2.3.181 Problems 18001 to 18100

Table 2.893: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18001	5616	\begin{align*} y^{\prime }+{y^{\prime }}^{3}&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✗	5.231
18002	9215	\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.231
18003	16569	\begin{align*} 3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.232
18004	16570	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	5.233
18005	21030	\begin{align*} x^{\prime }&=x^{2} \\ x \left (t_{0} \right ) &= a \\ \end{align*}	✓	✓	✓	✓	5.233
18006	21070	\begin{align*} y-x^{{1}/{3}}+\left (x +y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.233
18007	22537	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {y}{x}}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✗	5.233
18008	24222	\begin{align*} x^{4} y^{\prime }&=-x^{3} y-\csc \left (y x \right ) \\ \end{align*}	✓	✓	✓	✗	5.236
18009	3002	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=x \left (-x^{2}+1\right ) \sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✓	✓	✗	5.237
18010	12091	\begin{align*} y^{\prime }&=\frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \\ \end{align*}	✓	✓	✓	✗	5.237
18011	4628	\begin{align*} y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\ \end{align*}	✓	✓	✓	✓	5.238
18012	7573	\begin{align*} 2 y^{\prime \prime }+18 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.239
18013	17350	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.240
18014	21989	\begin{align*} y^{\prime }&=-\frac {2 y}{x} \\ \end{align*}	✓	✓	✓	✓	5.240
18015	25828	\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	5.241
18016	3464	\begin{align*} \left (y^{3}+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	5.244
18017	4813	\begin{align*} y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.244
18018	22021	\begin{align*} y^{\prime }&=\frac {x^{4}+3 y^{2} x^{2}+y^{4}}{x^{3} y} \\ \end{align*}	✓	✓	✓	✗	5.244
18019	7809	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	5.245
18020	25111	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	5.245
18021	2944	\begin{align*} \left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.246
18022	25105	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.246
18023	4887	\begin{align*} x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\ \end{align*}	✗	✓	✓	✗	5.247
18024	5833	\begin{align*} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.248
18025	19401	\begin{align*} \frac {3 y^{2}}{x^{2}+3 x}+\left (2 y \ln \left (\frac {5 x}{x +3}\right )+3 \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.250
18026	21571	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.250
18027	8832	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	5.251
18028	22373	\begin{align*} r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\ r \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.252
18029	6024	\begin{align*} \left (b +c \,x^{2 k}\right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.253
18030	17955	\begin{align*} \left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime }&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	5.253
18031	12008	\begin{align*} y^{\prime }&=-\frac {a b y-b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )} \\ \end{align*}	✓	✓	✓	✗	5.254
18032	19910	\begin{align*} \left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✗	5.254
18033	23108	\begin{align*} m s^{\prime \prime }&=\frac {g \,t^{2}}{2} \\ \end{align*}	✓	✓	✓	✓	5.254
18034	516	\begin{align*} y^{\prime \prime } x -y^{\prime }+36 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.256
18035	5899	\begin{align*} a \,x^{2} y+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.256
18036	5920	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	5.259
18037	11330	\begin{align*} y^{\prime }+x y^{2}-x^{3} y-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.259
18038	15625	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.259
18039	1153	\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.261
18040	5419	\begin{align*} {y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	5.263
18041	8367	\begin{align*} x \sinh \left (y\right ) y^{\prime }&=\cosh \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.263
18042	18936	\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.263
18043	13965	\begin{align*} \left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+\left (n \,{\mathrm e}^{\lambda x}+m \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.265
18044	16608	\begin{align*} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{\frac {x}{2}} \\ \end{align*}	✓	✓	✓	✓	5.265
18045	24225	\begin{align*} x \left (x^{2}-y^{2}-x \right )-y \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.266
18046	23097	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.268
18047	24374	\begin{align*} 4 y^{2}+10 y x -4 y+8+x \left (2 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.269
18048	110	\begin{align*} \left (x +2 y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	5.270
18049	5919	\begin{align*} -\left (1-x \right ) y+\left (1-2 x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	5.271
18050	21494	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.271
18051	22632	\begin{align*} i^{\prime \prime }-4 i^{\prime }+2 i&=0 \\ \end{align*}	✓	✓	✓	✓	5.271
18052	849	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.273
18053	9123	\begin{align*} y^{\prime } x&=2 x^{2} y+y \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.274
18054	23930	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.274
18055	17941	\begin{align*} \left (\frac {{\mathrm e}^{-y^{2}}}{2}-y x \right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	5.276
18056	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*}	✗	✓	✓	✗	5.277
18057	11752	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x -9 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.278
18058	19268	\begin{align*} 3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\ \end{align*}	✓	✓	✓	✓	5.278
18059	20607	\begin{align*} \left (-x +3\right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	5.279
18060	22592	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{y} \\ \end{align*}	✓	✓	✓	✓	5.279
18061	5133	\begin{align*} y y^{\prime } x +x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.280
18062	8467	\begin{align*} y^{\prime }-\sin \left (x^{2}\right ) y&=0 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	5.282
18063	11898	\begin{align*} y^{\prime }&=\frac {y}{x \left (-1+F \left (y x \right ) y\right )} \\ \end{align*}	✓	✓	✓	✗	5.282
18064	7413	\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	5.283
18065	24900	\begin{align*} y^{\prime \prime } x&=y^{\prime } \left (2-3 y^{\prime } x \right ) \\ \end{align*}	✓	✓	✓	✓	5.283
18066	9792	\begin{align*} \left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\ \end{align*}	✓	✓	✓	✗	5.285
18067	4352	\begin{align*} 2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.286
18068	8292	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.286
18069	9581	\begin{align*} y^{\prime \prime } x +y^{\prime }-7 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.287
18070	11497	\begin{align*} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	5.287
18071	9054	\begin{align*} y^{\prime } x +y&=y^{\prime } \sqrt {1-y^{2} x^{2}} \\ \end{align*}	✓	✓	✓	✗	5.289
18072	20250	\begin{align*} x +y+1-\left (2 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.290
18073	16146	\begin{align*} y^{\prime \prime }+y^{\prime }+8 y&=\left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	5.292
18074	17238	\begin{align*} t^{2} y+t^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.292
18075	19825	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.292
18076	10149	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x \\ \end{align*}	✓	✓	✓	✓	5.293
18077	25822	\begin{align*} y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\ \end{align*}	✓	✓	✓	✓	5.293
18078	17741	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.294
18079	23213	\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	5.294
18080	8381	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	5.296
18081	114	\begin{align*} y y^{\prime } x&=x^{2}+3 y^{2} \\ \end{align*}	✓	✓	✓	✓	5.297
18082	5031	\begin{align*} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.298
18083	8753	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.298
18084	10404	\begin{align*} y {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.299
18085	5074	\begin{align*} \left (a +b x +y\right ) y^{\prime }+a -b x -y&=0 \\ \end{align*}	✓	✓	✓	✓	5.301
18086	7625	\begin{align*} \left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.308
18087	20243	\begin{align*} \left (2 x +2 y+1\right ) y^{\prime }&=x +y+1 \\ \end{align*}	✓	✓	✓	✓	5.309
18088	18728	\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.311
18089	7928	\begin{align*} \left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.312
18090	18576	\begin{align*} 2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.312
18091	20590	\begin{align*} y^{\prime \prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.312
18092	5947	\begin{align*} -y-2 y^{\prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.313
18093	9014	\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}	✓	✓	✓	✓	5.313
18094	5905	\begin{align*} b y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	5.314
18095	24138	\begin{align*} 1+\ln \left (x \right )+\left (1+\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.314
18096	7291	\begin{align*} y^{\prime \prime }+16 y&=16 \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	5.315
18097	22648	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	5.315
18098	14561	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.316
18099	17850	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\ \end{align*}	✓	✓	✓	✓	5.316
18100	18871	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \\ \end{align*}	✓	✓	✓	✗	5.316