2.3.80 Problems 7901 to 8000

Table 2.691: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7901	22831	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.396
7902	23023	\begin{align*} x^{\prime \prime }+2 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 5 \\ x \left (\frac {\pi \sqrt {3}}{6}\right ) &= 2 \,{\mathrm e}^{-\frac {\pi \sqrt {3}}{6}} \\ \end{align*}	✓	✓	✓	✓	0.396
7903	964	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.397
7904	3187	\begin{align*} 4 y+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.397
7905	4476	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.397
7906	5622	\begin{align*} {y^{\prime }}^{3}+a x y^{\prime }-a y&=0 \\ \end{align*}	✓	✓	✓	✗	0.397
7907	6325	\begin{align*} y^{\prime \prime }&=\operatorname {f4} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	0.397
7908	6611	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=x^{3}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.397
7909	12909	\begin{align*} 2 \left (-x^{k}+4 x^{3}\right ) \left (-y^{3}+y^{\prime } y+y^{\prime \prime }\right )-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+a x y+b&=0 \\ \end{align*}	✗	✗	✗	✗	0.397
7910	14059	\begin{align*} {y^{\prime }}^{3}-4 x y^{\prime } y+8 y^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	0.397
7911	14395	\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.397
7912	14658	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=x^{3}+x +{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.397
7913	16676	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=5 \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.397
7914	23089	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.397
7915	24589	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x}-x +\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.397
7916	24702	\begin{align*} 4 y+y^{\prime \prime }&=20 \,{\mathrm e}^{x}-20 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.397
7917	840	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.398
7918	1788	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y&=\left (x +1\right )^{3} {\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	0.398
7919	1858	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398
7920	2597	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.398
7921	2702	\begin{align*} x^{\prime }&=x-3 y \\ y^{\prime }&=-2 x+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.398
7922	2718	\begin{align*} y^{\prime \prime \prime \prime }-y&=g \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.398
7923	3911	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{3} \\ x_{2}^{\prime }&=-x_{2} \\ x_{3}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.398
7924	5571	\begin{align*} y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
7925	6634	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.398
7926	6728	\begin{align*} y^{\prime \prime \prime \prime }&=\cos \left (x \right )+y \\ \end{align*}	✓	✓	✓	✓	0.398
7927	6952	\begin{align*} \arctan \left (y x \right )+\frac {y x -2 x y^{2}}{y^{2} x^{2}+1}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{y^{2} x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	0.398
7928	8095	\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398
7929	8747	\begin{align*} \left (x^{2}-y^{4}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
7930	8803	\begin{align*} x^{2} y y^{\prime \prime }&=-y^{2}+x^{2} {y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	0.398
7931	9370	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398
7932	9640	\begin{align*} y^{\prime }-3 y&=\delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.398
7933	9670	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=4 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.398
7934	9785	\begin{align*} y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.398
7935	10260	\begin{align*} y^{\prime }&=a \\ \end{align*}	✓	✓	✓	✓	0.398
7936	11714	\begin{align*} \left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.398
7937	14560	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.398
7938	14843	\begin{align*} f \left (t \right ) x^{\prime \prime }+x g \left (t \right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.398
7939	16124	\begin{align*} y^{\prime \prime }+3 y^{\prime }+y&=\cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.398
7940	16472	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.398
7941	16509	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.398
7942	16511	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	0.398
7943	18804	\begin{align*} x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.398
7944	18830	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=2 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.398
7945	19168	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✗	0.398
7946	21126	\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.398
7947	21220	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✓	0.398
7948	21585	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.398
7949	23022	\begin{align*} y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi \sqrt {3}}{3}\right ) &= 5 \,{\mathrm e}^{-\frac {\pi \sqrt {3}}{2}} \\ \end{align*}	✓	✓	✓	✓	0.398
7950	23612	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.398
7951	337	\begin{align*} y^{\prime \prime }+9 y&=2 x^{2} {\mathrm e}^{3 x}+5 \\ \end{align*}	✓	✓	✓	✓	0.399
7952	1423	\begin{align*} x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {3 x_{1}}{2}+\frac {x_{2}}{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.399
7953	2244	\begin{align*} y_{1}^{\prime }&=-6 y_{1}-3 y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.399
7954	2595	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{t} t^{2} \\ \end{align*}	✓	✓	✓	✓	0.399
7955	7099	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.399
7956	7108	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.399
7957	7762	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.399
7958	10813	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.399
7959	14739	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y x&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.399
7960	19583	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.399
7961	20022	\begin{align*} y^{2} \left (1+{y^{\prime }}^{2}\right )&=r^{2} \\ \end{align*}	✓	✓	✓	✓	0.399
7962	20365	\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\left (x -1\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.399
7963	23927	\begin{align*} y^{\prime \prime } x +x {y^{\prime }}^{2}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.399
7964	24022	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.399
7965	24106	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (-x^{2}+9\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.399
7966	25115	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.399
7967	1447	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.400
7968	2241	\begin{align*} y_{1}^{\prime }&=-y_{1}-4 y_{2} \\ y_{2}^{\prime }&=-y_{1}-y_{2} \\ \end{align*}	✓	✓	✓	✓	0.400
7969	2625	\begin{align*} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{t}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.400
7970	3745	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.400
7971	14312	\begin{align*} x^{\prime \prime }-4 x&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.400
7972	15107	\begin{align*} y^{\prime \prime } x&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.400
7973	15242	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=3 \delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.400
7974	17110	\begin{align*} \sin \left (y \right )^{2}&=x^{\prime } \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.400
7975	18191	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.400
7976	18668	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=-5 x-y \\ \end{align*}	✓	✓	✓	✓	0.400
7977	20034	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}-b^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.400
7978	20893	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.400
7979	21539	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	0.400
7980	25327	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.400
7981	1885	\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.401
7982	8871	\begin{align*} y^{\prime }+i y&=x \\ \end{align*}	✓	✓	✓	✓	0.401
7983	10196	\begin{align*} \left (y-2 y^{\prime } x \right )^{2}&={y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.401
7984	10570	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.401
7985	10674	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \\ \end{align*}	✓	✓	✓	✗	0.401
7986	10789	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
7987	11291	\begin{align*} y^{\prime \prime }&=\frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.401
7988	11734	\begin{align*} \left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.401
7989	14196	\begin{align*} x^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.401
7990	14926	\begin{align*} x^{\prime \prime }+6 x^{\prime }+10 x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.401
7991	16393	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.401
7992	16507	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.401
7993	16741	\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=81 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.401
7994	17443	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=-256 t^{3} \\ \end{align*}	✓	✓	✓	✓	0.401
7995	17756	\begin{align*} y^{\prime \prime }+9 y^{\prime }+20 y&=-2 \,{\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	0.401
7996	18863	\begin{align*} y^{\prime \prime }+y&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.401
7997	20387	\begin{align*} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
7998	20440	\begin{align*} x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.401
7999	21278	\begin{align*} s y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.401
8000	21627	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.401