2.3.34 Problems 3301 to 3400

Table 2.599: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3301	11125	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
3302	11187	\begin{align*} y^{\prime \prime } x +y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
3303	11244	\begin{align*} 2 y^{\prime \prime } x +\left (x -2\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
3304	12906	\begin{align*} 24+12 y x +x^{3} \left (-y^{3}+y^{\prime } y+y^{\prime \prime }\right )&=0 \\ \end{align*}	✗	✗	✓	✗	0.190
3305	15221	\begin{align*} y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.190
3306	17674	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 y^{\prime } x +48 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.190
3307	23027	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.190
3308	235	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3309	310	\begin{align*} y^{\prime \prime }-i y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3310	440	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.191
3311	554	\begin{align*} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25}&=6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.191
3312	796	\begin{align*} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	0.191
3313	2211	\begin{align*} y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=-{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \\ \end{align*}	✓	✓	✓	✓	0.191
3314	4556	\begin{align*} x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\ y^{\prime }-2 y-4 z&=4 \,{\mathrm e}^{2 t} \\ x-z^{\prime }-z&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 9 \\ y \left (0\right ) &= 3 \\ z \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.191
3315	5427	\begin{align*} {y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3316	6768	\begin{align*} 12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3317	6926	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3318	9132	\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3319	9229	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3320	9339	\begin{align*} y^{\prime \prime }+y&=-8 \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.191
3321	10728	\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3322	10745	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3323	10781	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3324	10800	\begin{align*} 2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3325	10841	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3326	10861	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3327	11031	\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*}	✓	✓	✓	✗	0.191
3328	11044	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3329	11058	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3330	11106	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3331	11113	\begin{align*} 4 y^{\prime \prime } x -y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3332	11128	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3333	11191	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.191
3334	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*}	✓	✓	✓	✗	0.191
3335	12978	\begin{align*} x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+y^{3} b x&=0 \\ \end{align*}	✗	✗	✗	✗	0.191
3336	14559	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3337	14575	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3338	15695	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.191
3339	16670	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.191
3340	18472	\begin{align*} x^{\prime \prime }+x&=2 \cos \left (t \right ) \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.191
3341	18883	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✗	0.191
3342	19570	\begin{align*} y^{\prime \prime \prime \prime }-y&=-x^{3}+1 \\ \end{align*}	✓	✓	✓	✓	0.191
3343	20010	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3344	22072	\begin{align*} y^{\prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.191
3345	23356	\begin{align*} y^{\prime \prime }+20 y^{\prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3346	23645	\begin{align*} y^{\prime \prime \prime }-y&=-1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.191
3347	23646	\begin{align*} y^{\prime \prime \prime }+y&=-1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.191
3348	25099	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3349	25541	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.191
3350	309	\begin{align*} y^{\prime \prime }+2 i y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
3351	1742	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
3352	4558	\begin{align*} x^{\prime }-x-2 y&=0 \\ x-y^{\prime }&=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= x_{0} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	0.192
3353	10787	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
3354	10810	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
3355	10853	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
3356	11224	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.192
3357	15248	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y&=8 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -3 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.192
3358	18033	\begin{align*} \left (y^{\prime }-1\right )^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.192
3359	23281	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
3360	23330	\begin{align*} 2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.192
3361	1486	\begin{align*} y^{\prime \prime }-2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.193
3362	2166	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y&=-{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right ) \\ \end{align*}	✓	✓	✓	✓	0.193
3363	4062	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.193
3364	4607	\begin{align*} y^{\prime }&=a f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.193
3365	5811	\begin{align*} \left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
3366	10461	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
3367	10803	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
3368	11061	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
3369	11107	\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.193
3370	14563	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
3371	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.	✓	✓	✓	✓	0.193
3372	15328	\begin{align*} {y^{\prime }}^{2}-y^{\prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
3373	20332	\begin{align*} 9 x^{\prime \prime }+18 x^{\prime }-16 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
3374	23418	\begin{align*} x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 \ln \left (x \right ) x^{2}\right ) y^{\prime }-\left (2+4 x \right ) y&=0 \\ \end{align*}	✓	✓	✗	✗	0.193
3375	23661	\begin{align*} y^{\prime \prime \prime }+y&=18 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 13 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.193
3376	24115	\begin{align*} y^{\prime }&=2 y \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.193
3377	25084	\begin{align*} y^{\prime \prime }-3 y&=4 t^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.193
3378	25097	\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
3379	25098	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.193
3380	534	\begin{align*} x^{\prime \prime }+x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
3381	831	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3382	832	\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3383	1250	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3384	1252	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3385	1305	\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3386	3198	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	0.194
3387	3370	\begin{align*} x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.194
3388	5958	\begin{align*} \left (b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3389	6681	\begin{align*} 4 y^{\prime }+5 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.194
3390	6938	\begin{align*} {\mathrm e}^{x}-\sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3391	7903	\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3392	7967	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.194
3393	9618	\begin{align*} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.194
3394	10464	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
3395	10593	\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
3396	10683	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
3397	11050	\begin{align*} x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
3398	11096	\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
3399	11148	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194
3400	11169	\begin{align*} \left (-x +2\right ) x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.194