2.3.190 Problems 18901 to 19000

Table 2.929: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18901	7539	\begin{align*} y^{\prime }+\tan \left (x \right ) y+\sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.984
18902	5471	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✗	✓	3.985
18903	23946	\begin{align*} y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.985
18904	2540	\begin{align*} y^{\prime }&={\mathrm e}^{t} y^{2}-2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.986
18905	19086	\begin{align*} x -y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.986
18906	11446	\begin{align*} x^{2} y^{\prime }+y^{3} a \,x^{2}+b y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	3.987
18907	20302	\begin{align*} \ln \left (y\right ) y+y^{\prime } x&=y x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	3.987
18908	8304	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	3.989
18909	11764	\begin{align*} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	3.991
18910	5881	\begin{align*} a k \,x^{-1+k} y+2 a \,x^{k} y^{\prime }+2 y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.992
18911	4190	\begin{align*} y^{\prime }-y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	3.993
18912	17266	\begin{align*} \sqrt {t^{2}+1}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.994
18913	11563	\begin{align*} f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.995
18914	12148	\begin{align*} y^{\prime }&=2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6} \\ \end{align*}	✓	✓	✓	✗	3.995
18915	22375	\begin{align*} x^{3} {\mathrm e}^{2 x^{2}+3 y^{2}}-y^{3} {\mathrm e}^{-x^{2}-2 y^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.995
18916	5132	\begin{align*} y y^{\prime } x&=\left (x^{2}+1\right ) \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.996
18917	16240	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.997
18918	23158	\begin{align*} y^{\prime } x +6 y&=1+3 x \\ \end{align*}	✓	✓	✓	✓	3.997
18919	4622	\begin{align*} y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}+\cos \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.999
18920	23174	\begin{align*} \left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \\ y \left (-1\right ) &= 16 \\ \end{align*}	✓	✓	✓	✓	3.999
18921	24260	\begin{align*} \left (a +x \right ) y^{\prime }&=b x +y \\ \end{align*}	✓	✓	✓	✓	3.999
18922	17316	\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	4.000
18923	20755	\begin{align*} \left (a +x \right )^{2} y^{\prime \prime }-4 \left (a +x \right ) y^{\prime }+6 y&=x \\ \end{align*}	✓	✓	✓	✗	4.000
18924	3430	\begin{align*} y^{\prime }&=\frac {y}{t} \\ \end{align*}	✓	✓	✓	✓	4.002
18925	4032	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.003
18926	19079	\begin{align*} \cos \left (x \right ) y^{\prime }&=\sin \left (x \right ) y+\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.003
18927	26281	\begin{align*} \left (a^{2}-x^{2}\right ) y^{\prime }+y x&=a^{2} \\ \end{align*}	✓	✓	✓	✓	4.004
18928	3971	\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.005
18929	26356	\begin{align*} y&=y^{\prime } \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	4.007
18930	15506	\begin{align*} y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.010
18931	17236	\begin{align*} -2 x -y \cos \left (y x \right )+\left (2 y-x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.010
18932	23969	\begin{align*} y^{\prime }+\frac {3 y}{2}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	4.011
18933	3444	\begin{align*} y^{\prime }&=\frac {2 t y}{t^{2}+1}+t +1 \\ \end{align*}	✓	✓	✓	✓	4.013
18934	3521	\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}	✓	✓	✓	✓	4.013
18935	7698	\begin{align*} -y+y^{\prime } x&=x^{2} \\ \end{align*}	✓	✓	✓	✓	4.013
18936	22441	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ y \left (3\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.013
18937	1606	\begin{align*} y^{\prime }-y&=\frac {\left (x +1\right ) {\mathrm e}^{4 x}}{\left ({\mathrm e}^{x}+y\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.016
18938	11841	\begin{align*} \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	4.016
18939	5484	\begin{align*} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.017
18940	21669	\begin{align*} x^{4} \left (x^{2}+1\right ) \left (x -1\right )^{2} y^{\prime \prime }+4 x^{3} \left (x -1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	4.018
18941	1143	\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.019
18942	5472	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.019
18943	18525	\begin{align*} \frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.019
18944	1698	\begin{align*} \left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left ({\mathrm e}^{x}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.020
18945	4058	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.020
18946	7481	\begin{align*} x^{4}-x +y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.020
18947	18807	\begin{align*} 2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.020
18948	14498	\begin{align*} x^{\prime }+\frac {\left (1+t \right ) x}{2 t}&=\frac {1+t}{t x} \\ \end{align*}	✓	✓	✓	✓	4.021
18949	1600	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	4.022
18950	2977	\begin{align*} y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.022
18951	9650	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=\delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.022
18952	12400	\begin{align*} 4 y^{\prime \prime } x -\left (a +x \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.022
18953	14236	\begin{align*} x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	4.023
18954	781	\begin{align*} x^{2} y^{\prime }&=y x +3 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.024
18955	7697	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	4.024
18956	15120	\begin{align*} y^{\prime } x +y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	4.024
18957	17213	\begin{align*} 2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.024
18958	25857	\begin{align*} x^{3}+2 y+\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.024
18959	8357	\begin{align*} y^{\prime }&=\frac {y x +2 y-x -2}{y x -3 y+x -3} \\ \end{align*}	✓	✓	✓	✓	4.025
18960	61	\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.026
18961	6003	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=a -x +x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.026
18962	7402	\begin{align*} y^{\prime }&=2 t \cos \left (y\right )^{2} \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	4.026
18963	24148	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.027
18964	12358	\begin{align*} \left (a +x \right ) y+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	4.029
18965	18527	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.031
18966	21626	\begin{align*} L i^{\prime }+R i&=E_{0} \\ i \left (0\right ) &= i_{0} \\ \end{align*}	✓	✓	✓	✓	4.032
18967	1702	\begin{align*} {\mathrm e}^{x} \left (y^{2} x^{4}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.033
18968	22287	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✗	✗	✗	4.035
18969	15914	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	4.037
18970	17120	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.037
18971	18364	\begin{align*} y^{\prime \prime }+\lambda ^{2} y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.037
18972	2311	\begin{align*} t y+\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✓	4.039
18973	3455	\begin{align*} y^{\prime }&=-\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \\ y \left (\frac {\pi }{4}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.039
18974	22360	\begin{align*} y^{\prime }&=-\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.040
18975	15402	\begin{align*} y^{\prime \prime }&=\frac {a}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	4.041
18976	18359	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.042
18977	6838	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	4.045
18978	26035	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.045
18979	19409	\begin{align*} 3 x^{2} {\mathrm e}^{y}-2 x +\left (x^{3} {\mathrm e}^{y}-\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.046
18980	19872	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	4.046
18981	5867	\begin{align*} \left (a \cos \left (x \right )^{2}-\sec \left (x \right )^{2}\right ) y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.047
18982	20773	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.047
18983	2541	\begin{align*} y^{\prime }&=t y^{3}-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.048
18984	4061	\begin{align*} y^{\prime \prime } x -y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.048
18985	17024	\begin{align*} y \cos \left (y x \right )+\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.048
18986	3465	\begin{align*} y^{\prime }&=-\frac {2 x^{2}+y^{2}+x}{y x} \\ \end{align*}	✓	✓	✓	✓	4.049
18987	22985	\begin{align*} y^{\prime }-\frac {6 y}{x}&=7 x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.049
18988	26194	\begin{align*} y^{\prime }&=\frac {1+y}{x -1} \\ \end{align*}	✓	✓	✓	✓	4.049
18989	750	\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{4} \\ \end{align*}	✓	✓	✓	✓	4.052
18990	3019	\begin{align*} r^{\prime }&=r \cot \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	4.052
18991	24032	\begin{align*} y^{\left (8\right )}+8 y^{\left (7\right )}+28 y^{\left (6\right )}+56 y^{\left (5\right )}+70 y^{\prime \prime \prime \prime }+56 y^{\prime \prime \prime }+28 y^{\prime \prime }+8 y^{\prime }&={\mathrm e}^{-x} x^{9} \\ \end{align*}	✓	✓	✓	✗	4.052
18992	3304	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	4.053
18993	15720	\begin{align*} 4 y+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.056
18994	4430	\begin{align*} 2 x +y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.059
18995	2968	\begin{align*} x^{2} y^{\prime }+y-2 y x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.060
18996	15343	\begin{align*} r^{\prime }+r \tan \left (t \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.061
18997	20796	\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	4.061
18998	14222	\begin{align*} R^{\prime }&=\left (1+t \right ) \left (1+R^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.062
18999	18801	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.062
19000	16236	\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	4.066