2.3.177 Problems 17601 to 17700

Table 2.885: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17601	22424	\begin{align*} \left (x^{2}+2 y \,{\mathrm e}^{2 x}\right ) y^{\prime }+2 y x +2 y^{2} {\mathrm e}^{2 x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.883
17602	19145	\begin{align*} y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✓	✓	4.886
17603	7433	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-x^{2} y&=\left (x +1\right ) \sqrt {-x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	4.889
17604	8707	\begin{align*} x^{2}+y x +y^{2}&=x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.889
17605	25827	\begin{align*} \left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.889
17606	6012	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{2} \left (x^{2}-1\right ) \\ \end{align*}	✓	✓	✓	✓	4.891
17607	7027	\begin{align*} y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.891
17608	3327	\begin{align*} y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	4.892
17609	9182	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.892
17610	9079	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.893
17611	12448	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x&=0 \\ \end{align*}	✓	✓	✓	✓	4.894
17612	17619	\begin{align*} 2 x^{2} y^{\prime \prime }-2 y^{\prime } x +20 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.894
17613	23112	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	4.894
17614	3320	\begin{align*} 3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\ \end{align*}	✓	✓	✗	✗	4.895
17615	6981	\begin{align*} x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.895
17616	23502	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	4.895
17617	3256	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	4.898
17618	4237	\begin{align*} y y^{\prime } x&=\sqrt {y^{2}-9} \\ y \left ({\mathrm e}^{4}\right ) &= 5 \\ \end{align*}	✓	✓	✓	✗	4.898
17619	5596	\begin{align*} \left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.898
17620	21545	\begin{align*} 4 y+y^{\prime \prime }&=\sec \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.898
17621	3544	\begin{align*} y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.901
17622	4119	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.901
17623	6272	\begin{align*} b y+\left (a -x \right )^{2} x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.901
17624	9212	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.901
17625	25819	\begin{align*} y^{\prime } x&=4 y \\ \end{align*}	✓	✓	✓	✓	4.901
17626	5184	\begin{align*} x \left (2-y x \right ) y^{\prime }+2 y-x y^{2} \left (y x +1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.902
17627	15605	\begin{align*} x y \left (1-y\right )-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.902
17628	13624	\begin{align*} \left (x^{2}+y x +a \right ) y^{\prime }&=y^{2}+y x +b \\ \end{align*}	✓	✓	✓	✓	4.903
17629	18837	\begin{align*} y^{\prime \prime }+y&=t \left (1+\sin \left (t \right )\right ) \\ \end{align*}	✓	✓	✓	✓	4.903
17630	25268	\begin{align*} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	4.903
17631	8040	\begin{align*} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	4.904
17632	22642	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.904
17633	10417	\begin{align*} y^{\prime } y^{\prime \prime }+y^{n}&=0 \\ \end{align*}	✓	✓	✓	✗	4.905
17634	10281	\begin{align*} c y^{\prime }&=\frac {a x +b y^{2}}{y} \\ \end{align*}	✓	✓	✓	✓	4.906
17635	17284	\begin{align*} -2 y+y^{\prime }&=t^{2} \sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.906
17636	5839	\begin{align*} a \left (1+k \right ) x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✗	✗	4.907
17637	1288	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ y \left (\frac {\pi }{4}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	4.908
17638	4848	\begin{align*} \left (a +x \right ) y^{\prime }&=y \left (1-a y\right ) \\ \end{align*}	✓	✓	✓	✓	4.909
17639	8402	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.909
17640	13310	\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} {\mathrm e}^{\lambda x} y-a \,{\mathrm e}^{\lambda x} \\ \end{align*}	✓	✓	✓	✗	4.909
17641	23120	\begin{align*} y^{\prime }+y x&=3 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.910
17642	7693	\begin{align*} y^{\prime }+\frac {2 y}{x}-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	4.911
17643	8665	\begin{align*} y^{\prime } x +y&=y^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	4.911
17644	11781	\begin{align*} \left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +\left (-a^{2}+1\right ) x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.911
17645	11306	\begin{align*} y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.912
17646	17221	\begin{align*} 2 t \sin \left (y\right )-2 \sin \left (t^{2}\right ) y t +\left (\cos \left (y\right ) t^{2}+\cos \left (t^{2}\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.912
17647	3491	\begin{align*} -\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {y^{\prime \prime }}{y}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y}&=2 a^{2} \\ \end{align*}	✗	✓	✓	✗	4.914
17648	19746	\begin{align*} y^{\prime }&=1+\frac {2 y}{x -y} \\ \end{align*}	✓	✓	✓	✓	4.915
17649	16747	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x -2 y&=10 x^{2} \\ \end{align*}	✓	✓	✓	✓	4.916
17650	16291	\begin{align*} \cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right )&=1+\sin \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	4.917
17651	24586	\begin{align*} y^{\prime \prime }+y&=4 x +1 \\ \end{align*}	✓	✓	✓	✓	4.917
17652	13974	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.918
17653	14142	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	4.918
17654	22429	\begin{align*} \frac {y}{\left (x +y\right )^{2}}-1+\left (1-\frac {x}{\left (x +y\right )^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.918
17655	12020	\begin{align*} y^{\prime }&=\frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 y^{2} a^{2} x +32 a^{3}} \\ \end{align*}	✓	✓	✓	✗	4.920
17656	12404	\begin{align*} 4 y^{\prime \prime } x +4 m y^{\prime }-\left (x -2 m -4 n \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.921
17657	15566	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	4.921
17658	24248	\begin{align*} y^{\prime }-m_{2} y&=c \,{\mathrm e}^{m_{1} x} \\ \end{align*}	✓	✓	✓	✓	4.921
17659	273	\begin{align*} y^{\prime \prime }+y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.922
17660	278	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.922
17661	6021	\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	4.922
17662	8301	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.923
17663	24901	\begin{align*} x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.924
17664	210	\begin{align*} y^{\prime }&=x y^{3}-y x \\ \end{align*}	✓	✓	✓	✓	4.925
17665	3572	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.925
17666	19483	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.925
17667	3528	\begin{align*} y^{\prime }&=y^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.927
17668	17797	\begin{align*} 9 x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= -{\frac {1}{2}} \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.927
17669	20689	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	4.927
17670	1693	\begin{align*} {\mathrm e}^{x} \left (y^{2} x^{2}+2 x y^{2}\right )+6 x +\left (2 x^{2} y \,{\mathrm e}^{x}+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.928
17671	11477	\begin{align*} 2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3&=0 \\ \end{align*}	✓	✓	✓	✓	4.929
17672	23467	\begin{align*} y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	4.929
17673	5836	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	4.930
17674	17115	\begin{align*} y^{\prime }&=\frac {y}{\ln \left (y\right )} \\ y \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	4.932
17675	3041	\begin{align*} x \,{\mathrm e}^{-y^{2}}+y y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.934
17676	10116	\begin{align*} y^{\prime \prime }-x^{2} y-x^{4}+2&=0 \\ \end{align*}	✓	✓	✓	✗	4.935
17677	20823	\begin{align*} \sin \left (y x \right )+x y \cos \left (y x \right )+x^{2} \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.935
17678	20975	\begin{align*} y^{\prime }&=f \left (x \right ) y \ln \left (\frac {1}{y}\right ) \\ \end{align*}	✓	✓	✓	✓	4.935
17679	24245	\begin{align*} y^{\prime }&=x -2 y \cot \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.935
17680	2967	\begin{align*} y^{\prime } x&=5 y+x +1 \\ \end{align*}	✓	✓	✓	✓	4.936
17681	22568	\begin{align*} y^{\prime }&=\frac {\left (3+y\right )^{2}}{4 x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.936
17682	12365	\begin{align*} y^{\prime \prime } x -y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.937
17683	18779	\begin{align*} 4 y^{\prime \prime }+9 y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.937
17684	9390	\begin{align*} x^{2} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.938
17685	11617	\begin{align*} \left (a y^{3} x +c \right ) x y^{\prime }+\left (b \,x^{3} y+c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.940
17686	1292	\begin{align*} y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.941
17687	16493	\begin{align*} 3 y^{\prime \prime }+7 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.941
17688	17219	\begin{align*} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.941
17689	3566	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.942
17690	4964	\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=c x y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	4.943
17691	23199	\begin{align*} x^{4}+y^{4}-x y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.943
17692	25228	\begin{align*} t^{2} y^{\prime \prime }+7 y^{\prime } t +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.943
17693	13759	\begin{align*} y^{\prime \prime } x +\left (a b \,x^{n}+b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y&=0 \\ \end{align*}	✗	✗	✗	✗	4.945
17694	17672	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (-1\right ) &= 0 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.945
17695	23057	\begin{align*} \left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	4.945
17696	13369	\begin{align*} y^{\prime }&=y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2} \\ \end{align*}	✓	✓	✓	✗	4.946
17697	16080	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.948
17698	19479	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.948
17699	4680	\begin{align*} y^{\prime }&=a x y^{2} \\ \end{align*}	✓	✓	✓	✓	4.949
17700	20262	\begin{align*} y^{\prime }&=\frac {1+2 x -y}{x +2 y-3} \\ \end{align*}	✓	✓	✓	✓	4.950