934	\begin{align*} y^{\prime }&=t^{r} y+4 \\ \end{align*}	✓	✓	✓	✗	2.183
16075	1821	\begin{align*} x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=8 x^{5} \\ \end{align*}	✓	✓	✓	✗	2.184
16076	6231	\begin{align*} -6 y x +2 y^{\prime }+x \left (3 x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.184
16077	9240	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.184
16078	12449	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-x^{2} \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.184
16079	13933	\begin{align*} y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.185
16080	26142	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.185
16081	11317	\begin{align*} y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1&=0 \\ \end{align*}	✓	✓	✓	✓	2.186
16082	8652	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=10 \sin \left (t \right )+10 \delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.187
16083	10022	\begin{align*} x y^{\prime }-2 y+b y^{2}&=c \,x^{4} \\ \end{align*}	✓	✓	✓	✗	2.187
16084	25295	\begin{align*} y^{\prime }+5 y&=\left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.187
16085	26198	\begin{align*} y^{\prime }&=\left (1-y\right ) \left (1-x \right ) \\ \end{align*}	✓	✓	✓	✓	2.187
16086	12953	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (b +a y\right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.189
16087	11678	\begin{align*} {y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	2.190
16088	16216	\begin{align*} y^{\prime }&=\sin \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	2.190
16089	19234	\begin{align*} x y^{\prime }&=y+x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.190
16090	3387	\begin{align*} x y^{\prime \prime }+3 y^{\prime }-y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.192
16091	24477	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.192
16092	5653	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\ \end{align*}	✓	✓	✓	✓	2.193
16093	12554	\begin{align*} \left (27 x^{2}+4\right ) y^{\prime \prime }+27 x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.193
16094	5048	\begin{align*} y y^{\prime }&=\sqrt {y^{2}-a^{2}} \\ \end{align*}	✓	✓	✓	✓	2.194
16095	9244	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.195
16096	22491	\begin{align*} y^{\prime \prime }+x y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	2.195
16097	1531	\begin{align*} y^{\prime }&=\frac {x^{2}-2 x^{2} y+2}{x^{3}} \\ y \left (1\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	2.196
16098	7418	\begin{align*} x^{2} y^{\prime }+\sin \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.196
16099	15175	\begin{align*} y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	2.196
16100	6382	\begin{align*} -2 y^{\prime }+2 {y^{\prime }}^{2} x +x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.197