2.3.159 Problems 15801 to 15900

Table 2.861: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15801	13956	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.170
15802	17356	\begin{align*} 3 t^{2} y^{\prime \prime }-5 y^{\prime } t -3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= {\frac {17}{3}} \\ \end{align*}	✓	✓	✓	✓	2.170
15803	26145	\begin{align*} y^{\prime } x +y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.170
15804	6250	\begin{align*} -x^{2} y-\left (-x^{3}+1\right ) y^{\prime }+x \left (x^{3}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.171
15805	15865	\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	2.171
15806	16818	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.171
15807	21602	\begin{align*} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u&=0 \\ u \left (1\right ) &= -1 \\ u^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.172
15808	19774	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	2.173
15809	20721	\begin{align*} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.173
15810	14152	\begin{align*} \left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.174
15811	10379	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=x \\ \end{align*}	✓	✓	✓	✗	2.175
15812	22330	\begin{align*} 2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	2.176
15813	24985	\begin{align*} y^{\prime }+2 y&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.176
15814	19793	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	2.177
15815	9780	\begin{align*} y^{\prime \prime }&=-{\mathrm e}^{-2 y} \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	2.178
15816	17381	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.178
15817	21624	\begin{align*} y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.178
15818	20097	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.179
15819	9730	\begin{align*} 3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.180
15820	11309	\begin{align*} y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{-\sin \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	2.180
15821	18528	\begin{align*} 4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.180
15822	5626	\begin{align*} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	2.181
15823	12959	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}-4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.181
15824	18587	\begin{align*} y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\ \end{align*}	✓	✓	✓	✓	2.182
15825	24836	\begin{align*} 2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✗	2.182
15826	4268	\begin{align*} y^{\prime } x -3 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.184
15827	15903	\begin{align*} y^{\prime }&=3 y-4 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	2.184
15828	1157	\begin{align*} y^{\prime }&=\frac {a y+b}{d +c y} \\ \end{align*}	✓	✓	✓	✓	2.186
15829	8025	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x +\ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	2.186
15830	8426	\begin{align*} y x +x^{2} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.187
15831	14190	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.187
15832	25692	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.188
15833	25786	\begin{align*} y^{\prime }&=x +y \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.188
15834	18047	\begin{align*} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.190
15835	19381	\begin{align*} y+x^{2}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	2.190
15836	14132	\begin{align*} y^{\prime \prime \prime }-y&=x \,{\mathrm e}^{x}+\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.191
15837	3523	\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+32 \\ \end{align*}	✓	✓	✓	✗	2.192
15838	12963	\begin{align*} 2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	2.192
15839	20773	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.192
15840	1168	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.193
15841	8391	\begin{align*} y^{\prime }&=y-y^{3} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✗	✓	2.193
15842	18525	\begin{align*} \frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.193
15843	21081	\begin{align*} x +2 y+\left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.193
15844	160	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	2.194
15845	11860	\begin{align*} y^{\prime }&=F \left (\frac {y}{a +x}\right ) \\ \end{align*}	✓	✓	✓	✗	2.194
15846	16259	\begin{align*} y^{\prime }&=1+\left (y x +3 y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.194
15847	20785	\begin{align*} \left (2+x \right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✗	2.194
15848	28	\begin{align*} y^{\prime }&=\ln \left (y\right ) x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.195
15849	203	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\ \end{align*}	✓	✓	✓	✓	2.195
15850	19891	\begin{align*} y^{\prime }-2 y-2 z&={\mathrm e}^{3 x} \\ z^{\prime }+5 y-2 z&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	2.195
15851	21063	\begin{align*} x^{\prime }&=-\left (1+p \right ) t^{p} x^{2} \\ \end{align*}	✓	✓	✓	✓	2.195
15852	16260	\begin{align*} y^{\prime }&=1+y x +3 y \\ \end{align*}	✓	✓	✓	✓	2.196
15853	23051	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=7 \\ \end{align*}	✓	✓	✓	✓	2.196
15854	9743	\begin{align*} x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.197
15855	20795	\begin{align*} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.199
15856	2769	\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }&=-4 x_{2}-x_{3}+t \\ x_{3}^{\prime }&=5 x_{2}+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.200
15857	8029	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=\ln \left (x +1\right )^{2}+x -1 \\ \end{align*}	✓	✓	✓	✗	2.200
15858	20304	\begin{align*} x \left (-a^{2}+x^{2}+y^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.200
15859	26170	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	2.200
15860	705	\begin{align*} y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.201
15861	1000	\begin{align*} x_{1}^{\prime }&=23 x_{1}-18 x_{2}-16 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4} \\ x_{3}^{\prime }&=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4} \\ x_{4}^{\prime }&=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4} \\ \end{align*}	✓	✓	✓	✓	2.201
15862	1098	\begin{align*} 3 y+y^{\prime }&={\mathrm e}^{-2 t}+t \\ \end{align*}	✓	✓	✓	✓	2.201
15863	1236	\begin{align*} y^{\prime }&=\frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}} \\ \end{align*}	✓	✓	✓	✗	2.201
15864	7918	\begin{align*} y^{\prime }-y&=y x \\ \end{align*}	✓	✓	✓	✓	2.201
15865	18534	\begin{align*} 2 y+y^{\prime } t&=\frac {\sin \left (t \right )}{t} \\ y \left (-\frac {\pi }{2}\right ) &= a \\ \end{align*}	✓	✓	✓	✓	2.201
15866	13296	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{s x}+d \,{\mathrm e}^{-k x} \\ \end{align*}	✓	✓	✓	✗	2.202
15867	14977	\begin{align*} 2 y^{\prime \prime } x +y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.202
15868	25699	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.202
15869	11491	\begin{align*} y^{\prime } \sqrt {a^{2}+x^{2}}+y-\sqrt {a^{2}+x^{2}}+x&=0 \\ \end{align*}	✓	✓	✓	✓	2.203
15870	14983	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.203
15871	3594	\begin{align*} {\mathrm e}^{x +y} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.204
15872	12286	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.204
15873	13212	\begin{align*} y^{\prime }&=a y^{2}+b \,x^{2 n}+c \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	2.204
15874	15340	\begin{align*} z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.204
15875	17179	\begin{align*} y+y^{\prime }&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.204
15876	21263	\begin{align*} x^{\prime \prime }-x+3 x^{2}&=0 \\ x \left (0\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.204
15877	1180	\begin{align*} y^{\prime }&=-y \left (3-t y\right ) \\ \end{align*}	✓	✓	✓	✓	2.205
15878	12938	\begin{align*} y y^{\prime \prime }+a {y^{\prime }}^{2}+y^{3} b&=0 \\ \end{align*}	✓	✓	✓	✗	2.205
15879	12448	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x&=0 \\ \end{align*}	✓	✓	✓	✓	2.206
15880	3449	\begin{align*} y^{\prime }&=-\tan \left (t \right ) y+\sec \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.207
15881	8240	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.207
15882	191	\begin{align*} 4 x y^{2}+y^{\prime }&=5 y^{2} x^{4} \\ \end{align*}	✓	✓	✓	✓	2.208
15883	3003	\begin{align*} \left (1-x \right ) y^{\prime }-1-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.208
15884	16095	\begin{align*} y^{\prime \prime }+2 y&=-3 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.208
15885	17329	\begin{align*} y+y^{\prime }&=5 \\ \end{align*}	✓	✓	✓	✓	2.209
15886	11307	\begin{align*} y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{2 x}&=0 \\ \end{align*}	✓	✓	✓	✓	2.210
15887	19489	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.210
15888	11627	\begin{align*} \left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	2.211
15889	21013	\begin{align*} x^{\prime }&=2 t x \\ x \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.211
15890	21617	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.211
15891	24951	\begin{align*} \frac {y^{\prime }}{y}&=y-t \\ \end{align*}	✓	✓	✓	✓	2.211
15892	21254	\begin{align*} x^{\prime \prime }&=x-x^{3} \\ \end{align*}	✓	✓	✓	✗	2.212
15893	1177	\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ \end{align*}	✓	✓	✓	✓	2.213
15894	1238	\begin{align*} \frac {-4+6 y x +2 y^{2}}{3 x^{2}+4 y x +3 y^{2}}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.213
15895	3447	\begin{align*} y^{\prime }&=2 y \\ y \left (\ln \left (3\right )\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.214
15896	16426	\begin{align*} y^{\prime \prime }&=-{\mathrm e}^{-y} y^{\prime } \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	2.214
15897	13738	\begin{align*} y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.215
15898	1135	\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x} \\ \end{align*}	✗	✗	✗	✗	2.216
15899	11317	\begin{align*} y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1&=0 \\ \end{align*}	✓	✓	✓	✓	2.217
15900	14881	\begin{align*} x^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	2.217