2.3.125 Problems 12401 to 12500

Table 2.781: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
12401	15394	\begin{align*} y&=y^{\prime } x +y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.072
12402	18530	\begin{align*} y^{\prime }-\frac {y}{3}&=3 \cos \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	2.072
12403	16402	\begin{align*} 3 y y^{\prime \prime }&=2 {y^{\prime }}^{2} \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	2.073
12404	17136	\begin{align*} y^{\prime }&=12+4 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.073
12405	11709	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	2.074
12406	18536	\begin{align*} \frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.074
12407	18791	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{3}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{3}\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	2.074
12408	22986	\begin{align*} y^{\prime }-\sin \left (x \right ) y&=\sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.074
12409	20265	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.075
12410	22949	\begin{align*} 1+y^{2}&=\left (x^{2}+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.075
12411	24914	\begin{align*} y^{\prime }&=\frac {y^{2}-4 t y+6 t^{2}}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	2.075
12412	8317	\begin{align*} y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.076
12413	10080	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -2 x&=0 \\ \end{align*}	✓	✓	✓	✗	2.076
12414	15783	\begin{align*} y^{\prime }&=\frac {t}{y+t^{2} y} \\ \end{align*}	✓	✓	✓	✓	2.076
12415	7129	\begin{align*} r^{\prime \prime }&=\frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \\ \end{align*}	✓	✓	✓	✓	2.077
12416	10136	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.077
12417	12324	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y-{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	2.077
12418	20819	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.077
12419	21406	\begin{align*} y^{\prime }&=2 y x -x \\ \end{align*}	✓	✓	✓	✓	2.077
12420	5159	\begin{align*} 2 y y^{\prime } x&=a x +y^{2} \\ \end{align*}	✓	✓	✓	✓	2.078
12421	15788	\begin{align*} y^{\prime }&=\frac {4 t}{1+3 y^{2}} \\ \end{align*}	✓	✓	✓	✗	2.078
12422	19687	\begin{align*} t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	2.079
12423	20462	\begin{align*} x {y^{\prime }}^{2}-\left (x -a \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.079
12424	22081	\begin{align*} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }+\left (x +1\right ) y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.079
12425	8641	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.080
12426	4521	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.081
12427	5848	\begin{align*} 3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.081
12428	8452	\begin{align*} \left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.081
12429	13724	\begin{align*} b x y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	2.081
12430	15359	\begin{align*} x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.081
12431	16222	\begin{align*} y^{\prime } \cos \left (y\right )&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.081
12432	21497	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.081
12433	14219	\begin{align*} x^{\prime }&=\frac {2 x}{1+t} \\ \end{align*}	✓	✓	✓	✓	2.082
12434	22095	\begin{align*} y^{\prime \prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.082
12435	2769	\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }&=-4 x_{2}-x_{3}+t \\ x_{3}^{\prime }&=5 x_{2}+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.083
12436	3136	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.083
12437	825	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.084
12438	16079	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.084
12439	12255	\begin{align*} y^{\prime }&=y^{3}+y^{2} x^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \\ \end{align*}	✓	✓	✓	✓	2.085
12440	4770	\begin{align*} y^{\prime } x&=a x -\left (-b \,x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.086
12441	13928	\begin{align*} y^{\prime \prime }-\left (a^{2} {\mathrm e}^{2 x}+a \left (2 b +1\right ) {\mathrm e}^{x}+b^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.086
12442	2497	\begin{align*} \cos \left (y\right ) y^{\prime }&=-\frac {t \sin \left (y\right )}{t^{2}+1} \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	2.087
12443	5132	\begin{align*} y y^{\prime } x&=\left (x^{2}+1\right ) \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.087
12444	21584	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) {\mathrm e}^{x} x \\ \end{align*}	✓	✓	✓	✓	2.087
12445	22598	\begin{align*} y^{\prime }&=\tan \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	2.087
12446	23295	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.088
12447	24983	\begin{align*} y^{\prime } t +m y&=t \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.088
12448	1146	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.089
12449	16492	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.089
12450	21407	\begin{align*} y^{\prime }+\left (b x +a \right ) y&=f \left (x \right ) \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	2.090
12451	7732	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=y x +1 \\ \end{align*}	✓	✓	✓	✓	2.091
12452	15369	\begin{align*} y^{\prime }-\frac {n y}{x}&={\mathrm e}^{x} x^{n} \\ \end{align*}	✓	✓	✓	✓	2.091
12453	17105	\begin{align*} y^{\prime }&=y^{3}-y \\ \end{align*}	✓	✓	✓	✓	2.091
12454	3026	\begin{align*} y^{\prime }+x +\cot \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.092
12455	5123	\begin{align*} y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.092
12456	16228	\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}	✓	✓	✓	✓	2.092
12457	14274	\begin{align*} t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.093
12458	7155	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.094
12459	22306	\begin{align*} x^{\prime \prime }&=t^{2}-4 t +8 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.094
12460	8765	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=2 x \,{\mathrm e}^{x}-1 \\ \end{align*}	✓	✓	✓	✗	2.095
12461	15538	\begin{align*} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.095
12462	16288	\begin{align*} y^{\prime }&=1+\left (-x +y\right )^{2} \\ y \left (0\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	2.095
12463	16422	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=6 \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.095
12464	19665	\begin{align*} x^{\prime }&=x^{2}-3 x+2 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.095
12465	2486	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=t \\ y \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	2.096
12466	9784	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.096
12467	14254	\begin{align*} x^{\prime }+\frac {5 x}{t}&=1+t \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.096
12468	4754	\begin{align*} y^{\prime } x&=1+x^{3}+y \\ \end{align*}	✓	✓	✓	✓	2.097
12469	15936	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	2.097
12470	4232	\begin{align*} \left (1-x \right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	2.098
12471	14192	\begin{align*} x^{\prime }&=\frac {2 x}{t} \\ \end{align*}	✓	✓	✓	✓	2.098
12472	14921	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=0 \\ y \left (0\right ) &= 13 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.098
12473	8278	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.099
12474	8417	\begin{align*} \left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x&=0 \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.099
12475	6004	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.100
12476	25498	\begin{align*} y^{\prime }&={\mathrm e}^{y+t} \\ \end{align*}	✓	✓	✓	✓	2.100
12477	4616	\begin{align*} y^{\prime }&=x \left ({\mathrm e}^{-x^{2}}+a y\right ) \\ \end{align*}	✓	✓	✓	✓	2.102
12478	4976	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\ \end{align*}	✓	✓	✓	✓	2.102
12479	12416	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.102
12480	14842	\begin{align*} x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x&=0 \\ \end{align*}	✗	✓	✓	✗	2.102
12481	5761	\begin{align*} \left (a +b \,{\mathrm e}^{x}+c \,{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.103
12482	13990	\begin{align*} \left (x^{3}+x \right ) y^{\prime }+4 x^{2} y&=2 \\ \end{align*}	✓	✓	✓	✓	2.103
12483	10104	\begin{align*} y^{\prime \prime }-8 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	2.104
12484	16213	\begin{align*} y^{\prime }+y x&=4 x \\ \end{align*}	✓	✓	✓	✓	2.104
12485	6837	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	2.105
12486	7954	\begin{align*} y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.105
12487	21493	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.105
12488	15484	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.106
12489	18357	\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	2.106
12490	25108	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.106
12491	4985	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=x -\left (5 x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✓	2.107
12492	16282	\begin{align*} y^{\prime }+6 y x&=\sin \left (x \right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.107
12493	18099	\begin{align*} 2 y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\ y \left (1\right ) &= \frac {\sqrt {2}}{5} \\ y^{\prime }\left (1\right ) &= \frac {\sqrt {2}}{2} \\ \end{align*}	✓	✓	✓	✓	2.108
12494	13689	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.109
12495	15542	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	2.110
12496	16090	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.110
12497	24821	\begin{align*} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✗	✗	2.110
12498	720	\begin{align*} \left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.111
12499	2409	\begin{align*} y^{\prime \prime }+\frac {t^{2} y}{4}&=f \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✗	2.111
12500	5267	\begin{align*} \left (1-4 x +3 x y^{2}\right ) y^{\prime }&=\left (2-y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	2.111