2.3.147 Problems 14601 to 14700

Table 2.867: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14601	9868	\begin{align*} 2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.605
14602	7556	\begin{align*} t +x+3+x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.606
14603	8744	\begin{align*} 2 y+\left (x^{2} y+1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.606
14604	3482	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.607
14605	8363	\begin{align*} y^{\prime }+2 y&=1 \\ y \left (0\right ) &= {\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	1.607
14606	9398	\begin{align*} 2 x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.607
14607	11751	\begin{align*} y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.607
14608	22030	\begin{align*} x \,{\mathrm e}^{y x}+y \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.607
14609	3006	\begin{align*} x \ln \left (x \right ) y^{\prime }-x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.608
14610	9870	\begin{align*} 3 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.608
14611	16747	\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y&=10 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.608
14612	17813	\begin{align*} x^{\prime \prime }+x&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.608
14613	9394	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.609
14614	19148	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✗	1.609
14615	9547	\begin{align*} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.610
14616	18117	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.611
14617	26658	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=\left (x -1\right )^{2} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	1.611
14618	19196	\begin{align*} y^{\prime \prime }+9 y&=\ln \left (2 \sin \left (\frac {x}{2}\right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.612
14619	22802	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.612
14620	22851	\begin{align*} 2 x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.612
14621	21332	\begin{align*} y^{\prime }&=-5 y \\ \end{align*}	✓	✓	✓	✓	1.613
14622	25534	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+\omega ^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.613
14623	1329	\begin{align*} 2 t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.614
14624	14754	\begin{align*} 2 x y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.614
14625	22699	\begin{align*} y^{\prime \prime }+y&=x^{2}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.614
14626	26480	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.614
14627	2830	\begin{align*} x_{1}^{\prime }&=2 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	1.615
14628	21027	\begin{align*} x^{\prime }+x&=a t \\ \end{align*}	✓	✓	✓	✓	1.615
14629	23540	\begin{align*} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	1.615
14630	27717	\begin{align*} x \left (x^{2}+6\right ) y^{\prime \prime }-4 \left (x^{2}+3\right ) y^{\prime }+6 y x&=0 \\ \end{align*}	✓	✓	✓	✗	1.615
14631	1295	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	1.616
14632	9734	\begin{align*} 4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	1.616
14633	10045	\begin{align*} y^{\prime }+\sin \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.616
14634	14158	\begin{align*} y^{\prime \prime }+x y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.616
14635	14164	\begin{align*} y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.616
14636	21619	\begin{align*} m y^{\prime \prime }+a y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	1.616
14637	22182	\begin{align*} x^{4} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x^{2}-3 x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	1.616
14638	23013	\begin{align*} y^{\prime \prime }-3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.616
14639	6236	\begin{align*} a^{2} y+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.617
14640	821	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ y \left (1\right ) &= 7 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.618
14641	833	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.618
14642	22754	\begin{align*} x^{2} y^{\prime \prime }-2 y&=x \\ \end{align*}	✓	✓	✓	✓	1.618
14643	8249	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.619
14644	9874	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.619
14645	14652	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.619
14646	23274	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.619
14647	27548	\begin{align*} {y^{\prime \prime }}^{2}-2 y^{\prime } y^{\prime \prime \prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	1.620
14648	2561	\begin{align*} 2 y^{\prime \prime }-y^{\prime }+3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.621
14649	9256	\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}	✓	✓	✓	✓	1.621
14650	16399	\begin{align*} y^{\prime \prime \prime }&=2 \sqrt {y^{\prime \prime }} \\ \end{align*}	✓	✓	✓	✓	1.621
14651	9541	\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.622
14652	23382	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.623
14653	7183	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.625
14654	8772	\begin{align*} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y&=x \left (1-\ln \left (x \right )\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.625
14655	22220	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.625
14656	2434	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.626
14657	15181	\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	1.626
14658	27338	\begin{align*} y^{\prime }&=y^{2}+2 y x \\ \end{align*}	✓	✓	✓	✓	1.627
14659	17525	\begin{align*} y^{\prime \prime }+9 y&=\csc \left (3 t \right ) \\ y \left (\frac {\pi }{12}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{12}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.628
14660	25741	\begin{align*} y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.628
14661	19135	\begin{align*} {y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.629
14662	20438	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+a^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	1.629
14663	26035	\begin{align*} x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.629
14664	14760	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.630
14665	15161	\begin{align*} x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✗	✗	1.630
14666	16724	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.630
14667	26647	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\left (\sin \left (x \right )^{7} \cos \left (x \right )^{8}\right )^{{1}/{3}}} \\ \end{align*}	✓	✓	✓	✗	1.630
14668	9581	\begin{align*} x y^{\prime \prime }+y^{\prime }-7 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.631
14669	13023	\begin{align*} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.631
14670	24718	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.631
14671	2437	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.632
14672	4035	\begin{align*} x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 y \,{\mathrm e}^{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.632
14673	11764	\begin{align*} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.632
14674	15179	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime }&=\left (25-6 x \right ) y \\ \end{align*}	✓	✓	✓	✗	1.632
14675	22909	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=x-y \\ z^{\prime }&=2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.632
14676	26052	\begin{align*} {y^{\prime }}^{3}&=a \,x^{4} \\ \end{align*}	✓	✓	✓	✓	1.632
14677	3983	\begin{align*} y^{\prime \prime }+16 y&=4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.633
14678	9961	\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.633
14679	5936	\begin{align*} 3 \left (2-x \right ) y-\left (9-4 x \right ) y^{\prime }+\left (-x +3\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.634
14680	6199	\begin{align*} 6 y x +\left (-x^{3}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.634
14681	9873	\begin{align*} 2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.634
14682	11752	\begin{align*} y {y^{\prime }}^{2}+2 x y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.634
14683	24787	\begin{align*} \left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✗	1.634
14684	27181	\begin{align*} x_{1}^{\prime }&=5 x_{1}-4 x_{2}+3 x_{3}-3 \,{\mathrm e}^{-3 t} \\ x_{2}^{\prime }&=12 x_{1}-11 x_{2}+12 x_{3}+t \\ x_{3}^{\prime }&=4 x_{1}-4 x_{2}+5 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= -1 \\ x_{3} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.634
14685	6566	\begin{align*} A y+\left (a +2 b x +c \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.635
14686	14304	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=5 \sin \left (2 t \right )+{\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	1.635
14687	16233	\begin{align*} y^{\prime }&=200 y-2 y^{2} \\ \end{align*}	✓	✓	✓	✓	1.635
14688	26161	\begin{align*} y^{\prime }&=3 y^{2} \\ \end{align*}	✓	✓	✓	✓	1.635
14689	6870	\begin{align*} u^{\prime }+u^{2}&=\frac {c}{x^{{4}/{3}}} \\ \end{align*}	✓	✓	✓	✗	1.636
14690	15285	\begin{align*} x^{\prime }&=-2 x-2 y+4 z \\ y^{\prime }&=-2 x+y+2 z \\ z^{\prime }&=-4 x-2 y+6 z+{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	1.636
14691	16681	\begin{align*} x^{2} y^{\prime \prime }-2 y&=15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.636
14692	21000	\begin{align*} u^{\prime \prime }+2 a u^{\prime }+\omega ^{2} u&=c \cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	1.636
14693	9760	\begin{align*} 5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.637
14694	1183	\begin{align*} y^{\prime }&=y \left (-2+y\right ) \left (-1+y\right ) \\ \end{align*}	✓	✓	✓	✓	1.638
14695	19416	\begin{align*} x y^{\prime }+y x +y-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.638
14696	21559	\begin{align*} -y^{\prime }+x y^{\prime \prime }&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.638
14697	22858	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-4 x^{2}+3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.638
14698	14263	\begin{align*} x^{\prime \prime }+x^{\prime }&=3 t \\ \end{align*}	✓	✓	✓	✓	1.639
14699	27277	\begin{align*} \left (x +1\right ) \left (y^{\prime }+y^{2}\right )&=-y \\ \end{align*}	✓	✓	✓	✓	1.639
14700	11313	\begin{align*} y^{\prime }+f \left (x \right ) y-g \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.640