2.3.159 Problems 15801 to 15900

Table 2.891: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15801	4481	\begin{align*} y^{\prime \prime }-y&=12 \,{\mathrm e}^{x} x^{2}+3 \,{\mathrm e}^{2 x}+10 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.675
15802	10326	\begin{align*} y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \\ \end{align*}	✓	✓	✓	✓	1.675
15803	12417	\begin{align*} x^{2} y^{\prime \prime }-\left (a \,x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.675
15804	20651	\begin{align*} \left (x^{2}+a \right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.675
15805	4283	\begin{align*} y^{\prime } x +y&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.676
15806	17728	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+k y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.676
15807	22350	\begin{align*} y^{\prime }&=2 x -y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.676
15808	1746	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.677
15809	15162	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+4 y x&=2 x \\ \end{align*}	✓	✓	✓	✗	1.677
15810	89	\begin{align*} \left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.678
15811	11749	\begin{align*} y {y^{\prime }}^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.678
15812	14700	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.678
15813	17444	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.678
15814	48	\begin{align*} y^{\prime }&=2 x \sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.679
15815	6287	\begin{align*} y+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.679
15816	8774	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\frac {y}{4}&=-\frac {x^{2}}{2}+\frac {1}{2} \\ \end{align*}	✓	✓	✓	✗	1.679
15817	21259	\begin{align*} x^{\prime \prime }&=x-x^{3} \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.680
15818	26639	\begin{align*} x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y&=x^{2} \left (2 x -3\right ) \\ \end{align*}	✓	✓	✓	✗	1.680
15819	12	\begin{align*} x^{\prime \prime }&=-20 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= -15 \\ \end{align*}	✓	✓	✓	✓	1.681
15820	21344	\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.681
15821	21568	\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.681
15822	23105	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	1.681
15823	26984	\begin{align*} y^{\prime \prime }+4 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.681
15824	22284	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.682
15825	7815	\begin{align*} y^{\prime \prime }-7 y^{\prime }&=-3 \\ \end{align*}	✓	✓	✓	✓	1.683
15826	15236	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \\ y \left (0\right ) &= -6 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.683
15827	54	\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	1.684
15828	4363	\begin{align*} 1+\left (x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.684
15829	8611	\begin{align*} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.684
15830	8875	\begin{align*} y^{\prime }+a y&=b \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.684
15831	20007	\begin{align*} x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\ \end{align*}	✓	✓	✓	✓	1.684
15832	22106	\begin{align*} y^{\prime \prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.684
15833	22318	\begin{align*} y^{\prime }&=2 y x +1 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.684
15834	6810	\begin{align*} 1-{y^{\prime \prime }}^{2}+2 x y^{\prime \prime } y^{\prime \prime \prime }+\left (-x^{2}+1\right ) {y^{\prime \prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.685
15835	19271	\begin{align*} y^{\prime }&=2 y x +1 \\ \end{align*}	✓	✓	✓	✓	1.685
15836	19632	\begin{align*} a^{2} y+y^{\prime \prime }&=f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.685
15837	10286	\begin{align*} y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	1.686
15838	14187	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	1.686
15839	20908	\begin{align*} 2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.686
15840	5816	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.687
15841	19231	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.687
15842	25778	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	1.687
15843	13870	\begin{align*} 2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \left (2-k \right ) x^{2}+b \left (1-k \right ) x -c k \right ) y^{\prime }+\lambda \,x^{1+k} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.688
15844	12609	\begin{align*} y^{\prime \prime }&=\frac {\left (a +b \right ) y^{\prime }}{x^{2}}-\frac {\left (\left (a +b \right ) x +a b \right ) y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	1.689
15845	13240	\begin{align*} y^{\prime } x&=x y^{2}+a y+b \,x^{n} \\ \end{align*}	✓	✓	✓	✗	1.689
15846	8239	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.690
15847	8547	\begin{align*} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.690
15848	21847	\begin{align*} R q^{\prime }+\frac {q}{c}&=E \\ q \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.690
15849	9647	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=1+\delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.691
15850	12314	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.691
15851	14746	\begin{align*} \left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.691
15852	14882	\begin{align*} x^{\prime }&=x \left (2-x\right ) \\ \end{align*}	✓	✓	✓	✓	1.691
15853	16079	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.691
15854	18376	\begin{align*} y^{\prime \prime } x +\sin \left (x \right ) y&=x \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*} Series expansion around \(x=\pi \).	✓	✓	✓	✗	1.691
15855	18947	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.691
15856	21035	\begin{align*} x^{\prime }&=x^{p} \\ \end{align*}	✓	✓	✓	✓	1.691
15857	771	\begin{align*} x^{3}+3 y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.692
15858	18544	\begin{align*} y+2 y^{\prime }&=3 t^{2} \\ \end{align*}	✓	✓	✓	✓	1.692
15859	18931	\begin{align*} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.692
15860	3275	\begin{align*} y y^{\prime \prime }-y^{2} y^{\prime }&={y^{\prime }}^{2} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.693
15861	18015	\begin{align*} y&=\frac {3 y^{\prime } x}{2}+{\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	1.693
15862	9417	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	1.694
15863	670	\begin{align*} y^{\prime }&=\ln \left (y\right ) x \\ \end{align*}	✓	✓	✓	✓	1.695
15864	14847	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.695
15865	10107	\begin{align*} y^{\prime \prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✓	1.697
15866	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*}	✓	✓	✓	✓	1.697
15867	16811	\begin{align*} y^{\prime \prime }+16 y&=\delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.697
15868	24717	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=2 x \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.697
15869	6138	\begin{align*} -3 y+3 y^{\prime } x +\left (2 x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.698
15870	20163	\begin{align*} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.698
15871	24471	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.698
15872	27562	\begin{align*} y y^{\prime \prime }&=y^{\prime } \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	1.698
15873	1297	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.699
15874	5520	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.699
15875	11390	\begin{align*} y^{\prime } x +y-x \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.699
15876	25205	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.700
15877	4361	\begin{align*} 1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.701
15878	11324	\begin{align*} y^{\prime }-y^{2}-y \sin \left (2 x \right )-\cos \left (2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.701
15879	12444	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✗	1.701
15880	14141	\begin{align*} y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+{\mathrm e}^{2 x} y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✗	1.701
15881	14902	\begin{align*} x^{\prime }+x \tanh \left (t \right )&=3 \\ \end{align*}	✓	✓	✓	✓	1.701
15882	1332	\begin{align*} t^{2} y^{\prime \prime }+5 y^{\prime } t +13 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.702
15883	17725	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.702
15884	26187	\begin{align*} y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\ \end{align*}	✓	✓	✓	✓	1.702
15885	132	\begin{align*} x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	1.703
15886	1298	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.704
15887	5817	\begin{align*} -y+y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.704
15888	5897	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-y x&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	1.704
15889	8736	\begin{align*} 2 x \left (x -y^{2}\right ) y^{\prime }+y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.704
15890	14646	\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.704
15891	17454	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	1.704
15892	19416	\begin{align*} y^{\prime } x +y x +y-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.704
15893	22369	\begin{align*} i^{\prime }+5 i&=10 \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.704
15894	23273	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.705
15895	698	\begin{align*} 1+y^{\prime }&=2 y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.707
15896	16106	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 t +{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.707
15897	16506	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.707
15898	18807	\begin{align*} 2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.707
15899	5139	\begin{align*} x \left (y+2\right ) y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✓	✓	1.708
15900	20505	\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=4 x \\ \end{align*}	✓	✓	✓	✓	1.708