2.3.150 Problems 14901 to 15000

Table 2.831: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14901	20188	\begin{align*} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.121
14902	24148	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.121
14903	4246	\begin{align*} y^{\prime }&=\sin \left (x -y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.122
14904	20286	\begin{align*} y y^{\prime }+x&=\frac {a^{2} \left (-y+y^{\prime } x \right )}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	3.122
14905	7851	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.123
14906	13317	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{-\lambda \,x^{2}} y^{2}+\lambda x y+b^{2} a \\ \end{align*}	✓	✓	✓	✗	3.124
14907	789	\begin{align*} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\ \end{align*}	✓	✓	✓	✓	3.125
14908	4678	\begin{align*} y^{\prime }&=x \left (2+x^{2} y-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.125
14909	11757	\begin{align*} y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.125
14910	14481	\begin{align*} y^{\prime }+\frac {3 y}{x}&=6 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.125
14911	21843	\begin{align*} y^{\prime }+3 x^{2} y&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.127
14912	11791	\begin{align*} x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.128
14913	12562	\begin{align*} \left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.129
14914	14969	\begin{align*} 4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x&=0 \\ x \left (1\right ) &= 2 \\ x^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.130
14915	24963	\begin{align*} y^{\prime }&=t^{m} y^{n} \\ \end{align*}	✓	✓	✓	✓	3.130
14916	2848	\begin{align*} \tan \left (x \right ) y^{\prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	3.131
14917	7563	\begin{align*} y^{\prime }-4 y&=2 x y^{2} \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	3.131
14918	14543	\begin{align*} 2 x +\tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.131
14919	11397	\begin{align*} y^{\prime } x +a y^{2}-y+b \,x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.132
14920	12321	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +a y&=0 \\ \end{align*}	✗	✓	✓	✗	3.132
14921	20501	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.132
14922	9770	\begin{align*} y^{\prime \prime } x&=y^{\prime }+x^{5} \\ y \left (1\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.133
14923	7753	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.134
14924	160	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	3.135
14925	21812	\begin{align*} 2 x^{2}+5 x y^{2}+\left (5 x^{2} y-2 y^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.135
14926	25011	\begin{align*} -y+y^{\prime }&=t y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.135
14927	1586	\begin{align*} \left (-1+y\right )^{2} y^{\prime }&=2 x +3 \\ \end{align*}	✓	✓	✓	✓	3.136
14928	2989	\begin{align*} \csc \left (y\right ) \cot \left (y\right ) y^{\prime }&=\csc \left (y\right )+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	3.136
14929	8596	\begin{align*} 3 t \left (1+t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	3.136
14930	3388	\begin{align*} y^{\prime \prime } x +3 y^{\prime }-y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.137
14931	7220	\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ y \left (5\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.137
14932	7224	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.137
14933	9060	\begin{align*} \left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.137
14934	23970	\begin{align*} y^{\prime }-5 y&=3 x^{3}+4 x \\ \end{align*}	✓	✓	✓	✓	3.138
14935	8583	\begin{align*} y^{\prime \prime } x +2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.139
14936	12370	\begin{align*} y^{\prime \prime } x +v y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	3.140
14937	15512	\begin{align*} x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.140
14938	22038	\begin{align*} y^{\prime }&=\frac {3 y x^{2}}{x^{3}+2 y^{4}} \\ \end{align*}	✓	✓	✓	✓	3.140
14939	16469	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	3.142
14940	4101	\begin{align*} y^{\prime }&={\mathrm e}^{x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.143
14941	2364	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.144
14942	16517	\begin{align*} 4 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.144
14943	24249	\begin{align*} v+\left (2 x +1-v x \right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.144
14944	24288	\begin{align*} 1+4 y x -4 x^{2} y+\left (-x^{3}+x^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	3.144
14945	15346	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.145
14946	15817	\begin{align*} y^{\prime }&=\left (y+\frac {1}{2}\right ) \left (y+t \right ) \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	3.145
14947	18803	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.145
14948	19695	\begin{align*} x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.145
14949	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 \(x=0\).	✓	✓	✓	✗	3.146
14950	7536	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.146
14951	13695	\begin{align*} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c \left (a \,x^{2}+b -c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.146
14952	19086	\begin{align*} x -y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.146
14953	22367	\begin{align*} 2 \cos \left (x \right ) y+3 \sin \left (x \right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.146
14954	14930	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 27 \\ y^{\prime }\left (0\right ) &= -54 \\ \end{align*}	✓	✓	✓	✓	3.147
14955	12312	\begin{align*} y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.148
14956	19907	\begin{align*} x +y y^{\prime }+\frac {-y+y^{\prime } x}{x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.148
14957	23098	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.148
14958	7494	\begin{align*} y \,{\mathrm e}^{-2 x}+y^{3}-{\mathrm e}^{-2 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.149
14959	14114	\begin{align*} y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{2 x}+1 \\ \end{align*}	✓	✓	✓	✓	3.149
14960	22365	\begin{align*} \sin \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✗	3.150
14961	229	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 7 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.152
14962	4302	\begin{align*} r y^{\prime }&=\frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \\ \end{align*}	✓	✓	✓	✓	3.152
14963	4309	\begin{align*} x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.152
14964	6415	\begin{align*} \left (c \,x^{2}+2 b x +a \right )^{{3}/{2}} y^{\prime \prime }&=f \left (\frac {x}{\sqrt {c \,x^{2}+2 b x +a}}\right ) \\ \end{align*}	✓	✓	✓	✓	3.152
14965	22581	\begin{align*} \cos \left (x \right ) y^{\prime }&=y-\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.152
14966	785	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	3.153
14967	15795	\begin{align*} x^{\prime }&=-t x \\ x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\ \end{align*}	✓	✓	✓	✓	3.153
14968	20305	\begin{align*} y^{\prime }&=\frac {1+x^{2}+y^{2}}{2 x y} \\ \end{align*}	✓	✓	✓	✓	3.153
14969	9203	\begin{align*} \csc \left (x \right ) y^{\prime }&=\csc \left (y\right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	3.154
14970	776	\begin{align*} 2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.155
14971	2844	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.155
14972	8442	\begin{align*} y^{\prime } x +\left (1+3 x \right ) y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	3.155
14973	22418	\begin{align*} y^{\prime }&=\frac {y \left (y-{\mathrm e}^{x}\right )}{{\mathrm e}^{x}-2 y x} \\ \end{align*}	✓	✓	✓	✗	3.155
14974	25488	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.155
14975	8222	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.156
14976	5268	\begin{align*} x \left (-3 y^{2}+x \right ) y^{\prime }+\left (2 x -y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.157
14977	16068	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.157
14978	2891	\begin{align*} y^{2} \left (y y^{\prime }-x \right )+x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.158
14979	3979	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.158
14980	16391	\begin{align*} y^{\prime \prime } x&=-y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.158
14981	17150	\begin{align*} y^{\prime }+\cot \left (t \right ) y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.158
14982	23855	\begin{align*} \left (x^{2}-1\right ) y+\left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.158
14983	18546	\begin{align*} y+\left (t -4\right ) t y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.159
14984	22302	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=2 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.159
14985	699	\begin{align*} \tan \left (x \right ) y^{\prime }&=y \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	3.160
14986	4633	\begin{align*} y^{\prime }&=2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	3.160
14987	11382	\begin{align*} y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1&=0 \\ \end{align*}	✗	✓	✓	✗	3.160
14988	1099	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✓	3.161
14989	15059	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.161
14990	18589	\begin{align*} y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.161
14991	23971	\begin{align*} y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✓	3.161
14992	12328	\begin{align*} y^{\prime \prime }+2 a x y^{\prime }+y a^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.163
14993	16236	\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.163
14994	3593	\begin{align*} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.164
14995	202	\begin{align*} 9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.165
14996	16145	\begin{align*} y^{\prime \prime }+y^{\prime }+5 y&=\operatorname {Heaviside}\left (-2+t \right ) \sin \left (-8+4 t \right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.165
14997	3387	\begin{align*} y^{\prime \prime } x +3 y^{\prime }-y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.167
14998	22555	\begin{align*} q^{\prime }&=\frac {p \,{\mathrm e}^{p^{2}-q^{2}}}{q} \\ \end{align*}	✓	✓	✓	✓	3.167
14999	12363	\begin{align*} y^{\prime \prime } x -y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	3.168
15000	17062	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.168