2.3.60 Problems 5901 to 6000

Table 2.663: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5901	9264	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.384
5902	16847	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.384
5903	18692	\begin{align*} x^{\prime }&=2 x+\frac {3 y}{2} \\ y^{\prime }&=-\frac {3 x}{2}-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.384
5904	19049	\begin{align*} x_{1}^{\prime }&=4 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.384
5905	19835	\begin{align*} y^{\prime \prime }-4 y^{\prime }+2 y&=x \\ \end{align*}	✓	✓	✓	✓	0.384
5906	21149	\begin{align*} x^{\prime \prime }+2 x&=\cos \left (\sqrt {2}\, t \right ) \\ \end{align*}	✓	✓	✓	✓	0.384
5907	23975	\begin{align*} y^{\prime \prime }-2 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.384
5908	337	\begin{align*} y^{\prime \prime }+9 y&=2 x^{2} {\mathrm e}^{3 x}+5 \\ \end{align*}	✓	✓	✓	✓	0.385
5909	767	\begin{align*} 3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.385
5910	1739	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.385
5911	3803	\begin{align*} y^{\prime \prime }-y&=4 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.385
5912	3819	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}+4 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.385
5913	8817	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.385
5914	9024	\begin{align*} {\mathrm e}^{x}+{\mathrm e}^{y} \left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.385
5915	9245	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.385
5916	9667	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.385
5917	14199	\begin{align*} t^{2} x^{\prime \prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.385
5918	15182	\begin{align*} \frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (1+3 x \right ) y^{\prime }}{x}+\frac {y}{x}&=3 x \\ \end{align*}	✓	✓	✓	✗	0.385
5919	16637	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.385
5920	17993	\begin{align*} x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.385
5921	18325	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	0.385
5922	19021	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.385
5923	19630	\begin{align*} y^{\prime \prime } x +\left (3+2 x \right ) y^{\prime }+\left (x +3\right ) y&=3 \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✗	0.385
5924	20180	\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.385
5925	22031	\begin{align*} 3 y^{2} x^{2}+\left (2 x^{3} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.385
5926	24071	\begin{align*} 4 y+y^{\prime \prime }&=x -4 \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.385
5927	25972	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.385
5928	2257	\begin{align*} y_{1}^{\prime }&=4 y_{1}+12 y_{2} \\ y_{2}^{\prime }&=-3 y_{1}-8 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.386
5929	2560	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.386
5930	4517	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.386
5931	5946	\begin{align*} y+2 y^{\prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.386
5932	6398	\begin{align*} b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.386
5933	7062	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.386
5934	9476	\begin{align*} x^{\prime }&=3 x+2 y \\ y^{\prime }&=-2 x-y \\ \end{align*}	✓	✓	✓	✓	0.386
5935	9601	\begin{align*} y^{\prime }+6 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.386
5936	10691	\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.386
5937	13154	\(\left [\begin {array}{ccc} 3 & 5 & -2 \\ 0 & 2 & 0 \\ 0 & 2 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.386
5938	14627	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y&=8 \,{\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	0.386
5939	18025	\begin{align*} y^{2} \left (1+{y^{\prime }}^{2}\right )-4 y y^{\prime }-4 x&=0 \\ \end{align*}	✓	✓	✓	✗	0.386
5940	18690	\begin{align*} x^{\prime }&=x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.386
5941	18691	\begin{align*} x^{\prime }&=-\frac {5 x}{2}+\frac {3 y}{2} \\ y^{\prime }&=-\frac {3 x}{2}+\frac {y}{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.386
5942	19499	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.386
5943	24677	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.386
5944	25135	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=6 \,{\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	0.386
5945	2255	\begin{align*} y_{1}^{\prime }&=-7 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-y_{1}-11 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.387
5946	5768	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.387
5947	9175	\begin{align*} y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.387
5948	9495	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.387
5949	9806	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x^{2}+2 x +1 \\ \end{align*}	✓	✓	✓	✓	0.387
5950	11668	\begin{align*} {y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.387
5951	14773	\begin{align*} x^{\prime }+y^{\prime }-x-3 y&={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+x&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✗	0.387
5952	19844	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.387
5953	22183	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.387
5954	22513	\begin{align*} y^{\prime }+2 x&=2 \\ \end{align*}	✓	✓	✓	✓	0.387
5955	23028	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.387
5956	24465	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.387
5957	24614	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.387
5958	373	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.388
5959	471	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.388
5960	877	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.388
5961	2229	\begin{align*} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 y^{\prime } x -16 y&=9 x^{4} \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.388
5962	2258	\begin{align*} y_{1}^{\prime }&=-10 y_{1}+9 y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.388
5963	2259	\begin{align*} y_{1}^{\prime }&=-13 y_{1}+16 y_{2} \\ y_{2}^{\prime }&=-9 y_{1}+11 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.388
5964	8114	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {25}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.388
5965	8272	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.388
5966	8574	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.388
5967	9688	\begin{align*} x^{\prime }&=-6 x+5 y \\ y^{\prime }&=-5 x+4 y \\ \end{align*}	✓	✓	✓	✓	0.388
5968	9689	\begin{align*} x^{\prime }&=-x+3 y \\ y^{\prime }&=-3 x+5 y \\ \end{align*}	✓	✓	✓	✓	0.388
5969	14559	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.388
5970	14575	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.388
5971	16066	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.388
5972	17398	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.388
5973	18004	\begin{align*} y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	0.388
5974	20144	\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=2 \\ \end{align*}	✓	✓	✓	✗	0.388
5975	22255	\begin{align*} y^{\prime }+z&=t \\ z^{\prime }+4 y&=0 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.388
5976	22480	\begin{align*} 2 y^{\prime \prime \prime \prime }&={\mathrm e}^{x}-{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.388
5977	22635	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.388
5978	24706	\begin{align*} y^{\prime \prime \prime \prime }-y&=x^{6} \\ \end{align*}	✓	✓	✓	✓	0.388
5979	25138	\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&=10 t \,{\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.388
5980	1089	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.389
5981	1629	\begin{align*} y^{\prime }+y&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.389
5982	1790	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=2+x \\ y \left (0\right ) &= -{\frac {1}{3}} \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	0.389
5983	1887	\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 y x^{5}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.389
5984	2269	\begin{align*} y_{1}^{\prime }&=-7 y_{1}+3 y_{2} \\ y_{2}^{\prime }&=-3 y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.389
5985	3694	\begin{align*} \sin \left (y\right )+\cos \left (x \right ) y+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.389
5986	14340	\begin{align*} x^{\prime \prime }-t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.389
5987	14563	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.389
5988	16632	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=\left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.389
5989	16740	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=576 x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.389
5990	17744	\begin{align*} 12 y^{\prime \prime }+8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.389
5991	19022	\begin{align*} x_{1}^{\prime }&=\frac {x_{1}}{2}-\frac {x_{2}}{4} \\ x_{2}^{\prime }&=x_{1}-\frac {x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.389
5992	19428	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.389
5993	19550	\begin{align*} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 y^{\prime \prime } x -8 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.389
5994	24016	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x} \ln \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	0.389
5995	24600	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.389
5996	24870	\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\ y \left (2\right ) &= 5 \\ y^{\prime }\left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.389
5997	25136	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.389
5998	2616	\begin{align*} y^{\prime \prime }-y t^{3}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.390
5999	3114	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.390
6000	7049	\begin{align*} y^{\prime \prime }-2 k y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.390