2.3.190 Problems 18901 to 19000

Table 2.923: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18901	13317	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{-\lambda \,x^{2}} y^{2}+\lambda x y+b^{2} a \\ \end{align*}	✓	✓	✓	✗	4.059
18902	22998	\begin{align*} v^{\prime }&=60 t -4 v \\ v \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.059
18903	1704	\begin{align*} 3 x^{2}+2 y+\left (2 y+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.061
18904	9927	\begin{align*} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.061
18905	7307	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	4.062
18906	4842	\begin{align*} \left (a +x \right ) y^{\prime }&=b x +y \\ \end{align*}	✓	✓	✓	✓	4.063
18907	12972	\begin{align*} a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0}&=0 \\ \end{align*}	✓	✓	✓	✗	4.064
18908	25398	\begin{align*} y^{\prime }&=a \left (t \right ) y \\ \end{align*}	✓	✓	✓	✓	4.064
18909	25821	\begin{align*} y^{\prime }&={\mathrm e}^{3 x +2 y} \\ \end{align*}	✓	✓	✓	✓	4.064
18910	2312	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.065
18911	6663	\begin{align*} -y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\cot \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	4.066
18912	7117	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	4.066
18913	14539	\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.066
18914	16359	\begin{align*} \ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.066
18915	17960	\begin{align*} \left (1+x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.066
18916	7791	\begin{align*} y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.067
18917	9932	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.067
18918	17157	\begin{align*} y^{\prime }&=\frac {1}{x +y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.067
18919	19895	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.068
18920	11571	\begin{align*} \left (x^{4}+y^{2}\right ) y^{\prime }-4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.069
18921	7359	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}+4&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.070
18922	9816	\begin{align*} {y^{\prime }}^{4}+y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✗	✗	4.070
18923	4714	\begin{align*} y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.072
18924	15058	\begin{align*} y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.072
18925	20755	\begin{align*} \left (a +x \right )^{2} y^{\prime \prime }-4 \left (a +x \right ) y^{\prime }+6 y&=x \\ \end{align*}	✓	✓	✓	✗	4.072
18926	13244	\begin{align*} y^{\prime } x&=x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m} \\ \end{align*}	✓	✓	✓	✗	4.073
18927	4116	\begin{align*} \left (x +y^{2}\right ) y^{\prime }-x^{2}+y&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.074
18928	3675	\begin{align*} y^{\prime }&=2 x \left (x +y\right )^{2}-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.075
18929	15875	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	4.076
18930	6877	\begin{align*} {y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1&=0 \\ \end{align*}	✓	✓	✓	✓	4.077
18931	20216	\begin{align*} y^{\prime } x +x +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.077
18932	13747	\begin{align*} y^{\prime \prime } x +\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	4.078
18933	4768	\begin{align*} y^{\prime } x +\left (b x +a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.080
18934	9933	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+5 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.081
18935	4635	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \left (1-\tan \left (x \right )^{2}+y\right ) \\ \end{align*}	✓	✓	✓	✗	4.082
18936	13229	\begin{align*} y^{\prime }&=y^{2}+a \,x^{n} y+a \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	4.082
18937	16924	\begin{align*} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	4.082
18938	25465	\begin{align*} y^{\prime }&=\sin \left (t \right ) y+Q \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.082
18939	24953	\begin{align*} y^{\prime }&=t y^{2}-y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	4.083
18940	20960	\begin{align*} x^{\prime }&=x-\frac {\mu x}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	4.084
18941	5452	\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.085
18942	10055	\begin{align*} a y^{2} y^{\prime \prime }+b y^{2}&=c \\ \end{align*}	✓	✓	✓	✗	4.085
18943	16318	\begin{align*} 1+3 y^{2} x^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.085
18944	5540	\begin{align*} x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.086
18945	11530	\begin{align*} y y^{\prime } x -y^{2}+a \,x^{3} \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.087
18946	20736	\begin{align*} \sin \left (y^{\prime } x \right ) \cos \left (y\right )&=\cos \left (y^{\prime } x \right ) \sin \left (y\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	4.088
18947	15763	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=-3 y_{1}+2 y_{3} \\ y_{3}^{\prime }&=y_{4} \\ y_{4}^{\prime }&=2 y_{1}-5 y_{3} \\ \end{align*}	✓	✓	✓	✓	4.089
18948	7434	\begin{align*} y^{\prime }-\frac {y}{x}&=x \,{\mathrm e}^{x} \\ y \left (1\right ) &= {\mathrm e}-1 \\ \end{align*}	✓	✓	✓	✓	4.091
18949	8279	\begin{align*} y^{\prime } x +y&=\frac {1}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.091
18950	24289	\begin{align*} 3-2 y x -\left (x^{2}+\frac {1}{y^{2}}+\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.091
18951	2305	\begin{align*} \sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\ y \left (0\right ) &= \sqrt {5} \\ \end{align*}	✓	✓	✓	✓	4.092
18952	4436	\begin{align*} \sin \left (x \right ) y+\cos \left (x \right )^{2}-\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.094
18953	7365	\begin{align*} y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	4.094
18954	15528	\begin{align*} y^{\prime }&=y^{2}-4 \\ \end{align*}	✓	✓	✓	✓	4.094
18955	8381	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	4.095
18956	12204	\begin{align*} y^{\prime }&=-\frac {\left (-\frac {\ln \left (y\right )^{2}}{2 x}-\textit {\_F1} \left (x \right )\right ) y}{\ln \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	4.095
18957	19265	\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.096
18958	84	\begin{align*} y^{\prime } x +3 y&=2 x^{5} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.098
18959	4978	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{3}+y \\ \end{align*}	✓	✓	✓	✓	4.098
18960	25501	\begin{align*} y^{\prime }&={\mathrm e}^{t} y \\ \end{align*}	✓	✓	✓	✓	4.098
18961	5453	\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.100
18962	7226	\begin{align*} y^{\prime }-y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.101
18963	16910	\begin{align*} \left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	4.101
18964	25499	\begin{align*} y^{\prime }&=t y+t +y+1 \\ \end{align*}	✓	✓	✓	✓	4.101
18965	15380	\begin{align*} y-3 x^{2}-\left (4 y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.102
18966	19348	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\ \end{align*}	✓	✓	✓	✓	4.103
18967	6841	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.104
18968	21353	\begin{align*} x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.104
18969	21683	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.104
18970	3017	\begin{align*} 2 y x +y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.106
18971	6817	\begin{align*} y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.107
18972	19946	\begin{align*} y^{\prime }+\frac {4 x y}{x^{2}+1}&=\frac {1}{\left (x^{2}+1\right )^{3}} \\ \end{align*}	✓	✓	✓	✓	4.107
18973	3683	\begin{align*} y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	4.108
18974	4625	\begin{align*} y^{\prime }&=\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	4.108
18975	10072	\begin{align*} y^{\prime }&=2 y \left (x \sqrt {y}-1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.108
18976	14699	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.108
18977	22003	\begin{align*} x^{2}+1+\frac {y^{\prime }}{y}&=0 \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.108
18978	3552	\begin{align*} x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\ \end{align*}	✓	✓	✓	✓	4.109
18979	19741	\begin{align*} n^{\prime }&=\left (n^{2}+1\right ) x \\ \end{align*}	✓	✓	✓	✓	4.109
18980	24261	\begin{align*} \left (3+2 x \right ) y^{\prime }&=y+\sqrt {3+2 x} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.109
18981	18597	\begin{align*} x \left (x -1\right ) y^{\prime }&=y \left (1+y\right ) \\ \end{align*}	✓	✓	✓	✓	4.111
18982	17783	\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.113
18983	15805	\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	4.114
18984	1588	\begin{align*} y^{\prime }+x \left (y^{2}+y\right )&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.116
18985	17042	\begin{align*} y^{\prime } t&=y \\ \end{align*}	✓	✓	✓	✓	4.116
18986	22561	\begin{align*} u^{\prime }&=-a \left (u-100 t \right ) \\ u \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.116
18987	4256	\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.117
18988	6328	\begin{align*} y^{\prime \prime }&=f \left (x \right ) y^{2}-y^{3}+\left (f \left (x \right )-3 y\right ) y^{\prime } \\ \end{align*}	✗	✓	✗	✗	4.118
18989	16203	\begin{align*} \left (x -2\right ) y^{\prime }&=3+y \\ \end{align*}	✓	✓	✓	✓	4.119
18990	8379	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.120
18991	25474	\begin{align*} y^{\prime }&=a y-b y^{n} \\ \end{align*}	✓	✓	✓	✗	4.120
18992	7011	\begin{align*} \left (y^{2}+a \sin \left (x \right )\right ) y^{\prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.121
18993	4225	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.122
18994	9528	\begin{align*} x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.122
18995	22933	\begin{align*} z+x^{\prime }&=x \\ y^{\prime }-2 x&=y+3 t \\ z^{\prime }+4 y&=z-\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.123
18996	22772	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.124
18997	4302	\begin{align*} r y^{\prime }&=\frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \\ \end{align*}	✓	✓	✓	✓	4.125
18998	8383	\begin{align*} 2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.126
18999	17638	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.126
19000	8743	\begin{align*} \frac {2 y y^{\prime } x}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\ \end{align*}	✓	✓	✓	✗	4.128