2.3.156 Problems 15501 to 15600

Table 2.843: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15501	25493	\begin{align*} y^{\prime }&=a \left (t \right ) y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.446
15502	25751	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.446
15503	7403	\begin{align*} y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.447
15504	10048	\begin{align*} y y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✗	3.447
15505	21787	\begin{align*} x^{\prime \prime }&=4 x^{3}-4 x \\ \end{align*}	✓	✓	✓	✗	3.447
15506	7792	\begin{align*} y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	3.448
15507	20978	\begin{align*} x y^{2}-y^{3}+\left (1-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.448
15508	17325	\begin{align*} t^{2}-y+\left (-t +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.449
15509	7736	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=\cos \left (x \right )-2 x \sin \left (x \right ) \\ y \left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.450
15510	12928	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.450
15511	1667	\begin{align*} y^{\prime }&=\frac {2 x +y+1}{x +2 y-4} \\ \end{align*}	✓	✓	✓	✗	3.451
15512	22097	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.451
15513	22414	\begin{align*} y^{\prime }&=\frac {x -\cos \left (x \right ) y}{y+\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	3.451
15514	1285	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.452
15515	9004	\begin{align*} x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.452
15516	5969	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.457
15517	18058	\begin{align*} x^{2}+y^{2}-y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.457
15518	12650	\begin{align*} y^{\prime \prime }&=\frac {3 y}{4 \left (x^{2}+x +1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	3.458
15519	16964	\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.459
15520	20240	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.459
15521	8801	\begin{align*} 3 {y^{\prime \prime }}^{2}-y^{\prime \prime \prime } y^{\prime }-y^{\prime \prime } {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.460
15522	14238	\begin{align*} x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t}&={\mathrm e}^{-t} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.460
15523	12076	\begin{align*} y^{\prime }&=\frac {y}{x \left (-1+y+x^{2} y^{3}+y^{4} x^{3}\right )} \\ \end{align*}	✓	✓	✓	✗	3.461
15524	15623	\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.461
15525	5825	\begin{align*} -\left (-x^{2}-x +1\right ) y-\left (2 x +1\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.462
15526	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*}	✓	✓	✓	✓	3.464
15527	2980	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y&=0 \\ y \left (0\right ) &= -6 \\ \end{align*}	✓	✓	✓	✓	3.465
15528	7004	\begin{align*} 2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.465
15529	3045	\begin{align*} y^{\prime } x&=x^{4}+4 y \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.466
15530	4426	\begin{align*} y+\left (y x -x -y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.466
15531	8433	\begin{align*} y^{\prime } x +\left (x +1\right ) y&={\mathrm e}^{-x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.467
15532	19100	\begin{align*} \frac {1}{x}-\frac {y^{2}}{\left (x -y\right )^{2}}+\left (\frac {x^{2}}{\left (x -y\right )^{2}}-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.467
15533	16382	\begin{align*} y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.468
15534	24131	\begin{align*} y x +x -\left (1+x^{2}+y^{2}+y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.468
15535	24842	\begin{align*} y {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.469
15536	9013	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (x_{0} \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.471
15537	3019	\begin{align*} r^{\prime }&=r \cot \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	3.473
15538	19367	\begin{align*} y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	3.473
15539	25096	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.474
15540	1250	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.475
15541	19461	\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.476
15542	11491	\begin{align*} y^{\prime } \sqrt {a^{2}+x^{2}}+y-\sqrt {a^{2}+x^{2}}+x&=0 \\ \end{align*}	✓	✓	✓	✓	3.477
15543	24954	\begin{align*} \left (t^{2}+3 y^{2}\right ) y^{\prime }&=-2 t y \\ \end{align*}	✓	✓	✓	✗	3.477
15544	4634	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \left (\sin \left (x \right )^{3}+y\right ) \\ \end{align*}	✓	✓	✓	✗	3.479
15545	24276	\begin{align*} \sin \left (\theta \right ) r^{\prime }&=-1-2 r \cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	3.479
15546	24906	\begin{align*} 3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	3.479
15547	8543	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.480
15548	16561	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +10 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.480
15549	19710	\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 \\ \end{align*}	✓	✓	✓	✓	3.480
15550	24274	\begin{align*} y^{\prime }-\cos \left (x \right )&=\tan \left (y\right )^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.480
15551	797	\begin{align*} 3 y+y^{4} x^{3}+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.481
15552	4354	\begin{align*} y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.481
15553	8311	\begin{align*} y^{\prime }&=\frac {1}{y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.482
15554	23984	\begin{align*} y^{\prime \prime }+y^{\prime }&=4 \\ \end{align*}	✓	✓	✓	✓	3.483
15555	3959	\begin{align*} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.484
15556	17167	\begin{align*} y^{\prime } t +y&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= \frac {4}{\pi } \\ \end{align*}	✓	✓	✓	✓	3.484
15557	22595	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	3.484
15558	4109	\begin{align*} 2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right )&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\ \end{align*}	✓	✓	✓	✓	3.485
15559	17844	\begin{align*} y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	3.485
15560	23969	\begin{align*} y^{\prime }+\frac {3 y}{2}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	3.485
15561	4764	\begin{align*} y^{\prime } x&=a \,x^{2}+b y \\ \end{align*}	✓	✓	✓	✓	3.487
15562	23384	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.487
15563	24320	\begin{align*} y^{\prime }&=\sin \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	3.488
15564	4999	\begin{align*} x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	3.490
15565	11569	\begin{align*} \left (x^{2}+y^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	3.491
15566	7367	\begin{align*} y^{\prime \prime }&=-4 y \\ \end{align*}	✓	✓	✓	✓	3.492
15567	20788	\begin{align*} y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y&=\cos \left (x \right ) x \\ \end{align*}	✗	✓	✗	✗	3.492
15568	11784	\begin{align*} 3 y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.493
15569	14011	\begin{align*} y^{\prime } x -y+2 x^{2} y-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.493
15570	14233	\begin{align*} x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	3.493
15571	14495	\begin{align*} y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	3.495
15572	15599	\begin{align*} y^{\prime }&=\frac {y}{x}+\sin \left (x^{2}\right ) \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.496
15573	2849	\begin{align*} y+3+\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.497
15574	10034	\begin{align*} \left (t^{2}+9\right ) y^{\prime \prime }+2 y^{\prime } t&=0 \\ y \left (3\right ) &= 2 \pi \\ y^{\prime }\left (3\right ) &= {\frac {2}{3}} \\ \end{align*}	✓	✓	✓	✓	3.497
15575	25468	\begin{align*} y^{\prime }&=\frac {y}{1+t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.497
15576	1275	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.498
15577	14925	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.498
15578	22560	\begin{align*} r^{\prime }&=\frac {r \left (1+\ln \left (t \right )\right )}{t \left (1+\ln \left (r\right )\right )} \\ \end{align*}	✓	✓	✓	✓	3.498
15579	22512	\begin{align*} 3-y+2 y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.499
15580	8351	\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.500
15581	16321	\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.500
15582	12693	\begin{align*} y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	3.501
15583	8343	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.502
15584	21761	\begin{align*} 2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.502
15585	23470	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.502
15586	10006	\begin{align*} y^{\prime }+\frac {y}{3}&=\frac {\left (1-2 x \right ) y^{4}}{3} \\ \end{align*}	✓	✓	✓	✓	3.503
15587	2553	\begin{align*} t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y&=0 \\ \end{align*}	✓	✓	✓	✓	3.504
15588	13690	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.504
15589	4852	\begin{align*} 2 y^{\prime } x&=y \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.505
15590	7321	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x -\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	3.505
15591	3258	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.506
15592	10124	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	3.506
15593	8429	\begin{align*} y^{\prime } x +2 y&=3 \\ \end{align*}	✓	✓	✓	✓	3.507
15594	8663	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.507
15595	2870	\begin{align*} x +y&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	3.510
15596	5276	\begin{align*} \left (1-y^{2} x^{2}\right ) y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	3.510
15597	5791	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.510
15598	2843	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.511
15599	12253	\begin{align*} y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x} \\ \end{align*}	✓	✓	✓	✓	3.511
15600	12676	\begin{align*} y^{\prime \prime }&=\frac {y^{\prime }}{x \left (\ln \left (x \right )-1\right )}-\frac {y}{x^{2} \left (\ln \left (x \right )-1\right )} \\ \end{align*}	✓	✓	✓	✗	3.512