2.3.67 Problems 6601 to 6700

Table 2.707: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6601	9717	\begin{align*} {y^{\prime }}^{2}-x^{2} y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.500
6602	10040	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.500
6603	10488	\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.500
6604	12914	\begin{align*} \sqrt {x}\, y^{\prime \prime }-y^{{3}/{2}}&=0 \\ \end{align*}	✗	✗	✗	✗	0.500
6605	15224	\begin{align*} -y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.500
6606	16186	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 20 \\ \end{align*}	✓	✓	✓	✓	0.500
6607	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*}	✓	✓	✓	✓	0.500
6608	16840	\begin{align*} y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.500
6609	16843	\begin{align*} y^{\prime \prime }-x y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.500
6610	16866	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.500
6611	17701	\begin{align*} 6 y-2 x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.500
6612	18762	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.500
6613	20935	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.500
6614	21128	\begin{align*} x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (\theta \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.500
6615	21917	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.500
6616	24048	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=x^{2}-4 \cos \left (3 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.500
6617	24083	\begin{align*} 4 \left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.500
6618	24585	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.500
6619	24686	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 x^{3}-9 x^{2}+2 x -16 \\ \end{align*}	✓	✓	✓	✓	0.500
6620	25907	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.500
6621	26928	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.500
6622	612	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.501
6623	885	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.501
6624	2734	\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}+2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.501
6625	10246	\begin{align*} y^{\prime \prime }&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.501
6626	16129	\begin{align*} y^{\prime \prime }+4 y&=-\cos \left (\frac {t}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.501
6627	16837	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.501
6628	16931	\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=6 x-7 y \\ \end{align*}	✓	✓	✓	✓	0.501
6629	20993	\begin{align*} x^{\prime }&=2 x-4 y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.501
6630	23494	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.501
6631	23752	\begin{align*} \left (x^{2}-\frac {1}{4}\right ) y^{\prime \prime }+2 y^{\prime }-6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.501
6632	23834	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{t \left (t -2\right )} \\ \end{align*}	✓	✓	✓	✓	0.501
6633	24700	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=72 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.501
6634	27679	\begin{align*} 4 y+y^{\prime \prime }&=2 \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.501
6635	7652	\begin{align*} y^{\prime }-y \,{\mathrm e}^{x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.502
6636	9465	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.502
6637	9977	\begin{align*} y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.502
6638	11290	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.502
6639	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*}	✓	✓	✓	✓	0.502
6640	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*}	✓	✓	✓	✓	0.502
6641	21731	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.502
6642	2381	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.503
6643	7105	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.503
6644	7992	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.503
6645	8843	\begin{align*} x_{1}^{\prime }&=-x_{1}+3 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+5 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.503
6646	9634	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.503
6647	10343	\begin{align*} \left (a t +1\right ) y^{\prime }+y&=t \\ y \left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.503
6648	17436	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-1 \\ \end{align*}	✓	✓	✓	✓	0.503
6649	17748	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=-t \\ \end{align*}	✓	✓	✓	✓	0.503
6650	18129	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	0.503
6651	18776	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.503
6652	19188	\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x}+{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.503
6653	23506	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.503
6654	24542	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=12 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.503
6655	24658	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=21 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.503
6656	26924	\begin{align*} y^{\prime }&=\cos \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.503
6657	27772	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.503
6658	1859	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }+\frac {y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.504
6659	1891	\begin{align*} \left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.504
6660	1910	\begin{align*} \left (3 x +2\right ) y^{\prime \prime }-x y^{\prime }+2 y x&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.504
6661	1938	\begin{align*} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+\left (1-x \right ) y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.504
6662	4380	\begin{align*} y^{\prime }-y \tan \left (x \right )+y^{2} \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.504
6663	5693	\begin{align*} a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.504
6664	6847	\begin{align*} x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.504
6665	7346	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=6 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.504
6666	7635	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.504
6667	17836	\begin{align*} x^{\prime \prime }+x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.504
6668	18741	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.504
6669	18765	\begin{align*} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.504
6670	19654	\begin{align*} x^{\prime }&=5 x+2 y \\ y^{\prime }&=-17 x-5 y \\ \end{align*}	✓	✓	✓	✓	0.504
6671	20028	\begin{align*} y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right )&=m^{2} \\ \end{align*}	✓	✓	✗	✗	0.504
6672	22184	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.504
6673	25237	\begin{align*} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.504
6674	25239	\begin{align*} t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.504
6675	26637	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }&=\frac {\cos \left (x \right )^{2}}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.504
6676	7638	\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.505
6677	7995	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.505
6678	14195	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.505
6679	16740	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=576 x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.505
6680	18759	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.505
6681	18887	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.505
6682	21558	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=4 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.505
6683	23343	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.505
6684	23452	\begin{align*} \left (x +1\right ) y^{\prime \prime }+3 y^{\prime }-2 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.505
6685	24932	\begin{align*} y^{\prime }&={\mathrm e}^{2 t}-1 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.505
6686	27030	\begin{align*} y^{\prime \prime }-8 y^{\prime }+12 y&=f \left (t \right ) \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.505
6687	226	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.506
6688	293	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.506
6689	877	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.506
6690	1290	\begin{align*} 5 u^{\prime \prime }+2 u^{\prime }+7 u&=0 \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.506
6691	9349	\begin{align*} y^{\prime }+y&=1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.506
6692	9824	\begin{align*} {y^{\prime }}^{2} x^{2}&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.506
6693	10386	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{2}+x +1 \\ \end{align*}	✓	✓	✓	✓	0.506
6694	12591	\begin{align*} y^{\prime \prime }&=\frac {2 y}{x \left (x -1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	0.506
6695	16185	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 16 \\ \end{align*}	✓	✓	✓	✓	0.506
6696	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*}	✓	✓	✓	✓	0.506
6697	16521	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.506
6698	16622	\begin{align*} y^{\prime \prime }+9 y&=54 x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.506
6699	16933	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=5 x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 7 \\ y \left (0\right ) &= -7 \\ \end{align*}	✓	✓	✓	✓	0.506
6700	18897	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.506