2.3.33 Problems 3201 to 3300

Table 2.597: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
3201	22254	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.184
3202	22256	\begin{align*} w^{\prime }+y&=\sin \left (t \right ) \\ y^{\prime }-z&={\mathrm e}^{t} \\ w+y+z^{\prime }&=1 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ w \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.184
3203	22793	\begin{align*} y^{\left (5\right )}-5 y^{\prime \prime }+4 y^{\prime }&=x^{2}-x +{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.184
3204	24786	\begin{align*} x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.184
3205	25241	\begin{align*} t y^{\prime \prime }-4 y^{\prime }+t y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.184
3206	1466	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3207	6767	\begin{align*} 6 y^{\prime \prime }+6 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3208	7588	\begin{align*} 6 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3209	8826	\begin{align*} u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3210	9715	\begin{align*} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3211	11039	\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.185
3212	11089	\begin{align*} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3213	11105	\begin{align*} y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.185
3214	11149	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.185
3215	11731	\begin{align*} x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 y x +x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3216	16196	\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.185
3217	18177	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=\sin \left (2 x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.185
3218	18779	\begin{align*} 4 y^{\prime \prime }+9 y^{\prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3219	20667	\begin{align*} x y^{\prime \prime } \left (\cos \left (x \right ) x -2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 y \left (x \sin \left (x \right )+\cos \left (x \right )\right )&=0 \\ \end{align*}	✓	✓	✗	✗	0.185
3220	23008	\begin{align*} 35 y^{\prime \prime }-29 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3221	23276	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.185
3222	23765	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.185
3223	243	\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
3224	276	\begin{align*} y^{\prime \prime }+5 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
3225	536	\begin{align*} x^{\prime \prime }+x&=\cos \left (3 t \right ) \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.186
3226	7977	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
3227	9033	\begin{align*} {\mathrm e}^{y}+x \,{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
3228	9217	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
3229	10103	\begin{align*} y^{\prime \prime }-6 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.186
3230	10513	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.186
3231	11177	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.186
3232	11199	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.186
3233	11252	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.186
3234	14811	\begin{align*} -y+y^{\prime }&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.186
3235	20386	\begin{align*} y^{\prime } \left (y^{\prime }-y\right )&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	0.186
3236	22655	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
3237	23092	\begin{align*} x^{\prime }+y&=4 \\ x-y^{\prime }&=3 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.186
3238	24052	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=\cosh \left (2 x \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.186
3239	24773	\begin{align*} y^{2} {y^{\prime }}^{2}-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
3240	25659	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.186
3241	339	\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }+4 y&={\mathrm e}^{x}-x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.187
3242	404	\begin{align*} y^{\prime }&=y x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.187
3243	827	\begin{align*} 2 y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
3244	4551	\begin{align*} x^{\prime }-x-2 y&=16 \,{\mathrm e}^{t} t \\ 2 x-y^{\prime }-2 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.187
3245	6385	\begin{align*} \left (-y+a x y^{\prime }\right )^{2}+y^{\prime \prime } x&=b \\ \end{align*}	✗	✗	✗	✗	0.187
3246	8188	\begin{align*} x^{2} y^{\prime \prime \prime }-3 y^{\prime \prime } x +3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
3247	8893	\begin{align*} y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
3248	10934	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.187
3249	11049	\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.187
3250	11197	\begin{align*} x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.187
3251	12955	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (b x +a y\right ) y^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.187
3252	15208	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= -20 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.187
3253	16170	\begin{align*} 1&=x^{2}-9 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.187
3254	16966	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
3255	17017	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
3256	17612	\begin{align*} t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }&=\frac {45}{8 t^{{7}/{2}}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ y^{\prime \prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.187
3257	19444	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
3258	21282	\begin{align*} x^{\prime \prime }-2 x^{\prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.187
3259	21534	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=4 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.187
3260	23003	\begin{align*} 3 x^{\prime \prime }+19 x^{\prime }-14 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.187
3261	545	\begin{align*} x^{\prime \prime \prime }+x^{\prime \prime }-6 x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.188
3262	2159	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y&=-3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right ) \\ \end{align*}	✓	✓	✓	✓	0.188
3263	2670	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.188
3264	2679	\begin{align*} y^{\prime \prime }+y&=t \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.188
3265	3211	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.188
3266	3793	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=\sqrt {x}\, \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.188
3267	4090	\begin{align*} y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.188
3268	5477	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.188
3269	6477	\begin{align*} 2 y y^{\prime \prime }&=-a^{2}-4 \left (-x^{2}+b \right ) y^{2}+8 x y^{3}+3 y^{4}+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.188
3270	7214	\begin{align*} y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.188
3271	7449	\begin{align*} y \,{\mathrm e}^{y x}+2 x +\left (x \,{\mathrm e}^{y x}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.188
3272	8932	\begin{align*} y^{\prime \prime }-2 i y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.188
3273	10453	\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.188
3274	10595	\begin{align*} 2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.188
3275	10918	\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.188
3276	11030	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.188
3277	11176	\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.188
3278	11287	\begin{align*} y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.188
3279	14352	\begin{align*} x^{\prime }+x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.188
3280	15149	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.188
3281	18882	\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✗	0.188
3282	21578	\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=96 \,{\mathrm e}^{-4 x} \\ \end{align*}	✓	✓	✓	✓	0.188
3283	21892	\begin{align*} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.188
3284	22876	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.188
3285	23665	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=13 t +17+40 \sin \left (t \right ) \\ y \left (0\right ) &= 30 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.188
3286	24008	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.188
3287	25540	\begin{align*} y^{\prime \prime }&=2 a y^{\prime }-\left (a^{2}-\omega ^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	0.188
3288	273	\begin{align*} y^{\prime \prime }+y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.189
3289	2191	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+8 y^{\prime \prime }+8 y^{\prime }+4 y&=-2 \,{\mathrm e}^{x} \left (-\sin \left (x \right )+\cos \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.189
3290	7901	\begin{align*} 3 x^{2}+y^{2}-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	0.189
3291	18920	\begin{align*} y_{1}^{\prime }&=y_{2}-y_{3} \\ y_{2}^{\prime }&=y_{1}+y_{3}-{\mathrm e}^{-t} \\ y_{3}^{\prime }&=y_{1}+y_{2}+{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 2 \\ y_{3} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.189
3292	23699	\begin{align*} y^{\prime \prime }-y x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.189
3293	848	\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.190
3294	2314	\begin{align*} y^{\prime }+\frac {y}{\sqrt {t}}&={\mathrm e}^{\frac {\sqrt {t}}{2}} \\ \end{align*}	✓	✓	✓	✓	0.190
3295	2545	\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.190
3296	5782	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.190
3297	6459	\begin{align*} 2 {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
3298	10856	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
3299	11055	\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190
3300	11077	\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.190