2.3.32 Problems 3101 to 3200

Table 2.595: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3101	22903	\begin{align*} x^{\prime }+x-5 y&=0 \\ y^{\prime }+4 x+5 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.180
3102	23010	\begin{align*} 12 x^{\prime \prime }-25 x^{\prime }+12 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.180
3103	23096	\begin{align*} 4 x^{\prime }+2 y^{\prime }+3 x&=E \sin \left (t \right ) \\ 4 x+2 x^{\prime }+3 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.180
3104	23334	\begin{align*} 8 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.180
3105	24923	\begin{align*} y^{\prime }&={\mathrm e}^{2 t}-1 \\ \end{align*}	✓	✓	✓	✓	0.180
3106	25067	\begin{align*} y^{\prime \prime }+a^{2} y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.180
3107	3570	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3108	4528	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.181
3109	5885	\begin{align*} 3 y-8 y^{\prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3110	6690	\begin{align*} y^{\prime }+8 y^{\prime \prime } x +4 x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3111	7043	\begin{align*} 6 y^{\prime \prime }-11 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3112	7719	\begin{align*} -y+y^{\prime } x&=\cos \left (x \right ) x^{3} \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.181
3113	9028	\begin{align*} 2 y \,{\mathrm e}^{2 x}+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.181
3114	9226	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3115	9338	\begin{align*} y^{\prime \prime }-y&=3 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.181
3116	9808	\begin{align*} 6 x {y^{\prime }}^{2}-\left (2 y+3 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3117	10557	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.181
3118	11048	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.181
3119	11090	\begin{align*} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.181
3120	11103	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.181
3121	11134	\begin{align*} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.181
3122	11223	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.181
3123	12746	\begin{align*} 6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3124	12889	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+a \,x^{v} y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.181
3125	14200	\begin{align*} 2 x^{\prime \prime }-5 x^{\prime }-3 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3126	14633	\begin{align*} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.181
3127	15249	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.181
3128	16195	\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.181
3129	16727	\begin{align*} y^{\prime \prime }+y^{\prime }-30 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3130	18764	\begin{align*} 6 y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3131	21533	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.181
3132	22102	\begin{align*} y^{\prime \prime }-y^{\prime }-30 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.181
3133	23759	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.181
3134	23831	\begin{align*} y^{\prime }&={\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	0.181
3135	25074	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=150 t \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.181
3136	828	\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.182
3137	2106	\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (-1\right ) &= -4 \\ y^{\prime }\left (-1\right ) &= -14 \\ y^{\prime \prime }\left (-1\right ) &= -20 \\ \end{align*}	✓	✓	✓	✓	0.182
3138	7943	\begin{align*} x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-\left (y-1\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	0.182
3139	8065	\begin{align*} x^{\prime }-x+y^{\prime }+3 y&={\mathrm e}^{-t}-1 \\ x^{\prime }+2 x+y^{\prime }+3 y&=1+{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✗	0.182
3140	9487	\begin{align*} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.182
3141	10582	\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*}	✓	✓	✓	✗	0.182
3142	11181	\begin{align*} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.182
3143	15209	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= -24 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.182
3144	18277	\begin{align*} y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.182
3145	18456	\begin{align*} x^{\prime }+3 x&={\mathrm e}^{-2 t} \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.182
3146	18890	\begin{align*} y^{\prime \prime }+4 y&=3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.182
3147	21772	\begin{align*} x^{2} {y^{\prime }}^{2}+4 x y^{\prime } y+3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.182
3148	22313	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.182
3149	23587	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-y \\ \end{align*}	✓	✓	✓	✓	0.182
3150	24410	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.182
3151	2184	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }-4 y&={\mathrm e}^{x} \left (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.183
3152	2777	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=x_{1}-x_{2}+{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.183
3153	3129	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\sin \left (k x \right ) \\ \end{align*}	✓	✓	✓	✓	0.183
3154	11084	\begin{align*} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
3155	15709	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ y \left (0\right ) &= {\frac {5}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.183
3156	16194	\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.183
3157	18756	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
3158	18757	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
3159	18763	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
3160	18766	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
3161	19453	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.183
3162	23253	\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
3163	23315	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.183
3164	24503	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+12 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.183
3165	242	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3166	824	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3167	847	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3168	1776	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3169	2216	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{-x} \left (4-8 x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.184
3170	2217	\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }-y&={\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ y^{\prime \prime }\left (0\right ) &= -17 \\ \end{align*}	✓	✓	✓	✓	0.184
3171	2676	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.184
3172	3788	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.184
3173	3953	\begin{align*} y^{\prime \prime }+9 y&=7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.184
3174	4091	\begin{align*} y^{\prime }&=1-x^{5}+\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.184
3175	4463	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }&=7 x -3 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.184
3176	5813	\begin{align*} \left (b +c \,{\mathrm e}^{x}\right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
3177	5882	\begin{align*} 3 y-10 y^{\prime }+3 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3178	7584	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3179	9024	\begin{align*} {\mathrm e}^{x}+{\mathrm e}^{y} \left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3180	9615	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.184
3181	10102	\begin{align*} y^{\prime \prime }-4 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
3182	10104	\begin{align*} y^{\prime \prime }-8 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
3183	10304	\begin{align*} y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3184	10731	\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3185	10858	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3186	11129	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
3187	11132	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
3188	11222	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
3189	14358	\begin{align*} x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.184
3190	14574	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3191	16712	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3192	16763	\begin{align*} y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.184
3193	16782	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.184
3194	17608	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=t \\ 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 ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.184
3195	18918	\begin{align*} y_{1}^{\prime }&=-y_{1}-5 y_{2}+3 \\ y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \cos \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.184
3196	18959	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (\alpha t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.184
3197	19447	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.184
3198	20036	\begin{align*} y^{\prime \prime }+3 y^{\prime }-54 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3199	20130	\begin{align*} x^{2} y^{\prime \prime \prime }-4 y^{\prime \prime } x +6 y^{\prime }&=4 \\ \end{align*}	✓	✓	✓	✓	0.184
3200	20702	\begin{align*} y^{\prime \prime \prime }+y&=\left ({\mathrm e}^{x}+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.184