2.3.151 Problems 15001 to 15100

Table 2.833: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15001	25707	\begin{align*} y^{\prime }&=y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	1.170
15002	13940	\begin{align*} y^{\prime \prime }+2 k \,{\mathrm e}^{\mu x} y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 \mu x}+k \mu \,{\mathrm e}^{\mu x}+c \right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	1.171
15003	14849	\begin{align*} y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0 \\ y \left (1\right ) &= 0 \\ y \left ({\mathrm e}^{\pi }\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.171
15004	23087	\begin{align*} y^{\prime \prime }-4 y&=12 \\ \end{align*}	✓	✓	✓	✓	1.171
15005	23396	\begin{align*} y^{\prime \prime }-\frac {5 y^{\prime }}{x}+\frac {5 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	1.171
15006	7310	\begin{align*} y^{\prime } y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	1.172
15007	11709	\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime } y+a&=0 \\ \end{align*}	✓	✓	✓	✗	1.172
15008	3927	\begin{align*} -2 y+y^{\prime }&=6 \,{\mathrm e}^{5 t} \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.173
15009	5838	\begin{align*} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.173
15010	23541	\begin{align*} 2 x^{2} y^{\prime \prime }+7 y^{\prime } x -3 y&=\frac {\ln \left (x \right )}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.173
15011	25751	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.173
15012	25802	\begin{align*} y^{\prime }&=y-y^{3} \\ \end{align*}	✓	✓	✓	✓	1.173
15013	2361	\begin{align*} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.174
15014	18941	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.174
15015	22591	\begin{align*} y^{\prime }&=1-\left (x -y\right )^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.174
15016	4061	\begin{align*} y^{\prime \prime } x -y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.175
15017	16475	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.175
15018	17141	\begin{align*} -y+y^{\prime }&=t^{2}-2 t \\ \end{align*}	✓	✓	✓	✓	1.175
15019	19200	\begin{align*} x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	1.175
15020	6062	\begin{align*} n^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.176
15021	17414	\begin{align*} t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.176
15022	20201	\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.176
15023	23382	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.176
15024	1264	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.177
15025	3296	\begin{align*} y \left (1+{y^{\prime }}^{2}\right )&=2 \\ \end{align*}	✓	✓	✓	✓	1.177
15026	5435	\begin{align*} 2 {y^{\prime }}^{2}+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.177
15027	7662	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.177
15028	12358	\begin{align*} \left (x +a \right ) y+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	1.177
15029	13748	\begin{align*} y^{\prime \prime } x +\left (a \,x^{2}+b \right ) x y^{\prime }+\left (3 a \,x^{2}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.177
15030	18364	\begin{align*} y^{\prime \prime }+\lambda ^{2} y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.177
15031	7367	\begin{align*} y^{\prime \prime }&=-4 y \\ \end{align*}	✓	✓	✓	✓	1.178
15032	11407	\begin{align*} y^{\prime } x +a \,x^{\alpha } y^{2}+b y-c \,x^{\beta }&=0 \\ \end{align*}	✓	✓	✓	✗	1.178
15033	15619	\begin{align*} y^{\prime }&=y^{3} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.178
15034	20169	\begin{align*} y^{3} y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	1.178
15035	2961	\begin{align*} x^{\prime }+x&={\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	1.179
15036	7988	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=5 \\ \end{align*}	✓	✓	✓	✓	1.179
15037	14252	\begin{align*} \theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \\ \end{align*}	✓	✓	✓	✓	1.179
15038	14698	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.179
15039	20498	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	1.179
15040	22765	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x^{2}-4 x +2 \\ \end{align*}	✓	✓	✓	✓	1.179
15041	22539	\begin{align*} y^{\prime } x&=x^{3}+2 y \\ \end{align*}	✓	✓	✓	✓	1.180
15042	13758	\begin{align*} y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.181
15043	15333	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.181
15044	16278	\begin{align*} y^{\prime }+5 y&={\mathrm e}^{-3 x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.181
15045	18878	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	1.181
15046	3432	\begin{align*} y^{\prime }&=y^{2}-y \\ \end{align*}	✓	✓	✓	✓	1.182
15047	11749	\begin{align*} y {y^{\prime }}^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.182
15048	18065	\begin{align*} y^{\prime }-1&={\mathrm e}^{x +2 y} \\ \end{align*}	✓	✓	✓	✓	1.182
15049	1944	\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (5 x^{2}+3 x +3\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.183
15050	5761	\begin{align*} \left (a +b \,{\mathrm e}^{x}+c \,{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.183
15051	19667	\begin{align*} x^{\prime }&=\left (x-1\right )^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.183
15052	22596	\begin{align*} y^{\prime }&=\frac {2}{x +2 y-3} \\ \end{align*}	✓	✓	✓	✓	1.183
15053	24938	\begin{align*} y^{\prime }&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.183
15054	3592	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	1.184
15055	16698	\begin{align*} y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	1.184
15056	19878	\begin{align*} V^{\prime \prime }+\frac {2 V^{\prime }}{r}&=0 \\ \end{align*}	✓	✓	✓	✓	1.184
15057	20409	\begin{align*} \left (2 x -b \right ) y^{\prime }&=y-a y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.184
15058	10035	\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.185
15059	14829	\begin{align*} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x&=0 \\ \end{align*}	✓	✓	✓	✓	1.185
15060	23368	\begin{align*} 5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.185
15061	217	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	1.186
15062	21921	\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\ y \left (0\right ) &= {\frac {7}{9}} \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{6}-1 \\ \end{align*}	✓	✓	✓	✓	1.186
15063	23175	\begin{align*} y^{\prime }-2 y x&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.186
15064	25	\begin{align*} y^{\prime }&=x^{2}-y \\ \end{align*}	✓	✓	✓	✓	1.187
15065	156	\begin{align*} y^{3} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.187
15066	586	\begin{align*} 10 x_{1}^{\prime }&=-x_{1}+x_{3} \\ 10 x_{2}^{\prime }&=x_{1}-x_{2} \\ 10 x_{3}^{\prime }&=x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	1.187
15067	3401	\begin{align*} \left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y&=x^{2} \left (x +1\right )^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.187
15068	7082	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.187
15069	7306	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.187
15070	25811	\begin{align*} y^{\prime }&=\left ({\mathrm e}^{y} y-9 y\right ) {\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	1.187
15071	2746	\begin{align*} x_{1}^{\prime }&=2 x_{2} \\ x_{2}^{\prime }&=-2 x_{1} \\ x_{3}^{\prime }&=-3 x_{4} \\ x_{4}^{\prime }&=3 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.188
15072	7595	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.188
15073	10227	\begin{align*} \frac {x y^{\prime \prime }}{1-x}+y&=\frac {1}{1-x} \\ \end{align*}	✗	✓	✓	✗	1.188
15074	10428	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -c^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.188
15075	16588	\begin{align*} y^{\prime \prime }-9 y&=36 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	1.188
15076	22095	\begin{align*} y^{\prime \prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.188
15077	16681	\begin{align*} x^{2} y^{\prime \prime }-2 y&=15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.189
15078	20372	\begin{align*} y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.189
15079	23123	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.189
15080	3270	\begin{align*} \left (1+y\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.190
15081	6283	\begin{align*} -y+y^{\prime } x +x^{5} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.190
15082	14973	\begin{align*} a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✓	1.190
15083	18078	\begin{align*} y^{\prime }+x {y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.190
15084	24920	\begin{align*} \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.190
15085	25001	\begin{align*} 2 t y+y^{\prime }&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.190
15086	839	\begin{align*} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.191
15087	4032	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.191
15088	9440	\begin{align*} 9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✓	✓	✓	✗	1.191
15089	11282	\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 \left (x -1\right ) x}\right ) y \\ \end{align*}	✓	✓	✓	✓	1.191
15090	11831	\begin{align*} {y^{\prime }}^{4}-\left (y-a \right )^{3} \left (y-b \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.191
15091	13294	\begin{align*} y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\ \end{align*}	✓	✓	✓	✗	1.191
15092	15586	\begin{align*} y^{\prime }&=y^{2}-2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	1.191
15093	17356	\begin{align*} 3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= {\frac {17}{3}} \\ \end{align*}	✓	✓	✓	✓	1.191
15094	69	\begin{align*} y^{\prime }&=y^{2} \\ y \left (a \right ) &= b \\ \end{align*}	✓	✓	✓	✓	1.192
15095	16800	\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.192
15096	17164	\begin{align*} y+y^{\prime }&={\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.192
15097	24829	\begin{align*} 8 y&={y^{\prime }}^{2}+3 x^{2} \\ \end{align*}	✓	✓	✓	✗	1.192
15098	1745	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.193
15099	6443	\begin{align*} y y^{\prime \prime }&=y^{2} y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.195
15100	6488	\begin{align*} 4 y y^{\prime \prime }&=-4 y+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.195