2.3.176 Problems 17501 to 17600

Table 2.925: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17501	14885	\begin{align*} x^{\prime }&=x^{2}-x^{4} \\ \end{align*}	✓	✓	✓	✓	2.844
17502	24184	\begin{align*} 6 x +y^{2}+y \left (2 x -3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.845
17503	10151	\begin{align*} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	2.846
17504	23056	\begin{align*} \frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	2.847
17505	10319	\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	2.848
17506	8980	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.849
17507	10163	\begin{align*} v v^{\prime }&=\frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \\ \end{align*}	✓	✓	✓	✓	2.849
17508	20743	\begin{align*} {y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.849
17509	21019	\begin{align*} x^{\prime }+a x&=b t \\ x \left (t_{0} \right ) &= x_{0} \\ \end{align*}	✓	✓	✓	✓	2.849
17510	1559	\begin{align*} y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.850
17511	4651	\begin{align*} y^{\prime }&=f \left (x \right )+g \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.850
17512	17614	\begin{align*} 3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.850
17513	17620	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.850
17514	19742	\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 v \\ \end{align*}	✓	✓	✓	✓	2.850
17515	26315	\begin{align*} y^{\prime }-y \ln \left (x \right )&=-\left (2 \ln \left (x \right )+1\right ) x^{-x} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.850
17516	25561	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.852
17517	27083	\begin{align*} y^{\prime }&=x \cos \left (2 x \right )-y \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.852
17518	16217	\begin{align*} y y^{\prime }&={\mathrm e}^{x -3 y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.853
17519	16234	\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}	✓	✓	✓	✓	2.853
17520	21050	\begin{align*} x^{\prime }&=x^{2}-1 \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.853
17521	21730	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	2.853
17522	8979	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=1 \\ \end{align*}	✓	✓	✓	✓	2.855
17523	2477	\begin{align*} \frac {t y}{t^{2}+1}+y^{\prime }&=1-\frac {t^{3} y}{t^{4}+1} \\ \end{align*}	✓	✓	✓	✗	2.856
17524	11582	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }-3 x y^{2}+x&=0 \\ \end{align*}	✓	✓	✓	✗	2.856
17525	1001	\begin{align*} x_{1}^{\prime }&=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\ x_{2}^{\prime }&=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\ x_{3}^{\prime }&=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\ x_{4}^{\prime }&=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \\ \end{align*}	✓	✓	✓	✓	2.857
17526	16197	\begin{align*} y^{\prime }+3 y x&=6 x \\ \end{align*}	✓	✓	✓	✓	2.857
17527	706	\begin{align*} y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	2.859
17528	1126	\begin{align*} \frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.859
17529	20677	\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.859
17530	24948	\begin{align*} y^{\prime }&=2 y \left (5-y\right ) \\ \end{align*}	✓	✓	✓	✓	2.859
17531	712	\begin{align*} x y^{\prime }-y&=x \\ y \left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	2.860
17532	3515	\begin{align*} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.860
17533	4612	\begin{align*} y^{\prime }&=a \cos \left (b x +c \right )+k y \\ \end{align*}	✓	✓	✓	✓	2.861
17534	15396	\begin{align*} y&=x y^{\prime }-\frac {1}{{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	2.861
17535	19100	\begin{align*} \frac {1}{x}-\frac {y^{2}}{\left (x -y\right )^{2}}+\left (\frac {x^{2}}{\left (x -y\right )^{2}}-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.861
17536	15963	\begin{align*} y^{\prime }&=\frac {t^{2}}{y+t^{3} y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.862
17537	14157	\begin{align*} \left (x y^{\prime \prime \prime }-y^{\prime \prime }\right )^{2}&={y^{\prime \prime \prime }}^{2}+1 \\ \end{align*}	✓	✓	✓	✗	2.864
17538	8686	\begin{align*} y^{\prime }&=\cos \left (x -y-1\right ) \\ \end{align*}	✓	✓	✓	✓	2.865
17539	9418	\begin{align*} \left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.865
17540	14699	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.865
17541	16311	\begin{align*} \cos \left (y\right ) y^{\prime }&={\mathrm e}^{-x}-\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.865
17542	27086	\begin{align*} y^{\prime }-\cos \left (x \right ) y&=-x^{2}+1 \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.865
17543	14722	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=10 x^{2} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -6 \\ \end{align*}	✓	✓	✓	✓	2.866
17544	26297	\begin{align*} 3 y^{\prime }+\frac {y \left (a^{2}+x^{2}\right )}{x \left (-a^{2}+x^{2}\right )}&=\frac {x \left (-a^{2}+3 x^{2}\right )}{y^{2} \left (-a^{2}+x^{2}\right )} \\ \end{align*}	✓	✓	✓	✓	2.866
17545	5574	\begin{align*} y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.867
17546	11699	\begin{align*} {y^{\prime }}^{2} x +4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.868
17547	17240	\begin{align*} y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.868
17548	17362	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.868
17549	17983	\begin{align*} 2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.868
17550	1719	\begin{align*} y^{2}+\left (x y^{2}+6 y x +\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.869
17551	14245	\begin{align*} 7 t^{2} x^{\prime }&=3 x-2 t \\ \end{align*}	✓	✓	✓	✓	2.870
17552	17167	\begin{align*} t y^{\prime }+y&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= \frac {4}{\pi } \\ \end{align*}	✓	✓	✓	✓	2.870
17553	20845	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.870
17554	690	\begin{align*} y^{\prime }&=\frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\ \end{align*}	✓	✓	✓	✗	2.871
17555	3408	\begin{align*} y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	2.871
17556	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*}	✓	✓	✓	✓	2.871
17557	1213	\begin{align*} y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.872
17558	3539	\begin{align*} 1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.872
17559	7847	\begin{align*} y&=x y^{\prime }+{y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	2.872
17560	9746	\begin{align*} 3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.872
17561	17848	\begin{align*} x y^{\prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.872
17562	7393	\begin{align*} x^{\prime }-x^{3}&=x \\ \end{align*}	✓	✓	✓	✓	2.873
17563	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*}	✓	✓	✓	✗	2.873
17564	3385	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.874
17565	6512	\begin{align*} \left (x -y\right ) y^{\prime }+{y^{\prime }}^{2} x +x \left (x +y\right ) y^{\prime \prime }&=y \\ \end{align*}	✓	✓	✓	✗	2.874
17566	12499	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	2.874
17567	23889	\begin{align*} \frac {y^{5} x^{2}+y^{2}+y}{x^{2} y^{4}+1}+\frac {\left (x^{3} y^{4}+2 y x +x \right ) y^{\prime }}{x^{2} y^{4}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	2.874
17568	2374	\begin{align*} t^{2} y^{\prime \prime }-t y^{\prime }-2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.875
17569	7801	\begin{align*} y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.875
17570	18876	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=g \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	2.875
17571	22315	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.876
17572	26431	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	2.876
17573	1667	\begin{align*} y^{\prime }&=\frac {2 x +y+1}{x +2 y-4} \\ \end{align*}	✓	✓	✓	✗	2.877
17574	8872	\begin{align*} L y^{\prime }+R y&=E \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.877
17575	16213	\begin{align*} y^{\prime }+y x&=4 x \\ \end{align*}	✓	✓	✓	✓	2.877
17576	16228	\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}	✓	✓	✓	✓	2.877
17577	26228	\begin{align*} x^{2} y^{2}+1+2 x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.877
17578	20827	\begin{align*} y&=x y^{\prime }+\frac {1}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	2.878
17579	12353	\begin{align*} 4 y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.879
17580	21615	\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.879
17581	25730	\begin{align*} y^{\prime }&=x -2 y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.880
17582	3384	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.881
17583	25235	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=0 \\ y \left (1\right ) &= -3 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.881
17584	3604	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\ y \left (0\right ) &= 2 a \\ \end{align*}	✓	✓	✓	✓	2.882
17585	7975	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=2 \\ \end{align*}	✓	✓	✓	✗	2.882
17586	3473	\begin{align*} y^{\prime }-\frac {y}{x}&=1 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.883
17587	78	\begin{align*} x y^{\prime }+5 y&=7 x^{2} \\ y \left (2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.884
17588	15495	\begin{align*} y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.884
17589	3619	\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\ \end{align*}	✓	✓	✓	✓	2.885
17590	4631	\begin{align*} y^{\prime }+\csc \left (x \right )+2 y \cot \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.885
17591	14662	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.885
17592	17374	\begin{align*} t^{2} y^{\prime \prime }+a t y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	2.885
17593	21344	\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.885
17594	23953	\begin{align*} \left (x +\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }+y-\frac {y}{x^{2}+y^{2}}&=0 \\ y \left (1\right ) &= \sqrt {3} \\ \end{align*}	✓	✓	✓	✗	2.885
17595	5692	\begin{align*} \cos \left (y^{\prime }\right )+x y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	2.886
17596	16592	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=10 x +12 \\ y \left (1\right ) &= 6 \\ y^{\prime }\left (1\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	2.886
17597	27254	\begin{align*} 2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.886
17598	57	\begin{align*} y^{\prime }&=1+x +y+y x \\ \end{align*}	✓	✓	✓	✓	2.887
17599	6579	\begin{align*} \left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime }&=b \\ \end{align*}	✗	✓	✓	✗	2.887
17600	26861	\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.890