2.3.181 Problems 18001 to 18100

Table 2.905: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18001	688	\begin{align*} y y^{\prime }&=x \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.372
18002	23104	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.372
18003	11559	\begin{align*} 2 x^{3}+y y^{\prime }+3 y^{2} x^{2}+7&=0 \\ \end{align*}	✓	✓	✓	✓	3.373
18004	4115	\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.374
18005	4603	\begin{align*} y^{\prime \prime } x -2 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.374
18006	12497	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {\left (n +1\right ) \operatorname {LegendreP}\left (n +1, x\right )-\left (n +1\right ) x \operatorname {LegendreP}\left (n , x\right )}{x^{2}-1}&=0 \\ \end{align*}	✗	✓	✓	✗	3.374
18007	22073	\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.374
18008	19084	\begin{align*} y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.375
18009	11463	\begin{align*} 2 x^{2} y^{\prime }-2 y^{2}-3 y x +2 a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✗	3.376
18010	13219	\begin{align*} x^{2} y^{\prime }&=y^{2} x^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right ) \\ \end{align*}	✓	✓	✓	✗	3.378
18011	1138	\begin{align*} y^{\prime }&=\frac {1-2 x}{y} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.379
18012	3525	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.379
18013	7418	\begin{align*} x^{2} y^{\prime }+\sin \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.379
18014	15864	\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	3.379
18015	19369	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	3.380
18016	5602	\begin{align*} 4 y^{2} {y^{\prime }}^{2} x^{2}&=\left (x^{2}+y^{2}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.381
18017	8858	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.381
18018	13301	\begin{align*} y^{\prime }&=y^{2}+a x \,{\mathrm e}^{\lambda x} y+a \,{\mathrm e}^{\lambda x} \\ \end{align*}	✓	✓	✓	✗	3.381
18019	1152	\begin{align*} y^{\prime }&=\frac {2-{\mathrm e}^{x}}{3+2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.382
18020	10113	\begin{align*} y^{\prime \prime }-x^{2} y-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.382
18021	14434	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.382
18022	22068	\begin{align*} y^{\prime }+x^{2} y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.382
18023	24251	\begin{align*} 2 x \left (-x^{2}+y\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.382
18024	13945	\begin{align*} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	3.383
18025	1166	\begin{align*} y \ln \left (t \right )+\left (t -3\right ) y^{\prime }&=2 t \\ \end{align*}	✓	✓	✓	✗	3.384
18026	11802	\begin{align*} \left (x^{2}+y^{2}\right ) f \left (\frac {x}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+y^{\prime } x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.386
18027	1542	\begin{align*} y^{\prime }+\frac {\left (x +1\right ) y}{x}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.388
18028	9769	\begin{align*} 2 a y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.389
18029	22000	\begin{align*} x +\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.389
18030	2075	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.390
18031	4735	\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}	✓	✓	✓	✓	3.391
18032	8371	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.391
18033	16269	\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}	✓	✓	✓	✓	3.391
18034	10127	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	3.392
18035	19302	\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.392
18036	23385	\begin{align*} x^{2} y^{\prime \prime }+\frac {7 y^{\prime } x}{2}-\frac {3 y}{2}&=0 \\ y \left (-4\right ) &= 1 \\ y^{\prime }\left (-4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.392
18037	15776	\begin{align*} y^{\prime }&=t^{4} y \\ \end{align*}	✓	✓	✓	✓	3.393
18038	1522	\begin{align*} 2 y^{\prime }+x \left (-1+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.394
18039	8346	\begin{align*} y \ln \left (x \right ) y^{\prime }&=\frac {\left (1+y\right )^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.394
18040	14215	\begin{align*} x^{\prime }&=a x+b \\ \end{align*}	✓	✓	✓	✓	3.394
18041	19267	\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.394
18042	19723	\begin{align*} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	3.394
18043	2322	\begin{align*} t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.395
18044	13657	\begin{align*} y^{\prime }&=-y^{3}+3 a^{2} {\mathrm e}^{2 \lambda x} y-2 a^{3} {\mathrm e}^{3 \lambda x}+a \lambda \,{\mathrm e}^{\lambda x} \\ \end{align*}	✗	✓	✓	✗	3.396
18045	16328	\begin{align*} 2 x \left (1+y\right )-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.397
18046	17154	\begin{align*} y^{\prime }+2 \cot \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.398
18047	10315	\begin{align*} {y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \\ \end{align*}	✓	✓	✓	✓	3.399
18048	25039	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.400
18049	7468	\begin{align*} {\mathrm e}^{t} x+1+\left ({\mathrm e}^{t}-1\right ) x^{\prime }&=0 \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.401
18050	6991	\begin{align*} y^{\prime } \cos \left (y\right )+\sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.402
18051	11545	\begin{align*} \left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.402
18052	6840	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	3.403
18053	2321	\begin{align*} \cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.405
18054	6554	\begin{align*} \operatorname {a2} x \left (1-y\right ) y^{2}+\operatorname {a3} \,x^{3} y^{2} \left (1+y\right )+\left (1-y\right )^{3} \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+2 x \left (1-y\right ) y y^{\prime }-x^{2} \left (1-3 y\right ) {y^{\prime }}^{2}+2 x^{2} \left (1-y\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	3.405
18055	6457	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.406
18056	9191	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	3.406
18057	15803	\begin{align*} x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\ x \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.406
18058	5967	\begin{align*} x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.408
18059	9006	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	3.410
18060	5666	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.411
18061	16228	\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}	✓	✓	✓	✓	3.411
18062	18849	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.411
18063	53	\begin{align*} y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.412
18064	1530	\begin{align*} y^{\prime }&=\cos \left (x \right )-\tan \left (x \right ) y \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi \sqrt {2}}{8} \\ \end{align*}	✓	✓	✓	✓	3.412
18065	21553	\begin{align*} y^{\prime \prime } x +y^{\prime }-\frac {4 y}{x}&=x^{3}+x \\ \end{align*}	✓	✓	✓	✗	3.412
18066	1848	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.413
18067	4968	\begin{align*} x^{3} y^{\prime }&=3-x^{2}+x^{2} y \\ \end{align*}	✓	✓	✓	✓	3.414
18068	22334	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.414
18069	2821	\begin{align*} z^{\prime \prime }+{\mathrm e}^{z^{2}}&=1 \\ \end{align*}	✓	✓	✓	✗	3.415
18070	2962	\begin{align*} y x^{\prime }+\left (1+y \right ) x&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	3.416
18071	25795	\begin{align*} y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.416
18072	17000	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.417
18073	22011	\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.417
18074	1104	\begin{align*} 2 t y+y^{\prime }&=2 t \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.418
18075	15789	\begin{align*} v^{\prime }&=t^{2} v-2-2 v+t^{2} \\ \end{align*}	✓	✓	✓	✓	3.418
18076	22757	\begin{align*} x^{2} y^{\prime \prime }+y&=16 \sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	3.418
18077	9091	\begin{align*} x y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.419
18078	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*}	✗	✗	✗	✗	3.419
18079	14045	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	3.420
18080	24236	\begin{align*} 3 y x +3 y-4+\left (x +1\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.420
18081	16255	\begin{align*} \left (-1+y^{2}\right ) y^{\prime }&=4 y x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.421
18082	781	\begin{align*} x^{2} y^{\prime }&=y x +3 y^{2} \\ \end{align*}	✓	✓	✓	✓	3.424
18083	4674	\begin{align*} y^{\prime }&=1+a \left (x -y\right ) y \\ \end{align*}	✓	✓	✓	✗	3.425
18084	9788	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.425
18085	21379	\begin{align*} 3 x \left (y x -2\right )+\left (x^{3}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.425
18086	8301	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.426
18087	1265	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{4}} \\ \end{align*}	✓	✓	✓	✓	3.427
18088	11596	\begin{align*} \left (y^{2} x^{2}+x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.427
18089	19747	\begin{align*} v^{\prime }+2 u v&=2 u \\ \end{align*}	✓	✓	✓	✓	3.428
18090	25018	\begin{align*} 2 y y^{\prime }&=y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	3.428
18091	2983	\begin{align*} \cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x}&=0 \\ \end{align*}	✓	✓	✓	✓	3.430
18092	20410	\begin{align*} x&=y+a \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.430
18093	1853	\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.431
18094	2070	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.431
18095	6976	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	3.431
18096	7137	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.431
18097	20979	\begin{align*} \left (y x +1\right ) y&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	3.431
18098	14218	\begin{align*} y^{\prime }&=r \left (a -y\right ) \\ \end{align*}	✓	✓	✓	✓	3.432
18099	17029	\begin{align*} 2 y+y^{\prime }&=x^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.432
18100	9182	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.434