2.3.156 Problems 15501 to 15600

Table 2.885: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15501	3266	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.559
15502	3270	\begin{align*} \left (1+y\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.559
15503	11858	\begin{align*} f \left (x {y^{\prime }}^{2}\right )+2 y^{\prime } x -y&=0 \\ \end{align*}	✗	✓	✓	✗	1.559
15504	16386	\begin{align*} y^{\prime \prime } x&=y^{\prime }-2 x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.559
15505	22656	\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.559
15506	12906	\begin{align*} 24+12 y x +x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\ \end{align*}	✗	✗	✓	✗	1.560
15507	18481	\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.560
15508	8261	\begin{align*} y^{\prime \prime }+9 y&=18 \\ \end{align*}	✓	✓	✓	✓	1.561
15509	12586	\begin{align*} y^{\prime \prime }&=-\frac {2 \left (x -2\right ) y^{\prime }}{x \left (x -1\right )}+\frac {2 \left (x +1\right ) y}{x^{2} \left (x -1\right )} \\ \end{align*}	✓	✓	✓	✗	1.561
15510	16808	\begin{align*} 3 y+y^{\prime }&=\delta \left (-2+t \right ) \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.562
15511	18040	\begin{align*} y^{\prime }&=\left (x -y\right )^{2}+1 \\ \end{align*}	✓	✓	✓	✓	1.562
15512	24879	\begin{align*} y^{\prime \prime }+\beta ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.562
15513	18365	\begin{align*} y^{\prime \prime }+\lambda ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.563
15514	20783	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✗	1.563
15515	24994	\begin{align*} y^{\prime }+a y&={\mathrm e}^{b t} \\ \end{align*}	✓	✓	✓	✓	1.563
15516	5597	\begin{align*} \left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.564
15517	10147	\begin{align*} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \\ \end{align*}	✓	✓	✓	✓	1.564
15518	14704	\begin{align*} 3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.564
15519	16494	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.564
15520	1316	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.565
15521	9441	\begin{align*} p \left (1+p \right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✓	✓	✓	✓	1.565
15522	17865	\begin{align*} y^{\prime }&=y+x^{2} \\ \end{align*}	✓	✓	✓	✓	1.565
15523	22768	\begin{align*} \left (2 x +3\right )^{2} y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }-2 y&=24 x^{2} \\ \end{align*}	✓	✓	✓	✗	1.566
15524	821	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 7 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.568
15525	24851	\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}	✓	✓	✓	✗	1.568
15526	7098	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.569
15527	14823	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.569
15528	26501	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=3 \\ \end{align*}	✓	✓	✓	✓	1.569
15529	8224	\begin{align*} y^{\prime }&=y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	1.570
15530	8324	\begin{align*} y^{\prime }&=x^{2}-2 y \\ \end{align*}	✓	✓	✓	✓	1.571
15531	9496	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.571
15532	17108	\begin{align*} y^{\prime }&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.571
15533	3958	\begin{align*} y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.572
15534	12470	\begin{align*} x^{2} y^{\prime \prime }+\left (a +2 b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) b \,x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.572
15535	8754	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	1.573
15536	16517	\begin{align*} 4 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.573
15537	11661	\begin{align*} {y^{\prime }}^{2}+y^{2}-a^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.574
15538	19691	\begin{align*} x^{\prime \prime }+3 x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.574
15539	27568	\begin{align*} x y y^{\prime \prime }-x {y^{\prime }}^{2}&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.574
15540	999	\begin{align*} x_{1}^{\prime }&=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4} \\ x_{2}^{\prime }&=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4} \\ x_{3}^{\prime }&=x_{1}+6 x_{2}-20 x_{3}-31 x_{4} \\ x_{4}^{\prime }&=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.575
15541	5999	\begin{align*} \left (b \,x^{2}+a \right ) y+2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.575
15542	21441	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.575
15543	1109	\begin{align*} y+2 y^{\prime }&=3 t^{2} \\ \end{align*}	✓	✓	✓	✓	1.576
15544	27006	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x -21 y&=0 \\ y \left (2\right ) &= 1 \\ y^{\prime }\left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.576
15545	25674	\begin{align*} y^{\prime }+2 y x&=1 \\ \end{align*}	✓	✓	✓	✓	1.577
15546	17945	\begin{align*} y^{\prime }-y&=-2 \,{\mathrm e}^{-x} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.578
15547	18529	\begin{align*} \left (1+t \right ) y+y^{\prime } t&=t \\ y \left (\ln \left (2\right )\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.578
15548	20134	\begin{align*} y^{\prime \prime }-a {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.578
15549	22024	\begin{align*} y x +x^{2}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.578
15550	26478	\begin{align*} x^{4} y^{\prime \prime }&=\left (y-y^{\prime } x \right )^{3} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✗	✓	✓	✗	1.578
15551	4086	\begin{align*} y&=y^{\prime }+\frac {{y^{\prime }}^{2}}{2} \\ \end{align*}	✓	✓	✓	✓	1.579
15552	9885	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.579
15553	20800	\begin{align*} y^{\prime \prime } x +\left (x -1\right ) y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✗	1.579
15554	26	\begin{align*} y^{\prime }&=x^{2}-y-2 \\ \end{align*}	✓	✓	✓	✓	1.580
15555	20843	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.580
15556	17197	\begin{align*} y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.581
15557	20562	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.582
15558	185	\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.583
15559	10438	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x^{m +1} \\ \end{align*}	✓	✓	✓	✗	1.583
15560	24288	\begin{align*} 1+4 y x -4 x^{2} y+\left (-x^{3}+x^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	1.583
15561	25432	\begin{align*} y^{\prime }-a \left (t \right ) y&=q \\ \end{align*}	✓	✓	✓	✓	1.583
15562	19491	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.585
15563	24818	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	1.585
15564	8882	\begin{align*} x^{2} y^{\prime }+2 y x&=1 \\ \end{align*}	✓	✓	✓	✓	1.586
15565	16734	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\ \end{align*}	✓	✓	✓	✓	1.586
15566	24831	\begin{align*} 9 x {y^{\prime }}^{2}+3 y y^{\prime }+y^{8}&=0 \\ \end{align*}	✓	✓	✓	✓	1.586
15567	7215	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.587
15568	12371	\begin{align*} b x y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	1.587
15569	20556	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=a x \\ \end{align*}	✓	✓	✓	✓	1.587
15570	4897	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-a +y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.588
15571	18250	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1 \\ \end{align*}	✓	✓	✓	✓	1.588
15572	18875	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=g \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.588
15573	7898	\begin{align*} x -y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.589
15574	25296	\begin{align*} y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.589
15575	16140	\begin{align*} y^{\prime \prime }+3 y&=5 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.590
15576	4662	\begin{align*} y^{\prime }&=\cos \left (2 x \right )+\left (\sin \left (2 x \right )+y\right ) y \\ \end{align*}	✓	✓	✓	✗	1.591
15577	26365	\begin{align*} y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \\ \end{align*}	✓	✓	✓	✗	1.591
15578	81	\begin{align*} -y+y^{\prime } x&=x \\ y \left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	1.592
15579	8620	\begin{align*} y^{\prime \prime }+\frac {y}{4 x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.592
15580	12419	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}-v \left (v -1\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.592
15581	23100	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.592
15582	26541	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2&=0 \\ \end{align*}	✓	✓	✓	✓	1.592
15583	786	\begin{align*} y^{\prime }&=x^{2}-2 y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	1.593
15584	5592	\begin{align*} 4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.593
15585	13927	\begin{align*} y^{\prime \prime }+a \left (\lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.593
15586	845	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.595
15587	11687	\begin{align*} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	1.595
15588	14846	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.595
15589	20459	\begin{align*} {y^{\prime }}^{2}+y^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	1.595
15590	22765	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x^{2}-4 x +2 \\ \end{align*}	✓	✓	✓	✓	1.595
15591	24941	\begin{align*} y^{\prime }&=y-t^{2} \\ \end{align*}	✓	✓	✓	✓	1.595
15592	18521	\begin{align*} y+2 y^{\prime }&=3 t^{2} \\ \end{align*}	✓	✓	✓	✓	1.596
15593	125	\begin{align*} y^{\prime }&=y+y^{3} \\ \end{align*}	✓	✓	✓	✓	1.597
15594	12359	\begin{align*} y^{\prime \prime } x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.597
15595	5216	\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.598
15596	6708	\begin{align*} -y+2 y^{\prime } x +x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=2 x^{3} \\ \end{align*}	✗	✓	✓	✗	1.598
15597	9243	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.598
15598	138	\begin{align*} 2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.599
15599	3131	\begin{align*} y^{\prime \prime }+9 y&=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.599
15600	7571	\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	1.599