2.3.178 Problems 17701 to 17800

Table 2.929: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17701	6077	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=-2 x +2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	2.938
17702	17943	\begin{align*} y^{\prime }+y x \,{\mathrm e}^{x}&={\mathrm e}^{{\mathrm e}^{x} \left (1-x \right )} \\ \end{align*}	✓	✓	✓	✓	2.938
17703	3517	\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	2.940
17704	14706	\begin{align*} 9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.940
17705	17353	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.940
17706	2073	\begin{align*} x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (14+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.941
17707	3669	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.941
17708	5634	\begin{align*} {y^{\prime }}^{3}+\left (-3 x +1\right ) {y^{\prime }}^{2}-x \left (-3 x +1\right ) y^{\prime }-1-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.941
17709	12937	\begin{align*} y y^{\prime \prime }+a \left (1+{y^{\prime }}^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.941
17710	26167	\begin{align*} x y^{\prime }+1&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	2.941
17711	1586	\begin{align*} \left (-1+y\right )^{2} y^{\prime }&=2 x +3 \\ \end{align*}	✓	✓	✓	✓	2.944
17712	6821	\begin{align*} y^{2} \left (1+{y^{\prime }}^{2}\right )&=R^{2} \\ \end{align*}	✓	✓	✓	✓	2.944
17713	7149	\begin{align*} y^{\prime }+y \tan \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.944
17714	14489	\begin{align*} x y^{\prime }+y x +y-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.945
17715	23963	\begin{align*} {\mathrm e}^{2 x +3 y}+{\mathrm e}^{4 x -5 y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.946
17716	4273	\begin{align*} 2 y-x^{3}&=x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.947
17717	26609	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✓	✓	2.948
17718	2307	\begin{align*} y^{\prime }-2 y t&=t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.949
17719	23172	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=-2 x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.950
17720	21405	\begin{align*} x^{\prime }-x \tan \left (t \right )&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.951
17721	15789	\begin{align*} v^{\prime }&=t^{2} v-2-2 v+t^{2} \\ \end{align*}	✓	✓	✓	✓	2.952
17722	6540	\begin{align*} \left (x +y^{2}\right ) y^{\prime \prime }&=2 \left (x -y^{2}\right ) {y^{\prime }}^{3}-y^{\prime } \left (1+4 y y^{\prime }\right ) \\ \end{align*}	✗	✓	✓	✗	2.953
17723	1210	\begin{align*} 2 y x +3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.954
17724	2356	\begin{align*} y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.954
17725	12946	\begin{align*} \left (x -y\right ) y^{\prime \prime }-h \left (y^{\prime }\right )&=0 \\ \end{align*}	✗	✓	✓	✗	2.954
17726	19344	\begin{align*} y^{\prime }+y \cot \left (x \right )&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.954
17727	27496	\begin{align*} y^{\prime }&=\frac {y^{2}-x}{2 \left (x +1\right ) y} \\ \end{align*}	✓	✓	✗	✓	2.955
17728	11618	\begin{align*} \left (2 x^{3} y^{3}-x \right ) y^{\prime }+2 x^{3} y^{3}-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.956
17729	12289	\begin{align*} y^{\prime \prime }+l y&=0 \\ \end{align*}	✓	✓	✓	✓	2.956
17730	23720	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.956
17731	7531	\begin{align*} y^{\prime }+\frac {2 y}{x}&=2 x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	2.957
17732	25473	\begin{align*} y^{\prime }&=y^{2}+y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.957
17733	1689	\begin{align*} 2 x^{2}+8 y x +y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	2.958
17734	3519	\begin{align*} y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\ \end{align*}	✓	✓	✓	✓	2.958
17735	22060	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.958
17736	789	\begin{align*} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.959
17737	2808	\begin{align*} x^{\prime }&=x \left (1-x\right ) \\ \end{align*}	✓	✓	✓	✓	2.960
17738	4094	\begin{align*} {\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.960
17739	5950	\begin{align*} c y^{\prime }+\left (b x +a \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.960
17740	20951	\begin{align*} y^{\prime }&=y \left (-2+y\right ) \left (y+3\right ) \\ \end{align*}	✓	✓	✓	✓	2.960
17741	21172	\begin{align*} t^{2} x^{\prime \prime }+x^{\prime } t +x&=t \\ \end{align*}	✓	✓	✓	✓	2.960
17742	23911	\begin{align*} y^{\prime }-y \tan \left (x \right )&=\sin \left (x \right ) \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.960
17743	20227	\begin{align*} y^{\prime }&={\mathrm e}^{x -y}+x^{2} {\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	2.961
17744	27739	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+\left (x +1\right )^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	2.961
17745	24795	\begin{align*} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.962
17746	2072	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (9-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.963
17747	23739	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-\left (x +3\right ) y&=0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	2.963
17748	25814	\begin{align*} y^{\prime }&=y^{2}-y-6 \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	2.963
17749	4269	\begin{align*} y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\ \end{align*}	✓	✓	✓	✓	2.964
17750	6862	\begin{align*} \left (x^{2} y^{2}+y x \right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.964
17751	7753	\begin{align*} y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.964
17752	21831	\begin{align*} 2 y+y^{\prime }&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.964
17753	4214	\begin{align*} y^{\prime }&={\mathrm e}^{y} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.965
17754	7735	\begin{align*} y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.965
17755	10281	\begin{align*} c y^{\prime }&=\frac {a x +b y^{2}}{y} \\ \end{align*}	✓	✓	✓	✓	2.965
17756	54	\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	2.966
17757	4624	\begin{align*} y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}-\cos \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.966
17758	15954	\begin{align*} x^{\prime }&=-x t \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	2.967
17759	26455	\begin{align*} y^{\prime \prime } {\mathrm e}^{y^{\prime }} \left (y^{\prime }+2\right )&=1 \\ \end{align*}	✓	✓	✓	✓	2.967
17760	26636	\begin{align*} y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=x \,{\mathrm e}^{2 x}-1 \\ \end{align*}	✓	✓	✓	✗	2.967
17761	4884	\begin{align*} x^{2} y^{\prime }&=a +b x y+c \,x^{4} y^{2} \\ \end{align*}	✓	✓	✓	✗	2.968
17762	8438	\begin{align*} \left (x +1\right ) y^{\prime }+\left (x +2\right ) y&=2 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	2.968
17763	21847	\begin{align*} R q^{\prime }+\frac {q}{c}&=E \\ q \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.968
17764	120	\begin{align*} y^{\prime }&=\sqrt {x +y+1} \\ \end{align*}	✓	✓	✓	✓	2.969
17765	4609	\begin{align*} y^{\prime }&=x^{2}+3 \cosh \left (x \right )+2 y \\ \end{align*}	✓	✓	✓	✓	2.969
17766	24131	\begin{align*} y x +x -\left (1+x^{2}+y^{2}+x^{2} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.969
17767	4627	\begin{align*} y^{\prime }&=x \csc \left (x \right )-y \cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.970
17768	18354	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.970
17769	5732	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.971
17770	8226	\begin{align*} x y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	2.971
17771	12286	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.971
17772	15106	\begin{align*} 6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.971
17773	19255	\begin{align*} y^{\prime }+y \tan \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.971
17774	26386	\begin{align*} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.972
17775	17150	\begin{align*} y^{\prime }+\cot \left (t \right ) y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.973
17776	20399	\begin{align*} {y^{\prime }}^{2}-y y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	2.973
17777	22318	\begin{align*} y^{\prime }&=1+2 y x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.973
17778	25754	\begin{align*} y^{\prime }-2 y x&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.973
17779	3244	\begin{align*} y^{\prime \prime }&=k^{2} y \\ \end{align*}	✓	✓	✓	✓	2.974
17780	3595	\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	2.974
17781	9058	\begin{align*} x y^{\prime }+y&=x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.974
17782	21775	\begin{align*} 2 {y^{\prime }}^{2}-2 y y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.974
17783	17474	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.975
17784	721	\begin{align*} x y^{\prime }&=2 y+x^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.976
17785	4032	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.976
17786	11354	\begin{align*} y^{\prime }-f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.976
17787	11444	\begin{align*} x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	2.976
17788	1621	\begin{align*} y^{\prime }&=y^{{2}/{5}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.977
17789	3520	\begin{align*} -x y^{\prime }+y&=3-2 x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.977
17790	18365	\begin{align*} y^{\prime \prime }+\lambda ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.977
17791	24986	\begin{align*} y^{\prime }-3 y&=25 \cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.977
17792	193	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	2.980
17793	14323	\begin{align*} t^{2} x^{\prime \prime }+3 x^{\prime } t +x&=0 \\ \end{align*}	✓	✓	✓	✓	2.980
17794	15320	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	2.980
17795	24248	\begin{align*} y^{\prime }-m_{2} y&=c \,{\mathrm e}^{m_{1} x} \\ \end{align*}	✓	✓	✓	✓	2.980
17796	25014	\begin{align*} y t +y^{\prime }&=t^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	2.980
17797	4106	\begin{align*} y^{\prime }-3 y&={\mathrm e}^{3 x}+{\mathrm e}^{-3 x} \\ y \left (5\right ) &= 5 \\ \end{align*}	✓	✓	✓	✗	2.981
17798	2092	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-\left (-x^{2}+3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.982
17799	15876	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✗	✓	2.982
17800	1181	\begin{align*} y^{\prime }&=t -1-y^{2} \\ \end{align*}	✓	✓	✓	✗	2.983