2.3.33 Problems 3201 to 3300

Table 2.615: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3201	10935	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.268
3202	11045	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.268
3203	11143	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.268
3204	220	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.269
3205	438	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.269
3206	587	\begin{align*} x^{\prime }&=-x+3 y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.269
3207	1759	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.269
3208	2418	\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 \(t=0\).	✓	✓	✓	✓	0.269
3209	7967	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.269
3210	9386	\begin{align*} x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.269
3211	10686	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.269
3212	10703	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.269
3213	10735	\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	0.269
3214	10968	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.269
3215	11116	\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*}	✓	✓	✓	✗	0.269
3216	11177	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.269
3217	11193	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.269
3218	15186	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.269
3219	16727	\begin{align*} y^{\prime \prime }+y^{\prime }-30 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.269
3220	16966	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.269
3221	19814	\begin{align*} \left (-2 y x +x^{2}\right ) y^{\prime }+x^{2}-3 y x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.269
3222	20988	\begin{align*} u^{\prime }&=u^{3} \\ u \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.269
3223	21946	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.269
3224	22813	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=100 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 20 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.269
3225	22999	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.269
3226	23000	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.269
3227	23630	\begin{align*} y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.269
3228	23765	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.269
3229	23824	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.269
3230	1769	\begin{align*} 2 y^{\prime \prime } x +\left (4 x +1\right ) y^{\prime }+\left (2 x +1\right ) y&=3 \sqrt {x}\, {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	0.270
3231	2638	\begin{align*} t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*} Series expansion around \(t=2\).	✗	✗	✓	✗	0.270
3232	9107	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.270
3233	10596	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.270
3234	10767	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.270
3235	11050	\begin{align*} x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.270
3236	11182	\begin{align*} y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.270
3237	13072	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&={\mathrm e}^{2 t}+t \\ x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\ \end{align*}	✓	✓	✓	✗	0.270
3238	16462	\begin{align*} x^{2} y^{\prime \prime }-20 y&=27 x^{5} \\ \end{align*}	✓	✓	✓	✓	0.270
3239	18179	\begin{align*} y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (x n +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	0.270
3240	18182	\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.270
3241	22029	\begin{align*} y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.270
3242	23002	\begin{align*} y^{\prime \prime }+7 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.270
3243	812	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.271
3244	2682	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=1+{\mathrm e}^{-t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.271
3245	2721	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime }&=t +\cos \left (t \right )+2 \,{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.271
3246	7916	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.271
3247	10752	\begin{align*} y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.271
3248	10907	\begin{align*} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.271
3249	11107	\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.271
3250	11120	\begin{align*} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.271
3251	11237	\begin{align*} 3 t \left (1+t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.271
3252	15195	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.271
3253	395	\begin{align*} x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\ x \left (0\right ) &= -30 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.272
3254	408	\begin{align*} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.272
3255	409	\begin{align*} 2 \left (x -1\right ) y^{\prime }&=3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.272
3256	7242	\begin{align*} x^{\prime }&=\frac {3 y^{{2}/{3}}-x}{3 y} \\ \end{align*}	✓	✓	✓	✓	0.272
3257	10533	\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.272
3258	10756	\begin{align*} 2 y^{\prime \prime } x -y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.272
3259	10876	\begin{align*} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.272
3260	11059	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.272
3261	11063	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.272
3262	11125	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.272
3263	11199	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.272
3264	11207	\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.272
3265	11236	\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.272
3266	15686	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=6 x -20-120 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.272
3267	22041	\begin{align*} y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.272
3268	24017	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\sin \left (x \right ) {\mathrm e}^{x} x \\ \end{align*}	✓	✓	✓	✓	0.272
3269	2221	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=2 x \\ \end{align*}	✓	✓	✓	✓	0.273
3270	2641	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y&=0 \\ \end{align*} Series expansion around \(t=-1\).	✗	✗	✓	✗	0.273
3271	8184	\begin{align*} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.273
3272	10611	\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
3273	10868	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
3274	10985	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
3275	11148	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
3276	11224	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.273
3277	14818	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.273
3278	18745	\begin{align*} a y^{\prime \prime }+b y^{\prime }+\frac {b^{2} y}{4 a}&=0 \\ \end{align*}	✓	✓	✓	✓	0.273
3279	19975	\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\ \end{align*}	✓	✓	✓	✓	0.273
3280	22194	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.273
3281	23005	\begin{align*} y^{\prime \prime }-9 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.273
3282	23632	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.273
3283	403	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.274
3284	1047	\begin{align*} \left (x -2\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.274
3285	1068	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.274
3286	2776	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=4 x_{1}+x_{2}-{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.274
3287	7804	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=\frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.274
3288	8533	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.274
3289	10788	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.274
3290	10857	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.274
3291	11029	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (4 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.274
3292	11030	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.274
3293	15693	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3 x +4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.274
3294	20088	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.274
3295	21804	\begin{align*} \left (x -y\right ) y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	0.274
3296	23806	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.274
3297	25097	\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.274
3298	8628	\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=21 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= {\frac {7}{2}} \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.275
3299	10527	\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.275
3300	10531	\begin{align*} \left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.275