2.3.178 Problems 17701 to 17800

Table 2.887: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17701	15453	\begin{align*} x \cos \left (\frac {y}{x}\right ) y^{\prime }&=y \cos \left (\frac {y}{x}\right )-x \\ \end{align*}	✓	✓	✓	✓	4.951
17702	25683	\begin{align*} 3 y^{\prime } x +5 y&=10 \\ \end{align*}	✓	✓	✓	✓	4.952
17703	17053	\begin{align*} y^{\prime } t +y&=t^{3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.954
17704	18799	\begin{align*} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✓	4.954
17705	19305	\begin{align*} 2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.954
17706	276	\begin{align*} y^{\prime \prime }+5 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.955
17707	8049	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=-\frac {2}{x}-\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.956
17708	21255	\begin{align*} x^{\prime \prime }&=x^{3}-x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✗	4.956
17709	6364	\begin{align*} y^{3} y^{\prime }+y^{\prime \prime }&=y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	4.957
17710	8690	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.957
17711	10439	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	4.957
17712	14965	\begin{align*} t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x&=0 \\ x \left (1\right ) &= 2 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.958
17713	12688	\begin{align*} y^{\prime \prime }&=-\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	4.962
17714	14451	\begin{align*} {\mathrm e}^{x} y+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 y x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	4.963
17715	5088	\begin{align*} \left (1-4 x -2 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.964
17716	14040	\begin{align*} 1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.964
17717	16374	\begin{align*} y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.964
17718	19749	\begin{align*} u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	4.964
17719	21451	\begin{align*} \frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✗	✗	4.964
17720	2974	\begin{align*} y x^{\prime }&=2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \\ \end{align*}	✓	✓	✓	✓	4.965
17721	4687	\begin{align*} y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.966
17722	15828	\begin{align*} y^{\prime }&=t y+t y^{2} \\ \end{align*}	✓	✓	✓	✓	4.967
17723	2936	\begin{align*} y^{\prime } x +\ln \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.968
17724	10115	\begin{align*} y^{\prime \prime }-x^{2} y-x^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	4.968
17725	13646	\begin{align*} y^{\prime }&=a \,x^{n} y^{3}+3 a b \,x^{n +m} y^{2}-b m \,x^{m -1}-2 a \,b^{3} x^{n +3 m} \\ \end{align*}	✓	✓	✓	✗	4.968
17726	23272	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.969
17727	13943	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+b \,{\mathrm e}^{2 \lambda x} y&=0 \\ \end{align*}	✓	✓	✓	✗	4.970
17728	14205	\begin{align*} x^{\prime \prime }&=-3 \sqrt {t} \\ x \left (1\right ) &= 4 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.970
17729	6446	\begin{align*} y y^{\prime \prime }&=2 {y^{\prime }}^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	4.971
17730	21341	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	4.971
17731	4858	\begin{align*} \left (2 x +1\right ) y^{\prime }&=4 \,{\mathrm e}^{-y}-2 \\ \end{align*}	✓	✓	✓	✓	4.972
17732	23245	\begin{align*} \sin \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=1 \\ \end{align*}	✓	✓	✓	✗	4.973
17733	7301	\begin{align*} y^{\prime \prime }+y&=x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	4.974
17734	22410	\begin{align*} 3 x +4 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.974
17735	21144	\begin{align*} x^{\prime \prime }-x^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	4.975
17736	4211	\begin{align*} \sqrt {\left (a +x \right ) \left (x +b \right )}\, y^{\prime }+y&=\sqrt {a +x}-\sqrt {x +b} \\ \end{align*}	✓	✓	✓	✗	4.977
17737	6015	\begin{align*} 13 y+5 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.977
17738	17923	\begin{align*} 8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.978
17739	5916	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	4.981
17740	4249	\begin{align*} \left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.982
17741	7031	\begin{align*} 2 y y^{\prime } x +3 x^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.982
17742	12432	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y-3 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	4.982
17743	20214	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	4.982
17744	23268	\begin{align*} y^{\prime \prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.985
17745	12407	\begin{align*} a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+3 b y&=0 \\ \end{align*}	✓	✓	✓	✗	4.986
17746	3476	\begin{align*} y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	4.987
17747	106	\begin{align*} 2 y y^{\prime } x&=x^{2}+2 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.990
17748	17327	\begin{align*} \tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.991
17749	16906	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.992
17750	12241	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 y^{2} x^{4}-2 x^{6}}} \\ \end{align*}	✓	✓	✓	✗	4.994
17751	19172	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	4.995
17752	16919	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } x +\left (4 x^{3}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.996
17753	20632	\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-y \sin \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.996
17754	19802	\begin{align*} y \sqrt {x^{2}-1}+x \sqrt {-1+y^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.997
17755	8434	\begin{align*} y-4 \left (x +y^{6}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.999
17756	15520	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (2\right ) &= -12 \\ \end{align*}	✓	✓	✓	✓	4.999
17757	9092	\begin{align*} y y^{\prime }&=x +1 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.000
17758	12471	\begin{align*} x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	5.000
17759	14576	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.000
17760	9119	\begin{align*} y^{\prime }+y x&=y^{4} x \\ \end{align*}	✓	✓	✓	✗	5.001
17761	19354	\begin{align*} -y^{\prime } x +y&=y^{\prime } y^{2} {\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	5.003
17762	25748	\begin{align*} y^{\prime }&=6 \sqrt {y}+5 x^{3} \\ y \left (-1\right ) &= 4 \\ \end{align*}	✗	✗	✗	✗	5.005
17763	13463	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+\lambda y+a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.006
17764	19265	\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.006
17765	2387	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.007
17766	19504	\begin{align*} y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\ \end{align*}	✓	✓	✓	✓	5.008
17767	2924	\begin{align*} \frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.009
17768	9759	\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.010
17769	17213	\begin{align*} 2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.010
17770	4081	\begin{align*} 3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.013
17771	4357	\begin{align*} 2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.013
17772	4791	\begin{align*} y^{\prime } x +\left (a +b \,x^{n} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.013
17773	6567	\begin{align*} \operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	5.014
17774	13314	\begin{align*} y^{\prime } x&=a \,{\mathrm e}^{\lambda x} y^{2}+k y+a \,b^{2} x^{2 k} {\mathrm e}^{\lambda x} \\ \end{align*}	✓	✓	✓	✗	5.016
17775	23956	\begin{align*} y^{\prime }&=\sin \left (y\right )^{3} \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.016
17776	13945	\begin{align*} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	5.018
17777	14018	\begin{align*} \left (-x +y\right )^{2} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	5.019
17778	19229	\begin{align*} y y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	5.020
17779	18330	\begin{align*} y^{\prime \prime } x -\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.021
17780	1823	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=8 x^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✗	5.023
17781	16555	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	5.023
17782	3457	\begin{align*} \frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	5.024
17783	7502	\begin{align*} y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\ \end{align*}	✓	✓	✓	✓	5.024
17784	20242	\begin{align*} \left (x +y-1\right ) y^{\prime }&=x +y+1 \\ \end{align*}	✓	✓	✓	✓	5.025
17785	4681	\begin{align*} y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.026
17786	15027	\begin{align*} x^{\prime }&={\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \\ \end{align*}	✓	✓	✓	✗	5.030
17787	15254	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=t^{7} \\ \end{align*}	✓	✓	✓	✓	5.033
17788	5004	\begin{align*} x^{n} y^{\prime }&=a +b \,x^{n -1} y \\ \end{align*}	✓	✓	✓	✗	5.034
17789	19387	\begin{align*} y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	5.036
17790	4407	\begin{align*} 2 y-x \left (\ln \left (x^{2} y\right )-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.037
17791	7318	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.037
17792	15628	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.037
17793	17151	\begin{align*} y^{\prime }-\frac {3 t y}{t^{2}-4}&=t \\ \end{align*}	✓	✓	✓	✓	5.038
17794	19722	\begin{align*} \left (T+\frac {1}{\sqrt {t^{2}-T^{2}}}\right ) T^{\prime }&=\frac {T}{t \sqrt {t^{2}-T^{2}}}-t \\ \end{align*}	✓	✓	✓	✗	5.038
17795	1536	\begin{align*} y^{\prime }&=-1-\frac {x}{2}+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \\ \end{align*}	✓	✓	✓	✓	5.043
17796	1619	\begin{align*} y^{\prime }&=\sqrt {x +y} \\ \end{align*}	✓	✓	✓	✓	5.043
17797	7000	\begin{align*} x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.043
17798	17646	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.043
17799	3606	\begin{align*} y^{\prime }&=y^{3} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.044
17800	19915	\begin{align*} y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.044