2.3.147 Problems 14601 to 14700

Table 2.837: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14601	25526	\begin{align*} m y^{\prime \prime }+k y&=\delta \left (-t +T \right ) \\ \end{align*}	✓	✓	✓	✓	1.635
14602	99	\begin{align*} \frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\ \end{align*}	✓	✓	✓	✓	1.636
14603	15122	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \\ \end{align*}	✓	✓	✓	✓	1.636
14604	1136	\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.637
14605	24477	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.637
14606	10271	\begin{align*} c y^{\prime }&=a \\ \end{align*}	✓	✓	✓	✓	1.638
14607	12616	\begin{align*} y^{\prime \prime }&=\frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	1.638
14608	14775	\begin{align*} 2 x^{\prime }+y^{\prime }-x-y&={\mathrm e}^{-t} \\ x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.638
14609	20628	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.638
14610	20715	\begin{align*} \left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.638
14611	3578	\begin{align*} y^{\prime }&=\frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.639
14612	15518	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y \left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	1.639
14613	20462	\begin{align*} x {y^{\prime }}^{2}-\left (x -a \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.639
14614	23828	\begin{align*} y^{\prime }&=\frac {1}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	1.639
14615	24839	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.639
14616	6008	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.640
14617	2384	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.641
14618	2400	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.641
14619	15410	\begin{align*} y^{\prime \prime }&=9 y \\ \end{align*}	✓	✓	✓	✓	1.641
14620	23676	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-p^{2}+x^{2}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.641
14621	25677	\begin{align*} 2 y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.641
14622	8972	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.642
14623	21045	\begin{align*} x^{\prime }&={\mathrm e}^{x}-t \\ \end{align*}	✓	✓	✓	✓	1.642
14624	3781	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +25 y&=0 \\ y \left (1\right ) &= \frac {3 \sqrt {3}}{2} \\ y^{\prime }\left (1\right ) &= {\frac {15}{2}} \\ \end{align*}	✓	✓	✓	✓	1.643
14625	14734	\begin{align*} \left (x -1\right ) y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.643
14626	2435	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.644
14627	8146	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.644
14628	8241	\begin{align*} y^{\prime }&=y^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.644
14629	8422	\begin{align*} y^{\prime }+y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	1.644
14630	1117	\begin{align*} \left (1+t \right ) y+y^{\prime } t&=t \\ y \left (\ln \left (2\right )\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.645
14631	5739	\begin{align*} y^{\prime \prime }+a^{2} y&=\cos \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	1.645
14632	1302	\begin{align*} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+y t^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	1.647
14633	8444	\begin{align*} y^{\prime }&=x +5 y \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.648
14634	22705	\begin{align*} s^{\prime \prime }+s^{\prime }&=t +{\mathrm e}^{-t} \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.648
14635	132	\begin{align*} x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	1.649
14636	5571	\begin{align*} y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.649
14637	5623	\begin{align*} {y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✗	1.649
14638	20141	\begin{align*} a^{2} y^{\prime \prime } y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.650
14639	16162	\begin{align*} y^{\prime }&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.651
14640	18612	\begin{align*} y^{\prime }&=y+\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	1.651
14641	22143	\begin{align*} y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.651
14642	3560	\begin{align*} y^{\prime }&=-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.652
14643	20464	\begin{align*} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.653
14644	25416	\begin{align*} y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -4\right )-\operatorname {Heaviside}\left (t -6\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.653
14645	41	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.654
14646	10155	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	1.654
14647	13707	\begin{align*} y^{\prime \prime }+2 a \,x^{n} y^{\prime }+a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.654
14648	8746	\begin{align*} \left (y^{2} x^{2}+1\right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.655
14649	11689	\begin{align*} 2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	1.655
14650	19779	\begin{align*} y^{\prime \prime }-2 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.655
14651	1819	\begin{align*} x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y&=x^{1+a} \\ \end{align*}	✓	✓	✓	✓	1.661
14652	2399	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.661
14653	14191	\begin{align*} 3 x^{\prime }+3 x+2 y&={\mathrm e}^{t} \\ 4 x-3 y^{\prime }+3 y&=3 t \\ \end{align*}	✓	✓	✓	✓	1.661
14654	17817	\begin{align*} x^{\prime \prime }+x&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.661
14655	21030	\begin{align*} x^{\prime }&=x^{2} \\ x \left (t_{0} \right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.661
14656	15388	\begin{align*} y&=2 y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.663
14657	18798	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.663
14658	1745	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.664
14659	8228	\begin{align*} \left (4-y^{2}\right ) y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.664
14660	11762	\begin{align*} 4 y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.665
14661	15665	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.665
14662	21003	\begin{align*} x^{\prime }+\ln \left (3\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	1.667
14663	24801	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.667
14664	25551	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+y&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	1.667
14665	9243	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.668
14666	13786	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\left (n +\frac {1}{2}\right )^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.668
14667	13686	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	1.669
14668	13850	\begin{align*} x \left (a \,x^{2}+b \right ) y^{\prime \prime }+2 \left (a \,x^{2}+b \right ) y^{\prime }-2 a x y&=0 \\ \end{align*}	✓	✓	✓	✗	1.669
14669	14103	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.669
14670	16710	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.669
14671	23108	\begin{align*} m s^{\prime \prime }&=\frac {g \,t^{2}}{2} \\ \end{align*}	✓	✓	✓	✓	1.669
14672	6215	\begin{align*} -\left (x +1\right )^{3} y+y^{\prime } x +x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.670
14673	13106	\begin{align*} a x^{\prime }&=b c \left (y-z\right ) \\ b y^{\prime }&=c a \left (z-x\right ) \\ c z^{\prime }&=a b \left (x-y\right ) \\ \end{align*}	✓	✓	✓	✓	1.670
14674	16101	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=3 t +2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.671
14675	17760	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y&={\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.671
14676	23742	\begin{align*} 2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=-3\).	✓	✓	✓	✓	1.671
14677	25203	\begin{align*} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}	✓	✓	✓	✗	1.671
14678	2439	\begin{align*} t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.672
14679	19206	\begin{align*} y^{\prime \prime } x -y^{\prime }-x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.672
14680	926	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=2 x_{3} \\ x_{3}^{\prime }&=3 x_{4} \\ x_{4}^{\prime }&=4 x_{1} \\ \end{align*}	✓	✓	✓	✓	1.674
14681	11472	\begin{align*} x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3&=0 \\ \end{align*}	✓	✓	✓	✓	1.674
14682	15112	\begin{align*} x^{\prime }+5 x+y&={\mathrm e}^{t} \\ y^{\prime }-x-3 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	1.674
14683	15596	\begin{align*} y^{\prime }&=y x +2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.674
14684	21101	\begin{align*} x&=t \left (1+x^{\prime }\right )+x^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.674
14685	9885	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.675
14686	13730	\begin{align*} y^{\prime \prime } x +a x y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	1.675
14687	9240	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.676
14688	12835	\begin{align*} y^{\prime \prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.676
14689	25201	\begin{align*} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.676
14690	138	\begin{align*} 2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.677
14691	8238	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.677
14692	23262	\begin{align*} y^{\prime \prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	1.677
14693	23670	\begin{align*} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.677
14694	5645	\begin{align*} 8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2}&=27 x +27 y \\ \end{align*}	✓	✓	✗	✗	1.678
14695	24248	\begin{align*} y^{\prime }-m_{2} y&=c \,{\mathrm e}^{m_{1} x} \\ \end{align*}	✓	✓	✓	✓	1.678
14696	6458	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	1.679
14697	16567	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -25 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.680
14698	17533	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y&=t^{3}+2 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	1.680
14699	14599	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= -4 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.681
14700	17468	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.681