2.3.136 Problems 13501 to 13600

Table 2.845: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13501	1823	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y&=8 x^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✗	1.284
13502	9551	\begin{align*} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.285
13503	9958	\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.285
13504	13676	\begin{align*} y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.285
13505	16100	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=3 t +2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.285
13506	26122	\begin{align*} y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \sin \left ({\mathrm e}^{x}\right ) \\ \end{align*}	✓	✓	✓	✓	1.285
13507	1095	\begin{align*} x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.286
13508	6019	\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.286
13509	9555	\begin{align*} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.286
13510	9575	\begin{align*} x y^{\prime \prime }-5 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.286
13511	11704	\begin{align*} {y^{\prime }}^{2} x +y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	1.286
13512	16422	\begin{align*} 2 y^{\prime }+x y^{\prime \prime }&=6 \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.286
13513	20562	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.286
13514	22156	\begin{align*} y^{\prime \prime }+2 y x&=x \\ \end{align*}	✓	✓	✓	✓	1.286
13515	11856	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.288
13516	3575	\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.289
13517	9542	\begin{align*} 2 x y^{\prime \prime }+5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.289
13518	15938	\begin{align*} y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	1.289
13519	23756	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\pi \right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.289
13520	24827	\begin{align*} {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.289
13521	6195	\begin{align*} \left (c x +b \right ) y+a \,x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.290
13522	6871	\begin{align*} u^{\prime }+b u^{2}&=\frac {c}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	1.290
13523	9576	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.290
13524	11820	\begin{align*} 4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.290
13525	12517	\begin{align*} y+\left (3 x +2\right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.290
13526	13717	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.290
13527	20863	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.290
13528	21703	\begin{align*} y^{\prime }-5 y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.290
13529	4458	\begin{align*} 4 y+y^{\prime \prime }&=\sinh \left (x \right ) \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.291
13530	15660	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.291
13531	25594	\begin{align*} y^{\prime \prime }+y^{\prime }&=t^{2}+1 \\ \end{align*}	✓	✓	✓	✓	1.291
13532	586	\begin{align*} 10 x_{1}^{\prime }&=-x_{1}+x_{3} \\ 10 x_{2}^{\prime }&=x_{1}-x_{2} \\ 10 x_{3}^{\prime }&=x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	1.292
13533	1106	\begin{align*} y+2 y^{\prime }&=3 t \\ \end{align*}	✓	✓	✓	✓	1.292
13534	9956	\begin{align*} x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.292
13535	16818	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.292
13536	18155	\begin{align*} y^{\prime \prime }+25 y&=\cos \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.292
13537	27292	\begin{align*} x y^{\prime }-\left (2 x +1\right ) y+y^{2}&=-x^{2} \\ \end{align*}	✓	✓	✓	✓	1.292
13538	5827	\begin{align*} -\left (-4 x^{2}+3\right ) y-4 x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.293
13539	6333	\begin{align*} 2 \cot \left (x \right ) y^{\prime }+2 \tan \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.293
13540	7686	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.293
13541	9238	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.293
13542	22203	\begin{align*} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.293
13543	22308	\begin{align*} y^{\prime \prime }&=12 x \left (4-x \right ) \\ y \left (0\right ) &= 7 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.293
13544	27424	\begin{align*} 2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\ \end{align*}	✓	✓	✗	✗	1.293
13545	12492	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.294
13546	8215	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{2}\right ) &= 0 \\ x^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.295
13547	9408	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.295
13548	12468	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.295
13549	12695	\begin{align*} y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	1.295
13550	20722	\begin{align*} y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.295
13551	26599	\begin{align*} y^{\prime \prime }-y^{\prime }&=-5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.295
13552	1792	\begin{align*} y^{\prime }+y^{2}-3 y+2&=0 \\ \end{align*}	✓	✓	✓	✓	1.296
13553	6721	\begin{align*} 4 x^{2} y^{\prime }-4 x^{3} y^{\prime \prime }+4 x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.296
13554	9963	\begin{align*} x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.296
13555	10486	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.296
13556	15864	\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	1.296
13557	18826	\begin{align*} y^{\prime \prime }+y&=3 \sin \left (2 t \right )+t \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.296
13558	20800	\begin{align*} x y^{\prime \prime }+\left (x -1\right ) y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✗	1.296
13559	25408	\begin{align*} y^{\prime }+4 y&=8 \\ \end{align*}	✓	✓	✓	✓	1.296
13560	26266	\begin{align*} \left (-x y^{\prime }+y\right )^{2}&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	1.296
13561	4378	\begin{align*} x y y^{\prime }+y^{2}-\sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.297
13562	5595	\begin{align*} \left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\ \end{align*}	✓	✓	✓	✓	1.297
13563	8648	\begin{align*} y^{\prime \prime }+16 y&=4 \delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.297
13564	13778	\begin{align*} x^{2} y^{\prime \prime }-\left (a^{2} x^{4}+a \left (2 b -1\right ) x^{2}+b \left (b +1\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.297
13565	14762	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\frac {3 y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.297
13566	20093	\begin{align*} x^{2} y^{\prime \prime }+y&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.297
13567	21025	\begin{align*} x^{\prime }-k^{2} x&=1 \\ \end{align*}	✓	✓	✓	✓	1.297
13568	10032	\begin{align*} f^{\prime }&=\frac {1}{f} \\ \end{align*}	✓	✓	✓	✓	1.298
13569	9896	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.299
13570	11407	\begin{align*} x y^{\prime }+a \,x^{\alpha } y^{2}+b y-c \,x^{\beta }&=0 \\ \end{align*}	✓	✓	✓	✗	1.299
13571	18332	\begin{align*} x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }&=\ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.299
13572	8220	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (-1\right ) &= 5 \\ y^{\prime }\left (-1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	1.300
13573	9900	\begin{align*} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.300
13574	24808	\begin{align*} x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4&=0 \\ \end{align*}	✓	✓	✓	✓	1.300
13575	25407	\begin{align*} y^{\prime }-4 y&=-8 \\ \end{align*}	✓	✓	✓	✓	1.300
13576	26519	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=2 \cos \left (4 x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.300
13577	8863	\begin{align*} y^{\prime }+5 y&=2 \\ \end{align*}	✓	✓	✓	✓	1.301
13578	15787	\begin{align*} y^{\prime }&=y \left (1-y\right ) \\ \end{align*}	✓	✓	✓	✓	1.301
13579	25619	\begin{align*} y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	1.301
13580	2628	\begin{align*} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.302
13581	8002	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	1.302
13582	19523	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=\left (x^{2}-1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.302
13583	19691	\begin{align*} x^{\prime \prime }+3 x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.302
13584	3565	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.303
13585	4455	\begin{align*} y^{\prime \prime }+6 y^{\prime }+10 y&=3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.303
13586	20720	\begin{align*} y^{\prime }&=\tan \left (x -\frac {y^{\prime }}{1+{y^{\prime }}^{2}}\right ) \\ \end{align*}	✓	✓	✗	✗	1.303
13587	22694	\begin{align*} y^{\prime \prime }+y&=6 \cos \left (x \right )^{2} \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.303
13588	22831	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	1.303
13589	9325	\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=\sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.305
13590	13921	\begin{align*} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✗	✗	1.305
13591	14960	\begin{align*} t^{2} x^{\prime \prime }-2 x&=t^{3} \\ \end{align*}	✓	✓	✓	✓	1.305
13592	16139	\begin{align*} y^{\prime \prime }+3 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.305
13593	16419	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.305
13594	7307	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.306
13595	9540	\begin{align*} x y^{\prime \prime }+y^{\prime }+10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.306
13596	9795	\begin{align*} x y^{\prime \prime }&=y^{\prime } \left (2-3 x y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	1.306
13597	9892	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.306
13598	25529	\begin{align*} y^{\prime \prime }&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.306
13599	4433	\begin{align*} 2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\ \end{align*}	✓	✓	✗	✗	1.307
13600	8770	\begin{align*} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✗	1.307