2.3.34 Problems 3301 to 3400

Table 2.641: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3301	5474	\begin{align*} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
3302	6398	\begin{align*} b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.418
3303	7182	\begin{align*} x^{3} y^{\prime \prime }-\left (2 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.418
3304	7614	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.418
3305	10283	\begin{align*} f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi &=0 \\ \end{align*}	✓	✓	✓	✓	0.418
3306	12599	\begin{align*} y^{\prime \prime }&=-\frac {\left (1-3 x \right ) y}{\left (-1+x \right ) \left (2 x -1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	0.418
3307	14830	\begin{align*} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
3308	17436	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-1 \\ \end{align*}	✓	✓	✓	✓	0.418
3309	21188	\begin{align*} x^{\prime \prime \prime \prime }-x^{\prime \prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.418
3310	21534	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=4 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.418
3311	21882	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=2 x^{2}-3 x -17 \\ \end{align*}	✓	✓	✓	✓	0.418
3312	23232	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.418
3313	24429	\begin{align*} 4 y^{\prime \prime \prime \prime }-45 y^{\prime \prime }-70 y^{\prime }-24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
3314	24515	\begin{align*} 4 y^{\prime \prime \prime \prime }+20 y^{\prime \prime \prime }+35 y^{\prime \prime }+25 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.418
3315	969	\begin{align*} x_{1}^{\prime }&=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.419
3316	1050	\begin{align*} \left (-1+x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.419
3317	2244	\begin{align*} y_{1}^{\prime }&=-6 y_{1}-3 y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.419
3318	2423	\begin{align*} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.419
3319	6936	\begin{align*} y^{2}+y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.419
3320	24497	\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.419
3321	580	\begin{align*} x^{\prime }&=\frac {y}{2} \\ y^{\prime }&=-8 x \\ \end{align*}	✓	✓	✓	✓	0.420
3322	968	\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2} \\ x_{2}^{\prime }&=6 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.420
3323	6374	\begin{align*} x y^{n}+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	0.420
3324	7916	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.420
3325	10527	\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.420
3326	16934	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=8 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.420
3327	18764	\begin{align*} 6 y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.420
3328	22478	\begin{align*} y^{\prime \prime \prime \prime }&=\frac {x}{3} \\ \end{align*}	✓	✓	✓	✓	0.420
3329	23264	\begin{align*} y^{\prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.420
3330	2824	\begin{align*} x_{1}^{\prime }&=-5 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.421
3331	3946	\begin{align*} y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.421
3332	9978	\begin{align*} y x -1+x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.421
3333	17617	\begin{align*} 4 x^{2} y^{\prime \prime }+17 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.421
3334	17722	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.421
3335	1075	\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.422
3336	1419	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.422
3337	3099	\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.422
3338	5477	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.422
3339	12415	\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.422
3340	12511	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 a x y^{\prime }+a \left (a -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.422
3341	16173	\begin{align*} y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.422
3342	20582	\begin{align*} n \,x^{3} y^{\prime \prime \prime }&=-y^{\prime } x +y \\ \end{align*}	✓	✓	✓	✗	0.422
3343	581	\begin{align*} x^{\prime }&=8 y \\ y^{\prime }&=-2 x \\ \end{align*}	✓	✓	✓	✓	0.423
3344	1272	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= \beta \\ \end{align*}	✓	✓	✓	✗	0.423
3345	1416	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.423
3346	3950	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=3 \cos \left (t \right )+\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.423
3347	5782	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.423
3348	12894	\begin{align*} y^{\prime \prime } x -x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	0.423
3349	14424	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.423
3350	448	\begin{align*} y^{\prime \prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.424
3351	863	\begin{align*} 3 x^{\prime \prime }+30 x^{\prime }+63 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.424
3352	1062	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.424
3353	1398	\begin{align*} \left (1-x \right ) y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.424
3354	1457	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.424
3355	1767	\begin{align*} \left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y&=\left (4 x^{2}-4 x +1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.424
3356	1771	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y&=4 x^{{5}/{2}} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.424
3357	5799	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.424
3358	6776	\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 }&=0 \\ \end{align*}	✓	✓	✓	✓	0.424
3359	19641	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.424
3360	21892	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.424
3361	24428	\begin{align*} 6 y^{\prime \prime \prime \prime }+23 y^{\prime \prime \prime }+28 y^{\prime \prime }+13 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.424
3362	342	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.425
3363	3232	\begin{align*} 4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right )+x \\ \end{align*}	✓	✓	✓	✓	0.425
3364	6482	\begin{align*} 2 y y^{\prime \prime }&=f \left (x \right ) y^{2}+3 {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.425
3365	6726	\begin{align*} y^{\prime \prime \prime \prime }&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.425
3366	12548	\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1&=0 \\ \end{align*}	✓	✓	✓	✗	0.425
3367	14565	\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.425
3368	18756	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.425
3369	24482	\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.425
3370	578	\begin{align*} x^{\prime }&=-2 y \\ y^{\prime }&=2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.426
3371	4125	\begin{align*} 4 y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.426
3372	13180	\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.426
3373	17427	\begin{align*} y^{\prime \prime }-y&=2 t -4 \\ \end{align*}	✓	✓	✓	✓	0.426
3374	18779	\begin{align*} 4 y^{\prime \prime }+9 y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.426
3375	21590	\begin{align*} y^{\left (5\right )}+y^{\prime \prime }&=x^{5}-3 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.426
3376	2237	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.427
3377	3573	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.427
3378	4128	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.427
3379	10650	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.427
3380	12918	\begin{align*} y y^{\prime \prime }-a \,x^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.427
3381	14708	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.427
3382	17437	\begin{align*} 5 y^{\prime \prime }+y^{\prime }-4 y&=-3 \\ \end{align*}	✓	✓	✓	✓	0.427
3383	1766	\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✗	0.428
3384	2623	\begin{align*} y^{\prime \prime }+y^{\prime }+t y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.428
3385	3947	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.428
3386	5882	\begin{align*} 3 y-10 y^{\prime }+3 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
3387	10614	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.428
3388	12563	\begin{align*} \left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
3389	12840	\begin{align*} y^{\prime \prime }-2 y^{3}-y x +a&=0 \\ \end{align*}	✗	✗	✗	✗	0.428
3390	3199	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{3}-\frac {\cos \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	0.429
3391	6331	\begin{align*} g \left (x , y\right )+f \left (x , y\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.429
3392	6775	\begin{align*} -4 y-2 y^{\prime } x +4 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.429
3393	11670	\begin{align*} {y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.429
3394	12746	\begin{align*} 6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.429
3395	16754	\begin{align*} y^{\prime \prime \prime }+8 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.429
3396	21415	\begin{align*} y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.429
3397	971	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.430
3398	3951	\begin{align*} y^{\prime \prime }+4 y&=9 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.430
3399	436	\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
3400	467	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431