2.3.30 Problems 2901 to 3000

Table 2.591: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
2901	10850	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2902	10916	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2903	11028	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.172
2904	11117	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.172
2905	11155	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}	✓	✓	✓	✗	0.172
2906	15685	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3+\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.172
2907	20750	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.172
2908	21200	\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.172
2909	22263	\begin{align*} w^{\prime }-y&=0 \\ w+y^{\prime }+z&=1 \\ w-y+z^{\prime }&=2 \sin \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ w \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.172
2910	23830	\begin{align*} y^{\prime }&=\frac {1}{t^{2}-1} \\ \end{align*}	✓	✓	✓	✓	0.172
2911	24017	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \sin \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.172
2912	25320	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.172
2913	400	\begin{align*} y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.173
2914	572	\begin{align*} x^{\prime \prime }+4 x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.173
2915	4490	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=2 \,{\mathrm e}^{x}+5 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.173
2916	5803	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
2917	8629	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= {\frac {81}{10}} \\ y^{\prime }\left (0\right ) &= {\frac {39}{10}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.173
2918	10094	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.173
2919	10497	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
2920	10821	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
2921	10852	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.173
2922	11154	\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.173
2923	11275	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.173
2924	14998	\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.173
2925	19449	\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.173
2926	19569	\begin{align*} y^{\prime \prime \prime }-8 y&=16 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.173
2927	21189	\begin{align*} x^{\prime \prime \prime \prime }-4 x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\infty \right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.173
2928	21952	\begin{align*} 5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5}&=p \\ \end{align*}	✗	✗	✗	✗	0.173
2929	22811	\begin{align*} y^{\prime \prime }+9 y&=20 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.173
2930	24806	\begin{align*} y&=y^{\prime } x +k {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.173
2931	239	\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2932	535	\begin{align*} x^{\prime \prime }+4 x&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.174
2933	1462	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y&=t \\ \end{align*}	✓	✓	✓	✓	0.174
2934	1525	\begin{align*} y^{\prime }&=-x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.174
2935	2167	\begin{align*} 2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y&=3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.174
2936	2168	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{x} \left (-3 x^{2}+x +3\right ) \\ \end{align*}	✓	✓	✓	✓	0.174
2937	2183	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y&={\mathrm e}^{x} \left (8 \cos \left (x \right )+16 \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.174
2938	3581	\begin{align*} y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.174
2939	5563	\begin{align*} x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2940	5787	\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2941	6962	\begin{align*} 2 y x +x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2942	8127	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.174
2943	8201	\begin{align*} y^{\prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.174
2944	9079	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2945	10349	\begin{align*} y^{\prime } x +y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.174
2946	10577	\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2947	10622	\begin{align*} \left (1-x \right )^{2} x^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2948	10762	\begin{align*} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2949	10809	\begin{align*} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2950	10843	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2951	10922	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2952	11016	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.174
2953	11085	\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2954	11204	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2955	12891	\begin{align*} b \,{\mathrm e}^{y} x +a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	0.174
2956	12898	\begin{align*} x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.174
2957	13050	\begin{align*} 2 y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2958	16785	\begin{align*} y^{\prime \prime }+4 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.174
2959	17761	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.174
2960	18744	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2961	18902	\begin{align*} y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right ) \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.174
2962	20352	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-12 y&=\cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.174
2963	22093	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.174
2964	22262	\begin{align*} w^{\prime }-w-2 y&=1 \\ y^{\prime }-4 w-3 y&=-1 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 2 \\ w \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.174
2965	24925	\begin{align*} y^{\prime }&=\frac {t +1}{t} \\ \end{align*}	✓	✓	✓	✓	0.174
2966	25077	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.174
2967	823	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2968	2215	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{x} \left (1-6 x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 7 \\ y^{\prime \prime }\left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.175
2969	2341	\begin{align*} 2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.175
2970	3341	\begin{align*} y^{\prime }&=\sqrt {y x +1} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.175
2971	4553	\begin{align*} x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\ 2 x+y^{\prime }-y&=2 \cos \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= x_{0} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	0.175
2972	4669	\begin{align*} y^{\prime }&=a +b x +c y^{2} \\ \end{align*}	✓	✓	✓	✗	0.175
2973	6437	\begin{align*} y-y^{\prime } x +{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.175
2974	6542	\begin{align*} \left (y^{2}+x^{2}\right ) y^{\prime \prime }&=2 \left (1+y^{2}\right ) \left (-y+y^{\prime } x \right ) \\ \end{align*}	✗	✗	✗	✗	0.175
2975	7853	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2976	8125	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.175
2977	8624	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 11 \\ y^{\prime }\left (0\right ) &= 28 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.175
2978	9443	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.175
2979	10013	\begin{align*} \frac {y^{\prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2980	10100	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2981	10798	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2982	10842	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2983	10845	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2984	10955	\begin{align*} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (-x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2985	10974	\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2986	11081	\begin{align*} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2987	11092	\begin{align*} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2988	11108	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2989	11269	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2990	11315	\begin{align*} y^{\prime }+y^{2}-a x -b&=0 \\ \end{align*}	✓	✓	✓	✗	0.175
2991	15206	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.175
2992	15223	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.175
2993	18008	\begin{align*} x&=\sin \left (y^{\prime }\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.175
2994	18737	\begin{align*} y^{\prime \prime }-\frac {t}{y}&=\frac {1}{\pi } \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}	✗	✗	✓	✗	0.175
2995	18912	\begin{align*} y_{1}^{\prime }&=4 y_{1}-4 y_{2} \\ y_{2}^{\prime }&=5 y_{1}-4 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.175
2996	22493	\begin{align*} y^{\left (5\right )}+2 y^{\prime \prime \prime \prime }&=x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.175
2997	23002	\begin{align*} y^{\prime \prime }+7 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175
2998	24011	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	0.175
2999	24012	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	0.175
3000	24412	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.175