2.3.157 Problems 15601 to 15700

Table 2.887: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15601	4382	\begin{align*} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	1.980
15602	26856	\begin{align*} y^{\prime }&=-\frac {2 y+{\mathrm e}^{x}}{2 x} \\ \end{align*}	✓	✓	✓	✓	1.980
15603	26900	\begin{align*} \frac {1}{x}+y^{\prime }&=\frac {2}{x^{3} y^{{4}/{3}}} \\ \end{align*}	✗	✗	✗	✗	1.980
15604	132	\begin{align*} x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	1.982
15605	199	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y&=1 \\ \end{align*}	✓	✓	✓	✓	1.982
15606	1150	\begin{align*} y^{\prime }&=\frac {3 x^{2}}{-4+3 y^{2}} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.982
15607	18818	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=3+4 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.982
15608	26211	\begin{align*} \left (y^{2}+x y^{2}\right ) y^{\prime }+x^{2}-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.982
15609	27273	\begin{align*} \left (2 x +y\right ) y^{\prime }&=y+4 \ln \left (y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.982
15610	3050	\begin{align*} 2 y+y^{\prime }&=3 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.983
15611	16469	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	1.983
15612	258	\begin{align*} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.985
15613	5738	\begin{align*} y^{\prime \prime }+a^{2} y&=x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	1.985
15614	2530	\begin{align*} y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	1.987
15615	3564	\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.987
15616	25834	\begin{align*} y^{\prime }&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.989
15617	26157	\begin{align*} x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	1.989
15618	7917	\begin{align*} y^{\prime }+y&=2 x +2 \\ \end{align*}	✓	✓	✓	✓	1.990
15619	9654	\begin{align*} x^{\prime }&=3 x-5 y \\ y^{\prime }&=4 x+8 y \\ \end{align*}	✓	✓	✓	✓	1.990
15620	20390	\begin{align*} {y^{\prime }}^{3}-a \,x^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	1.990
15621	1127	\begin{align*} -y+y^{\prime }&=1+3 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.991
15622	5937	\begin{align*} -2 y^{\prime }+\left (-x +a \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.991
15623	12443	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✗	1.991
15624	25313	\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.991
15625	21104	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.992
15626	18147	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=3 \\ \end{align*}	✓	✓	✓	✓	1.993
15627	24820	\begin{align*} 2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.993
15628	26088	\begin{align*} \left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.993
15629	4123	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.994
15630	8252	\begin{align*} y^{\prime }&=x -2 y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.994
15631	5829	\begin{align*} a^{2} x^{2} y-2 a x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.996
15632	14761	\begin{align*} \left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.996
15633	16711	\begin{align*} y^{\prime \prime }-36 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.996
15634	8390	\begin{align*} y^{\prime }&=y-y^{3} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	1.997
15635	9912	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✗	1.997
15636	13930	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{4 \lambda x}+b \,{\mathrm e}^{3 \lambda x}+c \,{\mathrm e}^{2 \lambda x}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.997
15637	839	\begin{align*} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.998
15638	9726	\begin{align*} x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right ) \\ \end{align*}	✓	✓	✓	✓	1.998
15639	17079	\begin{align*} y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	1.998
15640	18803	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.998
15641	15	\begin{align*} x^{\prime \prime }&=4 \left (t +3\right )^{2} \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.999
15642	5964	\begin{align*} -\left (\left (n -1\right ) n -a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.999
15643	13022	\begin{align*} \sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\ \end{align*}	✗	✓	✗	✗	2.000
15644	25309	\begin{align*} y+y^{\prime }&=\delta \left (t -1\right )-\delta \left (-3+t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.000
15645	26752	\begin{align*} x^{\prime }&=2 t \left (t +x\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.000
15646	2604	\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=t^{2}+\left (2 t +3\right ) \left (1+\cos \left (t \right )\right ) \\ \end{align*}	✓	✓	✓	✓	2.001
15647	18328	\begin{align*} y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \\ \end{align*}	✓	✓	✓	✓	2.001
15648	11346	\begin{align*} y^{\prime }+2 a \,x^{3} y^{3}+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.002
15649	14215	\begin{align*} x^{\prime }&=a x+b \\ \end{align*}	✓	✓	✓	✓	2.002
15650	18184	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=-2 \\ \end{align*}	✓	✓	✓	✓	2.002
15651	19677	\begin{align*} x^{\prime }+2 x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.002
15652	6217	\begin{align*} \left (2 x +1\right ) y-x \left (2 x +1\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.003
15653	6363	\begin{align*} y^{\prime \prime }&=a \left (b +c x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✗	✓	✓	✗	2.003
15654	26926	\begin{align*} y^{\prime \prime }-16 y&=0 \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.003
15655	26155	\begin{align*} -x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.004
15656	14181	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.005
15657	20710	\begin{align*} y^{\prime \prime }+a^{2} y&=\cos \left (a x \right ) \\ \end{align*}	✓	✓	✓	✓	2.006
15658	86	\begin{align*} x y^{\prime }-3 y&=x^{3} \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.007
15659	13931	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	2.007
15660	17381	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.007
15661	18092	\begin{align*} y^{\prime \prime }&=2 x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.007
15662	20603	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	2.007
15663	26352	\begin{align*} y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	2.007
15664	20201	\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.008
15665	461	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.009
15666	17624	\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.009
15667	24939	\begin{align*} y^{\prime }&=y-t \\ \end{align*}	✓	✓	✓	✓	2.009
15668	231	\begin{align*} y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.010
15669	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*}	✓	✓	✓	✓	2.010
15670	5446	\begin{align*} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	2.011
15671	10397	\begin{align*} y^{\prime \prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	2.011
15672	12348	\begin{align*} y^{\prime \prime }-\frac {a f^{\prime }\left (x \right ) y^{\prime }}{f \left (x \right )}+b f \left (x \right )^{2 a} y&=0 \\ \end{align*}	✓	✓	✗	✗	2.011
15673	20137	\begin{align*} 2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.011
15674	7675	\begin{align*} y^{\prime }-y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	2.013
15675	8745	\begin{align*} x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.013
15676	12498	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2&=0 \\ \end{align*}	✓	✓	✓	✓	2.013
15677	17623	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.013
15678	22857	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.013
15679	26148	\begin{align*} y y^{\prime }&=-2 x^{3}+x \\ \end{align*}	✓	✓	✓	✓	2.014
15680	27302	\begin{align*} {\mathrm e}^{-y}-\left (2 y+x \,{\mathrm e}^{-y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.014
15681	18393	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+4 \left (x^{4}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.015
15682	27749	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-y&=0 \\ \end{align*}	✗	✓	✓	✓	2.015
15683	6097	\begin{align*} x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.016
15684	9825	\begin{align*} \left (y^{\prime }+1\right )^{2} \left (-x y^{\prime }+y\right )&=1 \\ \end{align*}	✓	✓	✓	✗	2.016
15685	16993	\begin{align*} 2 y+y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.016
15686	22237	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.016
15687	24917	\begin{align*} y^{\prime }&=y^{2}-y \\ \end{align*}	✓	✓	✓	✓	2.016
15688	2352	\begin{align*} y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.017
15689	6339	\begin{align*} y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.017
15690	14218	\begin{align*} y^{\prime }&=r \left (a -y\right ) \\ \end{align*}	✓	✓	✓	✓	2.017
15691	16518	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.017
15692	16892	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}}&=0 \\ \end{align*} Series expansion around \(x=4\).	✓	✓	✓	✗	2.017
15693	19483	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.017
15694	8335	\begin{align*} y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.018
15695	9385	\begin{align*} x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.018
15696	12841	\begin{align*} y^{\prime \prime }-a y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.018
15697	25726	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.018
15698	4040	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 \,{\mathrm e}^{x} y^{\prime } x +9 \left (1+\tan \left (x \right )\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.019
15699	12334	\begin{align*} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.019
15700	15469	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	2.019