2.3.181 Problems 18001 to 18100

Table 2.911: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18001	24885	\begin{align*} y^{\prime \prime }+{\mathrm e}^{-2 y}&=0 \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	3.435
18002	13722	\begin{align*} y^{\prime \prime } x +\frac {y^{\prime }}{2}+a y&=0 \\ \end{align*}	✓	✓	✓	✓	3.437
18003	17796	\begin{align*} 4 x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.437
18004	19084	\begin{align*} y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.437
18005	5137	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.438
18006	6058	\begin{align*} -y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	3.438
18007	20968	\begin{align*} y^{\prime }&=\sqrt {y \left (1-y\right )} \\ \end{align*}	✓	✓	✓	✓	3.439
18008	699	\begin{align*} \tan \left (x \right ) y^{\prime }&=y \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	3.440
18009	24910	\begin{align*} y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.440
18010	5143	\begin{align*} x \left (a +y\right ) y^{\prime }&=y \left (B x +A \right ) \\ \end{align*}	✓	✓	✓	✓	3.441
18011	6144	\begin{align*} 8 y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.443
18012	7225	\begin{align*} \left (1+y\right ) y^{\prime }&=y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.443
18013	12909	\begin{align*} 2 \left (-x^{k}+4 x^{3}\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+a x y+b&=0 \\ \end{align*}	✗	✗	✗	✗	3.443
18014	5335	\begin{align*} \left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	3.444
18015	21481	\begin{align*} y^{\prime \prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.444
18016	8694	\begin{align*} 2 y^{\prime } x&=\left (2 x^{2}-y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	3.445
18017	3560	\begin{align*} y^{\prime }&=-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.446
18018	13944	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+c \left (a \,{\mathrm e}^{\lambda x}+b -c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.446
18019	15794	\begin{align*} y^{\prime }&=\sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.446
18020	14458	\begin{align*} y x +2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.447
18021	18716	\begin{align*} x^{\prime }&=\frac {x \sqrt {6 x-9}}{3} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.447
18022	23957	\begin{align*} y x -x&=\left (x y^{2}+x -y^{2}-1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.447
18023	1579	\begin{align*} \sin \left (x \right ) \sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.448
18024	17981	\begin{align*} x^{2}+y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.448
18025	19352	\begin{align*} y^{\prime } x +y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.448
18026	4935	\begin{align*} x \left (1-x \right ) y^{\prime }&=2 y x -2 \\ \end{align*}	✓	✓	✓	✓	3.450
18027	8510	\begin{align*} y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.451
18028	4904	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.452
18029	13726	\begin{align*} y^{\prime \prime } x +n y^{\prime }+b \,x^{-2 n +1} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.452
18030	787	\begin{align*} {\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.453
18031	6809	\begin{align*} 2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.453
18032	16247	\begin{align*} y^{\prime }-3 y^{2} x^{2}&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.453
18033	1152	\begin{align*} y^{\prime }&=\frac {2-{\mathrm e}^{x}}{3+2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.454
18034	20741	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	3.455
18035	4270	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.456
18036	6469	\begin{align*} 2 y y^{\prime \prime }&=a +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.456
18037	20743	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.456
18038	3016	\begin{align*} y^{\prime }+y \ln \left (y\right ) \tan \left (x \right )&=2 y \\ \end{align*}	✓	✓	✓	✓	3.457
18039	4631	\begin{align*} y^{\prime }+\csc \left (x \right )+2 \cot \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.457
18040	14017	\begin{align*} y^{\prime }-x^{2} y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	3.457
18041	14483	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	3.457
18042	20105	\begin{align*} \left (a +x \right )^{2} y^{\prime \prime }-4 \left (a +x \right ) y^{\prime }+6 y&=x \\ \end{align*}	✓	✓	✓	✗	3.457
18043	24198	\begin{align*} 2 x +y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.457
18044	3021	\begin{align*} 2 x^{3}-y^{3}-3 x +3 y^{\prime } y^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	3.458
18045	3045	\begin{align*} y^{\prime } x&=x^{4}+4 y \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.459
18046	1543	\begin{align*} y^{\prime } x +\left (1+\frac {1}{\ln \left (x \right )}\right ) y&=0 \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.460
18047	14558	\begin{align*} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	3.460
18048	5138	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.461
18049	8441	\begin{align*} p^{\prime }+2 t p&=p+4 t -2 \\ \end{align*}	✓	✓	✓	✓	3.461
18050	14503	\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right )^{2} \\ r \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.461
18051	15401	\begin{align*} y^{\prime \prime }&=a^{2} y \\ \end{align*}	✓	✓	✓	✓	3.461
18052	19963	\begin{align*} -y^{\prime } x +y&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.461
18053	20200	\begin{align*} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a}&=0 \\ \end{align*}	✓	✓	✓	✗	3.461
18054	23123	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.461
18055	12296	\begin{align*} y^{\prime \prime }+\left (a \,x^{2 c}+b \,x^{c -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.464
18056	14243	\begin{align*} \cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.464
18057	23914	\begin{align*} y^{\prime }-y x&=x^{3} \\ \end{align*}	✓	✓	✓	✓	3.464
18058	11743	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	3.465
18059	13002	\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.465
18060	18520	\begin{align*} y+y^{\prime }&=5 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	3.465
18061	22544	\begin{align*} \tan \left (x \right ) \sin \left (y\right )+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.465
18062	15076	\begin{align*} x^{3} x^{\prime \prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	3.466
18063	9596	\begin{align*} y^{\prime \prime } x +\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.467
18064	14497	\begin{align*} y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	3.467
18065	14530	\begin{align*} \left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.467
18066	19256	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.467
18067	1700	\begin{align*} \left (2 x -1\right ) \left (-1+y\right )+\left (2+x \right ) \left (x -3\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.468
18068	21119	\begin{align*} x^{\prime \prime }+p x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.468
18069	15562	\begin{align*} y^{\prime }&=y x +\frac {1}{x^{2}+1} \\ y \left (-5\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.470
18070	21339	\begin{align*} \sqrt {x}\, y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	3.470
18071	8119	\begin{align*} y^{\prime \prime } x -2 y^{\prime }+y&=\cos \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	3.471
18072	22437	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x \\ \end{align*}	✓	✓	✓	✓	3.471
18073	2298	\begin{align*} y \cos \left (t \right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.472
18074	5158	\begin{align*} 2 y y^{\prime } x +a +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.472
18075	11780	\begin{align*} \left (y^{2}-2 a x +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.472
18076	11897	\begin{align*} y^{\prime }&=\frac {x \left (-1+a \right ) \left (1+a \right )}{y+F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right ) a^{2}-F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right )} \\ \end{align*}	✓	✓	✓	✗	3.472
18077	22569	\begin{align*} y^{\prime } x -3 y&=x^{4} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	3.472
18078	1575	\begin{align*} {\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right )&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.473
18079	4282	\begin{align*} y+x^{2}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	3.473
18080	8782	\begin{align*} {\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.473
18081	1532	\begin{align*} y^{\prime }&=x \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.474
18082	22023	\begin{align*} x +\sin \left (y\right )+\left (x \cos \left (y\right )-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.474
18083	1822	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (-\cos \left (x \right )+\sin \left (x \right )\right ) y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	3.475
18084	5155	\begin{align*} y \left (1-x \right ) y^{\prime }+\left (1-y\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	3.475
18085	1166	\begin{align*} y \ln \left (t \right )+\left (t -3\right ) y^{\prime }&=2 t \\ \end{align*}	✓	✓	✓	✗	3.476
18086	1540	\begin{align*} y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.477
18087	4979	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=a -x^{2} y \\ \end{align*}	✓	✓	✓	✓	3.477
18088	19997	\begin{align*} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	3.477
18089	20037	\begin{align*} y^{\prime \prime }-m^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.477
18090	7319	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.478
18091	2307	\begin{align*} y^{\prime }-2 t y&=t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.480
18092	11453	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.480
18093	15601	\begin{align*} y^{\prime }&=\cot \left (x \right ) y+\sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.480
18094	19992	\begin{align*} x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +2 y^{2}-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.480
18095	1694	\begin{align*} x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.481
18096	14886	\begin{align*} x^{\prime }&=t^{3} \left (1-x\right ) \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.481
18097	24979	\begin{align*} 3 y+y^{\prime }&={\mathrm e}^{t} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.481
18098	4934	\begin{align*} x \left (1-x \right ) y^{\prime }&=2 y x +2 \\ \end{align*}	✓	✓	✓	✓	3.482
18099	18515	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.483
18100	22048	\begin{align*} 1-2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.483