2.3.197 Problems 19601 to 19700

Table 2.967: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19601	23851	\begin{align*} x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.027
19602	4714	\begin{align*} y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.028
19603	4735	\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}	✓	✓	✓	✓	4.028
19604	4980	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=\left (-x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	4.028
19605	25711	\begin{align*} \left (4-y^{2}\right ) y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	4.029
19606	7245	\begin{align*} 3 x y^{2} y^{\prime }+3 y^{3}&=1 \\ \end{align*}	✓	✓	✓	✓	4.033
19607	17252	\begin{align*} y+y^{\prime }&=t y^{2} \\ \end{align*}	✓	✓	✓	✓	4.033
19608	9257	\begin{align*} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \\ \end{align*}	✓	✓	✓	✓	4.034
19609	11939	\begin{align*} y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x} \\ \end{align*}	✓	✓	✓	✓	4.034
19610	162	\begin{align*} x y^{\prime }-4 x^{2} y+2 \ln \left (y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.036
19611	25047	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.036
19612	25791	\begin{align*} y^{\prime }&=\frac {x^{2}}{5}+y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	4.036
19613	5013	\begin{align*} y^{\prime } \sqrt {a^{2}+x^{2}}+x +y&=\sqrt {a^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.037
19614	20110	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{m} \\ \end{align*}	✓	✓	✓	✓	4.037
19615	4937	\begin{align*} x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y&=a \\ \end{align*}	✓	✓	✓	✓	4.038
19616	4342	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.039
19617	19090	\begin{align*} y^{\prime }&=y^{2}+\frac {1}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	4.039
19618	7940	\begin{align*} y^{\prime }+x \left (x +y\right )&=x^{3} \left (x +y\right )^{3}-1 \\ \end{align*}	✓	✓	✓	✓	4.040
19619	12057	\begin{align*} y^{\prime }&=\frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1} \\ \end{align*}	✓	✓	✓	✗	4.040
19620	8986	\begin{align*} x y^{\prime \prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.041
19621	17313	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\ \end{align*}	✓	✓	✓	✓	4.041
19622	11417	\begin{align*} x y^{\prime }-\ln \left (y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.042
19623	11895	\begin{align*} y^{\prime }&=\frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2 F \left (y \,{\mathrm e}^{-\frac {x^{2}}{4}}\right )\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \\ \end{align*}	✓	✓	✓	✗	4.043
19624	61	\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.045
19625	21812	\begin{align*} 2 x^{2}+5 x y^{2}+\left (5 x^{2} y-2 y^{4}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.045
19626	24966	\begin{align*} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	4.045
19627	1638	\begin{align*} y^{\prime }-2 y&=2 \sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.046
19628	5240	\begin{align*} \left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	4.046
19629	20113	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.046
19630	21014	\begin{align*} x^{\prime }&=-x t^{2} \\ \end{align*}	✓	✓	✓	✓	4.046
19631	8424	\begin{align*} y^{\prime }+3 x^{2} y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	4.049
19632	20971	\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )}{\cos \left (y\right )^{2}} \\ y \left (\pi \right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	4.049
19633	14504	\begin{align*} x^{\prime }-x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.050
19634	23177	\begin{align*} y^{\prime }&=\left (1-y\right ) \left (-\frac {1}{t \ln \left (t \right )}-\frac {3}{100}+\frac {3 y}{100}\right ) \\ \end{align*}	✓	✓	✓	✓	4.050
19635	24874	\begin{align*} 2 a y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	4.050
19636	20002	\begin{align*} \left (y y^{\prime }+n x \right )^{2}&=\left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✗	✓	4.053
19637	24124	\begin{align*} m y-n x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.055
19638	1232	\begin{align*} \left (1+{\mathrm e}^{x}\right ) y^{\prime }&=y-y \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	4.056
19639	5209	\begin{align*} y^{2} y^{\prime }&=x \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.056
19640	12021	\begin{align*} y^{\prime }&=\frac {1+2 y}{x \left (-2+y x +2 x y^{2}\right )} \\ \end{align*}	✓	✓	✓	✓	4.056
19641	21568	\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.056
19642	15560	\begin{align*} y^{\prime }&=b +a y \\ y \left (c \right ) &= d \\ \end{align*}	✓	✓	✓	✓	4.058
19643	62	\begin{align*} y^{\prime }&=4 x^{3} y-y \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	4.059
19644	2823	\begin{align*} z^{\prime \prime }+z-2 z^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	4.060
19645	4974	\begin{align*} x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.060
19646	12103	\begin{align*} y^{\prime }&=\frac {y \left (y x +1\right )}{x \left (-y x -1+x^{3} y^{4}\right )} \\ \end{align*}	✓	✓	✓	✗	4.060
19647	8767	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	4.061
19648	15840	\begin{align*} y^{\prime }&=y^{2}-4 t \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	4.061
19649	27554	\begin{align*} y y^{\prime \prime }+y&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.062
19650	21013	\begin{align*} x^{\prime }&=2 x t \\ x \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	4.064
19651	22095	\begin{align*} y^{\prime \prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.064
19652	737	\begin{align*} x^{2} y^{\prime }&=y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	4.065
19653	5288	\begin{align*} \left (3 x -y^{3}\right ) y^{\prime }&=x^{2}-3 y \\ \end{align*}	✓	✓	✓	✗	4.065
19654	14938	\begin{align*} x^{\prime \prime }+\omega ^{2} x&=\sin \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	4.065
19655	17941	\begin{align*} \left (\frac {{\mathrm e}^{-y^{2}}}{2}-y x \right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	4.066
19656	1554	\begin{align*} x y^{\prime }+\left (2 x^{2}+1\right ) y&=x^{3} {\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.067
19657	13812	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	4.067
19658	24238	\begin{align*} x^{\prime } t&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \\ \end{align*}	✓	✓	✓	✓	4.068
19659	8783	\begin{align*} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.069
19660	18045	\begin{align*} 3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.070
19661	15483	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.071
19662	22394	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.071
19663	3665	\begin{align*} y^{\prime }-\frac {y}{2 x \ln \left (x \right )}&=2 x y^{3} \\ \end{align*}	✓	✓	✓	✓	4.072
19664	7438	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=2 x \cos \left (x \right )^{2} \\ y \left (\frac {\pi }{4}\right ) &= -\frac {15 \sqrt {2}\, \pi ^{2}}{32} \\ \end{align*}	✓	✓	✓	✓	4.072
19665	14082	\begin{align*} {y^{\prime }}^{2} x^{2}-2 \left (y x -2\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.073
19666	27234	\begin{align*} y^{2}-2 y x +x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.074
19667	3010	\begin{align*} 2 y+6&=x y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.075
19668	18952	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{5}+y&=k \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.075
19669	3032	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )&=\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.076
19670	7928	\begin{align*} \left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.076
19671	22290	\begin{align*} y^{\prime }&=x^{2}+5 y \\ \end{align*}	✓	✓	✓	✓	4.076
19672	24837	\begin{align*} {y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	4.076
19673	6388	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+2 x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.077
19674	9120	\begin{align*} \left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	4.078
19675	14973	\begin{align*} a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✓	4.079
19676	22819	\begin{align*} y^{\prime \prime }+y&=3 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.081
19677	26282	\begin{align*} 2 x y^{\prime }-y&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	4.082
19678	3320	\begin{align*} 3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\ \end{align*}	✓	✓	✗	✗	4.083
19679	11651	\begin{align*} \sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.083
19680	8411	\begin{align*} x^{\prime }&=k \left (A -x\right )^{2} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.085
19681	13670	\begin{align*} y^{\prime \prime }-a \,x^{-2+n} \left (a \,x^{n}+n +1\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	4.086
19682	13785	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\left (n +\frac {1}{2}\right )^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.086
19683	14005	\begin{align*} x y^{\prime }-y&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	4.086
19684	4435	\begin{align*} \left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.087
19685	20451	\begin{align*} x^{2} y^{2}-3 x y y^{\prime }&=2 y^{2}+x^{3} \\ \end{align*}	✓	✓	✓	✗	4.087
19686	22004	\begin{align*} x \,{\mathrm e}^{x}+\left (y^{5}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.088
19687	3525	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.089
19688	8540	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.089
19689	18030	\begin{align*} \left (x y^{\prime }+y\right )^{2}+3 x^{5} \left (x y^{\prime }-2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.089
19690	25858	\begin{align*} 2 \cos \left (x \right ) y-1+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.089
19691	14268	\begin{align*} x^{\prime }&=x \left (1+{\mathrm e}^{t} x\right ) \\ \end{align*}	✓	✓	✓	✓	4.092
19692	17161	\begin{align*} p^{\prime }&=t^{3}+\frac {p}{t} \\ \end{align*}	✓	✓	✓	✓	4.092
19693	780	\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	4.093
19694	5808	\begin{align*} \left (a^{2}+b^{2}\right )^{2} y-4 a b y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.093
19695	20273	\begin{align*} y^{\prime }+3 x^{2} y&=x^{5} {\mathrm e}^{x^{3}} \\ \end{align*}	✓	✓	✓	✓	4.093
19696	20570	\begin{align*} a^{2} y^{\prime \prime } y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	4.093
19697	6574	\begin{align*} a y^{2}+x^{3} y^{\prime } y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	4.094
19698	15941	\begin{align*} y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \\ \end{align*}	✓	✓	✓	✓	4.094
19699	15119	\begin{align*} y^{\prime }&=\cos \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	4.096
19700	12255	\begin{align*} y^{\prime }&=y^{3}+x^{2} y^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \\ \end{align*}	✓	✓	✓	✓	4.097