2.3.155 Problems 15401 to 15500

Table 2.841: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15401	23003	\begin{align*} 3 x^{\prime \prime }+19 x^{\prime }-14 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.391
15402	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*}	✓	✓	✓	✓	3.392
15403	17942	\begin{align*} y^{\prime }-{\mathrm e}^{x} y&=2 x \,{\mathrm e}^{{\mathrm e}^{x}} \\ \end{align*}	✓	✓	✓	✓	3.392
15404	1298	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.395
15405	13368	\begin{align*} y^{\prime }&=y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \sin \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.395
15406	14910	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.395
15407	24389	\begin{align*} \left (2 x -1\right ) y+2 \left (x^{2}+y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.395
15408	12327	\begin{align*} b y+a x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.396
15409	4705	\begin{align*} y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\ \end{align*}	✗	✗	✗	✗	3.398
15410	16586	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=8 x^{2}-3 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.398
15411	18939	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.399
15412	24278	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	3.402
15413	3472	\begin{align*} y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.403
15414	5083	\begin{align*} \left (x -2 y+1\right ) y^{\prime }&=1+2 x -y \\ \end{align*}	✓	✓	✓	✓	3.404
15415	15647	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.404
15416	16069	\begin{align*} y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -\sqrt {2} \\ \end{align*}	✓	✓	✓	✓	3.405
15417	19267	\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.405
15418	10534	\begin{align*} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.406
15419	14718	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.407
15420	25036	\begin{align*} \left (y^{3}-t \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.407
15421	4434	\begin{align*} y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \\ \end{align*}	✓	✓	✓	✓	3.408
15422	5812	\begin{align*} \left (c \,x^{2}+b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.408
15423	21821	\begin{align*} x^{3} y^{\prime }-x^{2} y&=x^{5} y \\ \end{align*}	✓	✓	✓	✓	3.408
15424	24934	\begin{align*} y^{\prime \prime }&=6 \sin \left (3 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.408
15425	8359	\begin{align*} \left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.409
15426	15058	\begin{align*} y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.409
15427	12285	\begin{align*} y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.410
15428	3732	\begin{align*} y^{\prime \prime }+6 y&=\sin \left (x \right )^{2} \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.411
15429	10079	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\ \end{align*}	✓	✓	✓	✗	3.411
15430	13719	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	3.411
15431	15078	\begin{align*} {y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	3.411
15432	24488	\begin{align*} x^{\prime \prime }+2 b x^{\prime }+k^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= v_{0} \\ \end{align*}	✓	✓	✓	✓	3.411
15433	5044	\begin{align*} y y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	3.412
15434	14913	\begin{align*} \left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b&=0 \\ \end{align*}	✓	✓	✓	✓	3.412
15435	1151	\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.413
15436	18490	\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.413
15437	1722	\begin{align*} -y+\left (x^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.414
15438	8831	\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.414
15439	19392	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.414
15440	3426	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \\ y \left (\ln \left (2\right )\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	3.415
15441	11599	\begin{align*} \left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.417
15442	20871	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=20 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.417
15443	5258	\begin{align*} x \left (a +y\right )^{2} y^{\prime }&=b y^{2} \\ \end{align*}	✓	✓	✓	✓	3.418
15444	9886	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.418
15445	17355	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	3.419
15446	17849	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	3.419
15447	19896	\begin{align*} \left (1-x \right ) y^{\prime }-1-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.419
15448	20153	\begin{align*} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y&=0 \\ \end{align*}	✗	✗	✗	✗	3.420
15449	12063	\begin{align*} y^{\prime }&=\frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\ \end{align*}	✓	✓	✓	✗	3.421
15450	9095	\begin{align*} y^{2} y^{\prime }&=2+x \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.422
15451	16512	\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.423
15452	22767	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.423
15453	23010	\begin{align*} 12 x^{\prime \prime }-25 x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.423
15454	25738	\begin{align*} y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	3.423
15455	14472	\begin{align*} 8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime }&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✗	3.424
15456	17736	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.424
15457	21014	\begin{align*} x^{\prime }&=-t^{2} x \\ \end{align*}	✓	✓	✓	✓	3.424
15458	22366	\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.424
15459	25003	\begin{align*} t^{2} y^{\prime }&=y^{2}+t y+t^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.424
15460	723	\begin{align*} y^{\prime }&=1+x +y+y x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.425
15461	21720	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.425
15462	1575	\begin{align*} {\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right )&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.426
15463	12706	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	3.427
15464	17216	\begin{align*} {\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.427
15465	19255	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.427
15466	4714	\begin{align*} y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.428
15467	6255	\begin{align*} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.428
15468	7520	\begin{align*} 2 x -y+4+\left (x -2 y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.428
15469	14232	\begin{align*} y^{\prime }&=t^{2} \tan \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.428
15470	3281	\begin{align*} x^{\prime \prime }-k^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= v_{0} \\ \end{align*}	✓	✓	✓	✓	3.429
15471	5333	\begin{align*} y^{\prime } \sqrt {b^{2}+y^{2}}&=\sqrt {a^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.429
15472	10108	\begin{align*} y^{\prime \prime }-y x -x^{6}+64&=0 \\ \end{align*}	✓	✓	✓	✓	3.429
15473	19476	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.429
15474	1600	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.430
15475	16272	\begin{align*} y^{\prime } x&=\sqrt {x}+3 y \\ \end{align*}	✓	✓	✓	✓	3.430
15476	24323	\begin{align*} x +2 y-1+\left (2 x +4 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.432
15477	25005	\begin{align*} y^{\prime }&=\frac {y^{2}-4 t y+6 t^{2}}{t^{2}} \\ y \left (2\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.432
15478	15829	\begin{align*} y^{\prime }&=t^{2}+t^{2} y \\ \end{align*}	✓	✓	✓	✓	3.434
15479	88	\begin{align*} y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.435
15480	7865	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.435
15481	15597	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.435
15482	24801	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.435
15483	13901	\begin{align*} x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y&=0 \\ \end{align*}	✗	✗	✗	✗	3.436
15484	22761	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x&=5 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.437
15485	5186	\begin{align*} x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.438
15486	16208	\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.439
15487	2994	\begin{align*} 3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.440
15488	5863	\begin{align*} b \tan \left (x \right )^{2} y-2 \csc \left (2 x \right ) \left (1-a \sin \left (x \right )^{2}\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.440
15489	18492	\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-3 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.440
15490	7256	\begin{align*} y^{\prime }&=x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	3.443
15491	12640	\begin{align*} y^{\prime \prime }&=-\frac {b^{2} y}{\left (a^{2}+x^{2}\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	3.443
15492	1837	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=-2 x^{2} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.444
15493	4950	\begin{align*} 2 x^{2} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.444
15494	5670	\begin{align*} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.444
15495	15502	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.444
15496	17103	\begin{align*} y^{\prime }&=y^{3}+y \\ \end{align*}	✓	✓	✓	✓	3.444
15497	17463	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=t \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -{\frac {5}{16}} \\ y^{\prime }\left (0\right ) &= {\frac {9}{16}} \\ \end{align*}	✓	✓	✓	✓	3.444
15498	23056	\begin{align*} \frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	3.444
15499	15449	\begin{align*} \frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.445
15500	24275	\begin{align*} \cos \left (x \right ) y^{\prime }&=1-y-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.446