2.3.180 Problems 17901 to 18000

Table 2.933: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17901	27314	\begin{align*} y-\frac {1}{x}+\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.025
17902	5516	\begin{align*} {y^{\prime }}^{2} x^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.026
17903	20633	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	3.027
17904	3291	\begin{align*} y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}&=x^{2} \\ \end{align*}	✓	✓	✓	✗	3.028
17905	8661	\begin{align*} y^{\prime }&=\frac {x^{2}}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.028
17906	12292	\begin{align*} y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.028
17907	19326	\begin{align*} x y^{\prime }-y&=\left (1+y^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.028
17908	1520	\begin{align*} x y^{\prime }+y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.029
17909	8746	\begin{align*} \left (1+x^{2} y^{2}\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.029
17910	19669	\begin{align*} x^{\prime }&=2 \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.029
17911	19795	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	3.029
17912	21443	\begin{align*} y^{\prime }-\frac {y}{x}&=x \\ \end{align*}	✓	✓	✓	✓	3.029
17913	7704	\begin{align*} x y^{\prime }-2 y&=x^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.030
17914	20671	\begin{align*} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✗	3.030
17915	4770	\begin{align*} x y^{\prime }&=a x -\left (-b \,x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	3.031
17916	20550	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.031
17917	7625	\begin{align*} \left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.032
17918	17670	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.032
17919	2962	\begin{align*} y x^{\prime }+\left (y +1\right ) x&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	3.033
17920	8334	\begin{align*} y^{\prime }&=\left (y \,{\mathrm e}^{y}-9 y\right ) {\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	3.033
17921	84	\begin{align*} x y^{\prime }+3 y&=2 x^{5} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.034
17922	6480	\begin{align*} 2 y y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.034
17923	18303	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y&=x^{2}-2 x +2 \\ \end{align*}	✓	✓	✓	✓	3.034
17924	14850	\begin{align*} y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x}&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left ({\mathrm e}^{\pi }\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.035
17925	25691	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= -{\frac {1}{3}} \\ \end{align*}	✓	✓	✓	✓	3.035
17926	19682	\begin{align*} x^{\prime } t +x \ln \left (t \right )&=t^{2} \\ \end{align*}	✓	✓	✓	✓	3.036
17927	15874	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (3\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	3.038
17928	7386	\begin{align*} x y^{\prime }&=\frac {1}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	3.039
17929	23128	\begin{align*} x y^{\prime }-y&=1 \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.039
17930	2865	\begin{align*} {\mathrm e}^{y} \left (y^{\prime }+1\right )&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.040
17931	20298	\begin{align*} \left (x -y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	3.040
17932	23238	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.040
17933	26227	\begin{align*} x y^{2} \left (x y^{\prime }+y\right )&=a^{2} \\ \end{align*}	✓	✓	✓	✓	3.040
17934	22820	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=6 \delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.041
17935	6121	\begin{align*} 2 \left (1-x \right ) y-\left (-x^{2}+2\right ) y^{\prime }+\left (2-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.042
17936	7792	\begin{align*} y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	3.042
17937	25523	\begin{align*} y^{\prime \prime }+100 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	3.042
17938	26078	\begin{align*} y^{\prime }&=2 y x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.042
17939	19267	\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.043
17940	23898	\begin{align*} 2 x y^{2}+2 x +\left (6 y^{3}+2 y+4 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.043
17941	25205	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.043
17942	26301	\begin{align*} y^{\prime }&=\frac {y}{2 \ln \left (y\right ) y+y-x} \\ \end{align*}	✓	✓	✓	✓	3.043
17943	27335	\begin{align*} y^{\prime }&=x -y^{2} \\ \end{align*}	✓	✓	✓	✗	3.043
17944	11879	\begin{align*} y^{\prime }&=\frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x} \\ \end{align*}	✓	✓	✓	✗	3.044
17945	12279	\begin{align*} y^{\prime }&=\frac {\left (y-x +\ln \left (x +1\right )\right )^{2}+x}{x +1} \\ \end{align*}	✓	✓	✓	✓	3.044
17946	17154	\begin{align*} y^{\prime }+2 y \cot \left (x \right )&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.044
17947	19807	\begin{align*} x^{3}+4 y x +y^{2}+\left (2 x^{2}+2 y x +4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.046
17948	20185	\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.046
17949	1546	\begin{align*} y^{\prime }+\frac {k y}{x}&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.047
17950	23159	\begin{align*} y^{\prime }+\frac {y}{\sin \left (x \right )}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.047
17951	15053	\begin{align*} y \left (1+{y^{\prime }}^{2}\right )&=a \\ \end{align*}	✓	✓	✓	✓	3.048
17952	18896	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.048
17953	21830	\begin{align*} y x +x^{2} y^{\prime }&=8 x^{2} \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.048
17954	2821	\begin{align*} z^{\prime \prime }+{\mathrm e}^{z^{2}}&=1 \\ \end{align*}	✓	✓	✓	✗	3.049
17955	21624	\begin{align*} y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.050
17956	23970	\begin{align*} y^{\prime }-5 y&=3 x^{3}+4 x \\ \end{align*}	✓	✓	✓	✓	3.050
17957	13250	\begin{align*} 2 x^{2} y^{\prime }&=2 y^{2}+y x -2 a^{2} x \\ \end{align*}	✓	✓	✓	✗	3.052
17958	24274	\begin{align*} y^{\prime }-\cos \left (x \right )&=\tan \left (y\right )^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.052
17959	3444	\begin{align*} y^{\prime }&=\frac {2 t y}{t^{2}+1}+t +1 \\ \end{align*}	✓	✓	✓	✓	3.053
17960	23896	\begin{align*} 2 \cos \left (x \right ) y-1+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.053
17961	25424	\begin{align*} -y+y^{\prime }&=8 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.053
17962	4267	\begin{align*} x y^{\prime }&=y+x^{2}+9 y^{2} \\ \end{align*}	✓	✓	✓	✓	3.055
17963	3593	\begin{align*} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.056
17964	4653	\begin{align*} y^{\prime }+f \left (x \right )^{2}&=f^{\prime }\left (x \right )+y^{2} \\ \end{align*}	✓	✓	✗	✗	3.056
17965	11456	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 y x +1\right )&=0 \\ \end{align*}	✗	✓	✓	✗	3.056
17966	17169	\begin{align*} \left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y&=t \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.057
17967	17618	\begin{align*} 9 x^{2} y^{\prime \prime }-9 x y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.057
17968	11781	\begin{align*} \left (-a^{2} x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} \left (-a^{2}+1\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.059
17969	23946	\begin{align*} y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.059
17970	27389	\begin{align*} {y^{\prime }}^{2} x^{2}&=x y y^{\prime }+1 \\ \end{align*}	✓	✓	✓	✓	3.059
17971	142	\begin{align*} x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.060
17972	7665	\begin{align*} x^{\prime \prime }-\omega ^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	3.060
17973	6070	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=\left (-x^{2}+1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.061
17974	7321	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=x -\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	3.061
17975	12391	\begin{align*} x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	3.061
17976	17779	\begin{align*} t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.061
17977	180	\begin{align*} x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.063
17978	13942	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y&=0 \\ \end{align*}	✗	✓	✓	✗	3.064
17979	25311	\begin{align*} y^{\prime \prime }-y&=\delta \left (t -1\right )-\delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.064
17980	16225	\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.065
17981	2312	\begin{align*} 4 y t +\left (t^{2}+1\right ) y^{\prime }&=t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.067
17982	7702	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x&=x \\ \end{align*}	✓	✓	✓	✓	3.067
17983	24216	\begin{align*} y \left (x^{2}+y^{2}-1\right )+x \left (1+x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.067
17984	13344	\begin{align*} y^{\prime }&=y^{2}-2 \lambda ^{2} \tanh \left (\lambda x \right )^{2}-2 \lambda ^{2} \coth \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.068
17985	1218	\begin{align*} y^{\prime }&=\frac {x^{3}-2 y}{x} \\ \end{align*}	✓	✓	✓	✓	3.069
17986	4283	\begin{align*} x y^{\prime }+y&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.069
17987	5139	\begin{align*} x \left (y+2\right ) y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✓	✓	3.069
17988	5927	\begin{align*} 2 y x -\left (-x^{2}+4\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.069
17989	18858	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5}&=\cos \left (w t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	3.069
17990	22638	\begin{align*} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	3.070
17991	4752	\begin{align*} x y^{\prime }+x^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.071
17992	27319	\begin{align*} x^{2}+2 x +y&=\left (x -3 x^{2} y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	3.072
17993	14212	\begin{align*} x^{\prime }&={\mathrm e}^{-2 x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.075
17994	184	\begin{align*} 2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.076
17995	18937	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.076
17996	21529	\begin{align*} y^{\prime \prime }+y^{\prime }+8 y&=\left (10 x^{2}+21 x +9\right ) \sin \left (3 x \right )+x \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.076
17997	23148	\begin{align*} y^{\prime }&=\frac {y \left (b_{2} x +b_{1} \right )}{x \left (a_{1} +a_{2} y\right )} \\ \end{align*}	✓	✓	✓	✓	3.076
17998	25970	\begin{align*} 2 y^{\prime }+y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	3.076
17999	15872	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ \end{align*}	✓	✓	✓	✓	3.077
18000	17227	\begin{align*} 1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.077