2.3.63 Problems 6201 to 6300

Table 2.657: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6201	617	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 10 \\ x_{2} \left (0\right ) &= 12 \\ x_{3} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.513
6202	4594	\begin{align*} y^{\prime \prime }+\left (\cos \left (x \right )+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.513
6203	6686	\begin{align*} 10 y^{\prime }+8 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	0.513
6204	8070	\begin{align*} y^{\prime }&=2 x^{2}+3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.513
6205	9525	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.513
6206	10564	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.513
6207	12924	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.513
6208	13075	\begin{align*} 4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.513
6209	13102	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=3 x-2 y \\ z^{\prime }&=2 y+3 z \\ \end{align*}	✓	✓	✓	✓	0.513
6210	14786	\begin{align*} 2 x^{\prime }+y^{\prime }-x-y&=-2 t \\ x^{\prime }+y^{\prime }+x-y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	0.513
6211	20927	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-3 x \\ \end{align*}	✓	✓	✓	✓	0.513
6212	21239	\begin{align*} x^{\prime }-y&=3 \\ y^{\prime }-3 x^{\prime }&=-2 x \\ \end{align*}	✓	✓	✓	✓	0.513
6213	21690	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.513
6214	22192	\begin{align*} n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.513
6215	1389	\begin{align*} \left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.514
6216	9631	\begin{align*} y+y^{\prime }&=t \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.514
6217	16017	\begin{align*} x^{\prime }&=2 x-6 y \\ y^{\prime }&=2 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.514
6218	18319	\begin{align*} y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=x \,{\mathrm e}^{2 x}-1 \\ \end{align*}	✓	✓	✓	✗	0.514
6219	21242	\begin{align*} x^{\prime }&=1+x \\ y^{\prime }&=x+3 y-1 \\ \end{align*}	✓	✓	✓	✓	0.514
6220	21654	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y&={\mathrm e}^{x} \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.514
6221	9516	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.515
6222	10263	\begin{align*} y^{\prime }&=a x \\ \end{align*}	✓	✓	✓	✓	0.515
6223	19260	\begin{align*} y^{\prime }&=2 \cos \left (x \right ) \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.515
6224	1448	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.516
6225	8182	\begin{align*} 5 y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.516
6226	10962	\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.516
6227	11253	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.516
6228	15307	\begin{align*} y^{\prime \prime } x +4 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.516
6229	15719	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.516
6230	16212	\begin{align*} y^{\prime }+4 y&=8 \\ \end{align*}	✓	✓	✓	✓	0.516
6231	17822	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.516
6232	1861	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.517
6233	9696	\begin{align*} x^{\prime }&=4 x+y \\ y^{\prime }&=4 y+z \\ z^{\prime }&=4 z \\ \end{align*}	✓	✓	✓	✓	0.517
6234	10295	\begin{align*} y^{\prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	0.517
6235	11257	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.517
6236	18666	\begin{align*} x^{\prime }&=2 x-\frac {5 y}{2} \\ y^{\prime }&=\frac {9 x}{5}-y \\ \end{align*}	✓	✓	✓	✓	0.517
6237	1029	\begin{align*} x_{1}^{\prime }&=x_{1}+3 x_{2}+7 x_{3} \\ x_{2}^{\prime }&=-x_{2}-4 x_{3} \\ x_{3}^{\prime }&=x_{2}+3 x_{3} \\ x_{4}^{\prime }&=-6 x_{2}-14 x_{3}+x_{4} \\ \end{align*}	✓	✓	✓	✓	0.518
6238	3923	\begin{align*} x_{1}^{\prime }&=7 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.518
6239	7635	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.518
6240	9504	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.518
6241	10359	\begin{align*} y^{\prime } x +y&=\cos \left (x \right )+\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.518
6242	10605	\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.518
6243	11184	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.518
6244	11256	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.518
6245	16229	\begin{align*} y^{\prime }-4 y&=2 \\ \end{align*}	✓	✓	✓	✓	0.518
6246	16948	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=8 x+y \\ \end{align*}	✓	✓	✓	✓	0.518
6247	20904	\begin{align*} y^{\prime \prime }+\frac {y}{4 x^{2}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.518
6248	22273	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (1\right ) &= 1 \\ x_{2} \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.518
6249	23578	\begin{align*} N_{1}^{\prime }&=4 N_{1}-6 N_{2} \\ N_{2}^{\prime }&=8 N_{1}-10 N_{2} \\ \end{align*} With initial conditions \begin{align*} N_{1} \left (0\right ) &= 100000 \\ N_{2} \left (0\right ) &= 1000 \\ \end{align*}	✓	✓	✓	✓	0.518
6250	1421	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.519
6251	7372	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.519
6252	10829	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.519
6253	11669	\begin{align*} {y^{\prime }}^{2}+\left (a +x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.519
6254	21943	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.519
6255	23583	\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.519
6256	1035	\begin{align*} x_{1}^{\prime }&=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }&=17 x_{1}+7 x_{2}+5 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.520
6257	1873	\begin{align*} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\ y \left (3\right ) &= -2 \\ y^{\prime }\left (3\right ) &= 3 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	0.520
6258	1891	\begin{align*} \left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.520
6259	3428	\begin{align*} y^{\prime }&=\sin \left (t \right )^{2} \\ y \left (\frac {\pi }{6}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.520
6260	6297	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.520
6261	8386	\begin{align*} y^{\prime }&=\left (-1+y\right )^{2}+\frac {1}{100} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	0.520
6262	8866	\begin{align*} y^{\prime }-2 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.520
6263	9070	\begin{align*} \left (x^{3}+1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.520
6264	10509	\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.520
6265	11254	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.520
6266	11262	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.520
6267	14759	\begin{align*} y^{\prime \prime } x -\left (x^{2}+2\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.520
6268	15268	\begin{align*} x^{\prime }+5 x-2 y&=0 \\ 2 x+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.520
6269	16882	\begin{align*} \left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.520
6270	19033	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 4 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.520
6271	22270	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-9 x+6 y+t \\ \end{align*}	✓	✓	✓	✓	0.520
6272	24805	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.520
6273	1432	\begin{align*} x_{1}^{\prime }&=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }&=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \\ \end{align*}	✓	✓	✓	✓	0.521
6274	10566	\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.521
6275	16039	\begin{align*} x^{\prime }&=-2 x+3 y \\ y^{\prime }&=3 x-2 y \\ z^{\prime }&=-z \\ \end{align*}	✓	✓	✓	✓	0.521
6276	25407	\begin{align*} y^{\prime }-4 y&=-8 \\ \end{align*}	✓	✓	✓	✓	0.521
6277	3427	\begin{align*} y^{\prime }&={\mathrm e}^{2 t} t \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.522
6278	8621	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.522
6279	8853	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-8 \\ x_{2}^{\prime }&=x_{1}+x_{2}+3 \\ \end{align*}	✓	✓	✓	✓	0.522
6280	11677	\begin{align*} {y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.522
6281	15801	\begin{align*} y^{\prime }&=2 y+1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.522
6282	20107	\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 c +\frac {10}{x} \\ \end{align*}	✓	✓	✓	✓	0.522
6283	24790	\begin{align*} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.522
6284	155	\begin{align*} y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.523
6285	468	\begin{align*} \left (x -2\right )^{3} y^{\prime \prime }+3 \left (x -2\right )^{2} y^{\prime }+x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.523
6286	2747	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.523
6287	4010	\begin{align*} 4 x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.523
6288	6417	\begin{align*} f \left (x \right )^{2} y^{\prime \prime }&=-24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	0.523
6289	8585	\begin{align*} y^{\prime \prime } x +y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.523
6290	9074	\begin{align*} y^{\prime }&=\ln \left (x \right ) \\ y \left ({\mathrm e}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.523
6291	10825	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.523
6292	14859	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+5 y \\ \end{align*}	✓	✓	✓	✓	0.523
6293	15806	\begin{align*} y^{\prime }&=\frac {1}{2 y+3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.523
6294	16438	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+4 y&=y^{3} \\ \end{align*}	✗	✗	✗	✗	0.523
6295	18384	\begin{align*} y^{\prime \prime }-{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.523
6296	19611	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.523
6297	20455	\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}	✓	✓	✓	✓	0.523
6298	20509	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right )+x \\ \end{align*}	✓	✓	✓	✓	0.523
6299	22940	\begin{align*} x^{\prime }-y&=t \\ x+y^{\prime }&=t^{2} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.523
6300	25399	\begin{align*} y^{\prime }&=2-y \\ \end{align*}	✓	✓	✓	✓	0.523