2.3.180 Problems 17901 to 18000

Table 2.891: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17901	6064	\begin{align*} a^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.142
17902	1620	\begin{align*} y^{\prime }&=\frac {\tan \left (y\right )}{x -1} \\ \end{align*}	✓	✓	✓	✓	5.145
17903	2695	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=2 \delta \left (t -1\right )-\delta \left (-2+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.145
17904	5903	\begin{align*} -y+\left (1+a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	5.145
17905	4421	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.149
17906	17123	\begin{align*} y^{\prime }&=y \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.149
17907	17655	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.149
17908	18786	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.149
17909	6165	\begin{align*} \left (x^{4}+2 x^{2}+a \right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.151
17910	16488	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.152
17911	17744	\begin{align*} 12 y^{\prime \prime }+8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.152
17912	212	\begin{align*} y^{\prime }&=\frac {x +3 y}{-3 x +y} \\ \end{align*}	✓	✓	✓	✓	5.153
17913	17247	\begin{align*} -1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.154
17914	18322	\begin{align*} y^{\prime \prime }+y^{\prime }&=\frac {1}{{\mathrm e}^{x}+1} \\ \end{align*}	✓	✓	✓	✗	5.154
17915	18867	\begin{align*} 4 y^{\prime \prime }+y&=2 \sec \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	5.154
17916	13637	\begin{align*} y^{\prime }&=a y^{3}+\frac {b}{x^{{3}/{2}}} \\ \end{align*}	✓	✓	✓	✗	5.155
17917	15523	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (2\right ) &= -1 \\ \end{align*}	✗	✗	✗	✓	5.155
17918	22426	\begin{align*} y+\left (4 x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.155
17919	13941	\begin{align*} y^{\prime \prime }-\left (a +2 b \,{\mathrm e}^{a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{2 a x} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.156
17920	8376	\begin{align*} y^{\prime }&=y^{2}-4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	5.157
17921	7584	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.158
17922	18802	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	5.158
17923	8244	\begin{align*} y y^{\prime }&=3 x \\ y \left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	5.159
17924	15157	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	5.160
17925	21119	\begin{align*} x^{\prime \prime }+p x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.160
17926	3295	\begin{align*} y&=x +3 \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	5.161
17927	21473	\begin{align*} \frac {\ln \left (1+{y^{\prime }}^{2}\right )}{2}-\ln \left (y^{\prime }\right )-x +2&=0 \\ \end{align*}	✓	✓	✓	✓	5.161
17928	8839	\begin{align*} x +y y^{\prime }+y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.163
17929	4097	\begin{align*} x^{3}+y^{3}-y^{\prime } y^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	5.165
17930	18558	\begin{align*} y^{\prime }&=-\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2} \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.165
17931	25561	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.165
17932	9086	\begin{align*} y \ln \left (y\right )-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.168
17933	15528	\begin{align*} y^{\prime }&=y^{2}-4 \\ \end{align*}	✓	✓	✓	✓	5.168
17934	5992	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.169
17935	19797	\begin{align*} y^{\prime }+\sin \left (x \right ) y&=\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	5.169
17936	21024	\begin{align*} x^{\prime }&=\frac {x}{t^{2}+1} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.169
17937	9037	\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.170
17938	13233	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+b \,x^{m} y+x^{m} b c -a \,c^{2} x^{n} \\ \end{align*}	✓	✓	✓	✗	5.171
17939	20235	\begin{align*} \csc \left (x \right ) \ln \left (y\right ) y^{\prime }+y^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.171
17940	23153	\begin{align*} x^{2}+y^{2}-2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.171
17941	1162	\begin{align*} y^{\prime }&=\frac {x +3 y}{x -y} \\ \end{align*}	✓	✓	✓	✗	5.174
17942	9021	\begin{align*} y^{\prime }&=\frac {\left (x +y-1\right )^{2}}{2 \left (2+x \right )^{2}} \\ \end{align*}	✓	✓	✓	✓	5.174
17943	6062	\begin{align*} n^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.176
17944	3659	\begin{align*} y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	5.177
17945	1317	\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	5.178
17946	10456	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.178
17947	8777	\begin{align*} y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.179
17948	6486	\begin{align*} 3 y y^{\prime \prime }&=36 y^{2}+2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.181
17949	17127	\begin{align*} y^{\prime }&=-\frac {y-2}{x -2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.181
17950	21798	\begin{align*} 1+y+y^{2}+x \left (x^{2}-4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.181
17951	3589	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.182
17952	16507	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.182
17953	12349	\begin{align*} y^{\prime \prime }-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+2 a \right ) y^{\prime }+\left (\frac {a f^{\prime }\left (x \right )}{f \left (x \right )}+a^{2}-b^{2} f \left (x \right )^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.183
17954	382	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.184
17955	21560	\begin{align*} y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.185
17956	17119	\begin{align*} y^{\prime }&=\frac {3+y}{1+3 x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.186
17957	23343	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.186
17958	4404	\begin{align*} -y+y^{\prime } x&=x \tan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	5.187
17959	19101	\begin{align*} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.187
17960	240	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.188
17961	2408	\begin{align*} y^{\prime \prime }-y&=f \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.188
17962	3774	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=9 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.188
17963	20099	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	5.189
17964	7864	\begin{align*} 1+2 y-\left (4-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.190
17965	7710	\begin{align*} \cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	5.191
17966	20307	\begin{align*} y+\left (y^{n} a \,x^{2}-2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.191
17967	13629	\begin{align*} \left (A x y+B \,x^{2}+\left (-1+k \right ) A a y-\left (A b k +B a \right ) x \right ) y^{\prime }&=A y^{2}+B x y-\left (B a k +A b \right ) y+\left (-1+k \right ) B b x \\ \end{align*}	✓	✓	✓	✗	5.192
17968	17087	\begin{align*} \left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.193
17969	20502	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	5.193
17970	21084	\begin{align*} x^{\prime }&=\frac {x+2 t}{t} \\ \end{align*}	✓	✓	✓	✓	5.193
17971	3522	\begin{align*} y^{\prime }&=\frac {x \left (-1+y^{2}\right )}{2 \left (x -2\right ) \left (x -1\right )} \\ \end{align*}	✓	✓	✓	✓	5.194
17972	7267	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.197
17973	13453	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+x^{n -1} a n -a^{2} x^{2 n} f \left (x \right ) \\ \end{align*}	✓	✗	✗	✗	5.197
17974	16857	\begin{align*} \sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	5.197
17975	8874	\begin{align*} L y^{\prime }+R y&=E \,{\mathrm e}^{i \omega x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.198
17976	5173	\begin{align*} x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.201
17977	12148	\begin{align*} y^{\prime }&=2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6} \\ \end{align*}	✓	✓	✓	✗	5.201
17978	5913	\begin{align*} 2 \left (1-x \right ) y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	5.204
17979	8437	\begin{align*} \cos \left (x \right )^{2} \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{3} y&=1 \\ \end{align*}	✓	✓	✓	✓	5.204
17980	9152	\begin{align*} y^{\prime } x&=2 x -6 y \\ \end{align*}	✓	✓	✓	✓	5.204
17981	10117	\begin{align*} y^{\prime \prime }-2 x^{2} y-x^{4}+1&=0 \\ \end{align*}	✓	✓	✓	✗	5.205
17982	17391	\begin{align*} 7 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.207
17983	8231	\begin{align*} \left (-x +y\right ) y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	5.210
17984	9925	\begin{align*} 2 y^{\prime \prime } x +6 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.210
17985	858	\begin{align*} y^{\prime \prime }-i y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.211
17986	1676	\begin{align*} \left (y+{\mathrm e}^{x^{2}}\right ) y^{\prime }&=2 x \left (y^{2}+y \,{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x^{2}}\right ) \\ \end{align*}	✓	✓	✓	✗	5.211
17987	4712	\begin{align*} y^{\prime }&=\sqrt {a +b y^{2}} \\ \end{align*}	✓	✓	✓	✓	5.212
17988	8822	\begin{align*} \left (1+y^{2} x^{2}\right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.212
17989	13938	\begin{align*} y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.212
17990	24875	\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*}	✓	✓	✓	✓	5.212
17991	1742	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.214
17992	279	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.216
17993	5906	\begin{align*} b x y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	5.218
17994	23468	\begin{align*} y^{\prime \prime } x -2 y^{\prime }+\frac {\left (x^{2}+2\right ) y}{x}&=4+\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.218
17995	3482	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.219
17996	16478	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.219
17997	22676	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.221
17998	2935	\begin{align*} \frac {2 x^{2}}{x^{2}+y^{2}}+\ln \left (x^{2}+y^{2}\right )+\frac {2 x y y^{\prime }}{x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	5.227
17999	16224	\begin{align*} y^{\prime }&=\frac {x}{y} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.230
18000	16500	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.230