2.3.208 Problems 20701 to 20800

Table 2.989: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20701	22427	\begin{align*} \cos \left (x \right ) y^{\prime }-2 y \sin \left (x \right )+3&=0 \\ \end{align*}	✓	✓	✓	✓	4.970
20702	16857	\begin{align*} \sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x}&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	4.971
20703	24943	\begin{align*} y^{\prime }&=\frac {t y}{1+y} \\ \end{align*}	✓	✓	✓	✓	4.971
20704	9050	\begin{align*} y y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	4.972
20705	6837	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	4.973
20706	8357	\begin{align*} y^{\prime }&=\frac {y x +2 y-x -2}{y x -3 y+x -3} \\ \end{align*}	✓	✓	✓	✓	4.973
20707	19347	\begin{align*} y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.973
20708	16289	\begin{align*} x^{2} y^{\prime }-y x&=y^{2} \\ \end{align*}	✓	✓	✓	✓	4.974
20709	18304	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{m} \\ \end{align*}	✓	✓	✓	✓	4.974
20710	17072	\begin{align*} \frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.975
20711	59	\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x} \\ y \left (0\right ) &= 2 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✓	4.977
20712	5289	\begin{align*} \left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.977
20713	5312	\begin{align*} x \left (1-2 x y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.977
20714	5452	\begin{align*} {y^{\prime }}^{2} x +2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.977
20715	17143	\begin{align*} t y^{\prime }+y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	4.981
20716	19066	\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.982
20717	7891	\begin{align*} y \left (x -2 y\right )-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.983
20718	20241	\begin{align*} -x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.983
20719	15034	\begin{align*} y^{\prime }&=\frac {2 y-x -4}{2 x -y+5} \\ \end{align*}	✓	✓	✓	✓	4.987
20720	15601	\begin{align*} y^{\prime }&=y \cot \left (x \right )+\sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.987
20721	19249	\begin{align*} x y y^{\prime }&=-1+y \\ \end{align*}	✓	✓	✓	✓	4.989
20722	22452	\begin{align*} i^{\prime }+3 i&={\mathrm e}^{-2 t} \\ i \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.990
20723	11886	\begin{align*} y^{\prime }&=\frac {2 F \left (y+\ln \left (2 x +1\right )\right ) x +F \left (y+\ln \left (2 x +1\right )\right )-2}{2 x +1} \\ \end{align*}	✗	✓	✓	✗	4.993
20724	25734	\begin{align*} 2 y^{\prime \prime }-3 y^{2}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.993
20725	14503	\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right )^{2} \\ r \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.994
20726	12321	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+a y&=0 \\ \end{align*}	✗	✓	✓	✗	4.996
20727	2917	\begin{align*} 3 x^{2} y+x y^{2}+{\mathrm e}^{x}+\left (x^{3}+x^{2} y+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.997
20728	8543	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	4.999
20729	15367	\begin{align*} s^{\prime } \cos \left (t \right )+s \sin \left (t \right )&=1 \\ \end{align*}	✓	✓	✓	✓	5.000
20730	24122	\begin{align*} x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.000
20731	4846	\begin{align*} \left (x +a \right ) y^{\prime }&=-b -c y \\ \end{align*}	✓	✓	✓	✓	5.001
20732	17255	\begin{align*} -2 y+y^{\prime }&=\frac {\cos \left (t \right )}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✓	5.002
20733	5976	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.003
20734	20282	\begin{align*} x +y^{\prime }&=x \,{\mathrm e}^{\left (n -1\right ) y} \\ \end{align*}	✓	✓	✓	✗	5.003
20735	8663	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.004
20736	12121	\begin{align*} y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+x \,{\mathrm e}^{-\frac {y}{x}}+x^{3}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \\ \end{align*}	✓	✓	✓	✓	5.005
20737	4234	\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.006
20738	5163	\begin{align*} 2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right )&=6 y^{2} \\ \end{align*}	✓	✓	✓	✓	5.006
20739	5534	\begin{align*} x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.006
20740	9083	\begin{align*} y^{\prime }&=4 y x \\ \end{align*}	✓	✓	✓	✓	5.006
20741	13035	\begin{align*} 4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	5.006
20742	8350	\begin{align*} \left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left (1+{\mathrm e}^{x}\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.007
20743	25502	\begin{align*} y^{\prime }&=-4 y t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.008
20744	26293	\begin{align*} y^{\prime }&=\frac {2 x y}{-y^{2}-a^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.010
20745	12699	\begin{align*} y^{\prime \prime }&=-\frac {\left (4 v \left (v +1\right ) \sin \left (x \right )^{2}-\cos \left (x \right )^{2}+2-4 n^{2}\right ) y}{4 \sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	5.011
20746	5275	\begin{align*} x^{2} y^{2} y^{\prime }+1-x +x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.012
20747	21998	\begin{align*} \frac {1}{x}-\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.012
20748	22620	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	5.012
20749	5588	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-y \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.013
20750	6445	\begin{align*} y y^{\prime \prime }&=-y \left (f^{\prime }\left (x \right )-y^{2} g^{\prime }\left (x \right )\right )+\left (f \left (x \right )+g \left (x \right ) y^{2}\right ) y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	5.014
20751	18612	\begin{align*} y^{\prime }&=y+\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	5.015
20752	5453	\begin{align*} {y^{\prime }}^{2} x -2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.017
20753	17238	\begin{align*} t^{2} y+t^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.017
20754	13953	\begin{align*} y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a \,{\mathrm e}^{\lambda x} b +c \,{\mathrm e}^{2 \mu x}+d \,{\mathrm e}^{\mu x}+k \right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	5.018
20755	14823	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	5.018
20756	24245	\begin{align*} y^{\prime }&=x -2 y \cot \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	5.018
20757	25053	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.020
20758	23180	\begin{align*} y^{\prime }&=\frac {y-x +1}{3-x +y} \\ \end{align*}	✓	✓	✓	✓	5.021
20759	15895	\begin{align*} y^{\prime }&=\cos \left (\frac {\pi y}{2}\right ) \\ \end{align*}	✓	✓	✓	✗	5.023
20760	21821	\begin{align*} x^{3} y^{\prime }-x^{2} y&=x^{5} y \\ \end{align*}	✓	✓	✓	✓	5.023
20761	13972	\begin{align*} \left (x +1\right ) y^{2}-x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.024
20762	25720	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.024
20763	18811	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.028
20764	5375	\begin{align*} {y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.029
20765	15641	\begin{align*} y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.029
20766	13379	\begin{align*} y^{\prime }&=y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+a^{2} \cos \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	5.030
20767	17578	\begin{align*} 2 y y^{\prime \prime }+y^{2}&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.030
20768	21440	\begin{align*} y^{\prime }+\frac {\left (2 x +1\right ) y}{x}&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	5.033
20769	15383	\begin{align*} 6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.035
20770	13353	\begin{align*} y^{\prime }&=y^{2}+a \ln \left (\beta x \right ) y-a b \ln \left (\beta x \right )-b^{2} \\ \end{align*}	✓	✓	✓	✓	5.038
20771	18548	\begin{align*} 2 y t +\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\ y \left (-3\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.038
20772	12181	\begin{align*} y^{\prime }&=\frac {\left (y-a \ln \left (y\right ) x +x^{2}\right ) y}{\left (-\ln \left (y\right ) y-y \ln \left (x \right )-y+a x \right ) x} \\ \end{align*}	✓	✓	✓	✗	5.039
20773	25019	\begin{align*} y+y^{\prime }&=t y^{3} \\ \end{align*}	✓	✓	✓	✓	5.039
20774	17087	\begin{align*} \left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.040
20775	20286	\begin{align*} y y^{\prime }+x&=\frac {a^{2} \left (x y^{\prime }-y\right )}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	5.040
20776	19096	\begin{align*} y^{\prime }&=y^{2}-x^{2} \\ \end{align*}	✓	✓	✓	✗	5.041
20777	4632	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \sec \left (x \right )^{2}-2 y \cot \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	5.042
20778	21337	\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.042
20779	5267	\begin{align*} \left (1-4 x +3 x y^{2}\right ) y^{\prime }&=\left (2-y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	5.044
20780	24907	\begin{align*} 4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	5.044
20781	12162	\begin{align*} y^{\prime }&=-\frac {\left (-108 x^{{3}/{2}}-216-216 y^{2}+72 x^{3} y-6 x^{6}-216 y^{3}+108 x^{3} y^{2}-18 x^{6} y+x^{9}\right ) \sqrt {x}}{216} \\ \end{align*}	✓	✓	✓	✗	5.045
20782	14211	\begin{align*} x^{\prime }&=\sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.046
20783	19070	\begin{align*} y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\ \end{align*}	✓	✓	✓	✓	5.046
20784	18725	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.047
20785	27474	\begin{align*} y^{\prime }&=\left (2 x -y\right )^{{1}/{3}}+2 \\ \end{align*}	✓	✓	✓	✓	5.047
20786	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*}	✓	✓	✓	✓	5.049
20787	17106	\begin{align*} y^{\prime }&=y^{3}+y \\ \end{align*}	✓	✓	✓	✓	5.052
20788	4914	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	5.055
20789	8858	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.055
20790	22352	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	5.055
20791	1649	\begin{align*} y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.059
20792	13348	\begin{align*} x y^{\prime }&=a y^{2}+b \ln \left (x \right )^{k}+c \ln \left (x \right )^{2 k +2} \\ \end{align*}	✓	✓	✓	✗	5.061
20793	22808	\begin{align*} y^{\prime \prime }+y&=f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.062
20794	6973	\begin{align*} 2 y+y^{\prime }&=\frac {3 \,{\mathrm e}^{-2 x}}{4} \\ \end{align*}	✓	✓	✓	✓	5.063
20795	9006	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	5.063
20796	21379	\begin{align*} 3 x \left (y x -2\right )+\left (x^{3}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.063
20797	17219	\begin{align*} 2 t -y^{2} \sin \left (y t \right )+\left (\cos \left (y t \right )-t y \sin \left (y t \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.066
20798	26404	\begin{align*} \left (x -1\right ) \left (y^{2}-y+1\right )&=\left (y+1\right ) \left (x^{2}+x +1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.067
20799	1129	\begin{align*} y^{\prime }&=\frac {x^{2}}{y} \\ \end{align*}	✓	✓	✓	✓	5.070
20800	6015	\begin{align*} 13 y+5 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.070