2.3.144 Problems 14301 to 14400

Table 2.819: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14301	20852	\begin{align*} y^{\prime \prime }+y^{\prime }&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.008
14302	21141	\begin{align*} x^{\prime \prime }+x&=\sin \left (2 t \right )-\cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.008
14303	22705	\begin{align*} s^{\prime \prime }+s^{\prime }&=t +{\mathrm e}^{-t} \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.008
14304	24239	\begin{align*} y^{\prime }&=x -3 y \\ \end{align*}	✓	✓	✓	✓	1.008
14305	5400	\begin{align*} {y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.009
14306	6160	\begin{align*} 5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.009
14307	7686	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.009
14308	8459	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=\left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.009
14309	9871	\begin{align*} 2 y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.009
14310	15656	\begin{align*} x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2} \\ y \left (5\right ) &= 0 \\ y^{\prime }\left (5\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.009
14311	1348	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✗	1.010
14312	2178	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=-{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.010
14313	3393	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y&=-2 x^{2}+x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.010
14314	4227	\begin{align*} y^{\prime } x&=y x +y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.010
14315	17535	\begin{align*} t y^{\prime \prime }+2 y^{\prime }+t y&=-t \\ y \left (\pi \right ) &= -1 \\ y^{\prime }\left (\pi \right ) &= -\frac {1}{\pi } \\ \end{align*}	✓	✓	✓	✗	1.010
14316	17623	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.010
14317	17764	\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	1.010
14318	21738	\begin{align*} x^{\prime }&=2 x+2 y-z \\ y^{\prime }&=y+z \\ z^{\prime }&=z-y \\ \end{align*}	✓	✓	✓	✓	1.010
14319	23015	\begin{align*} 4 y^{\prime \prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.010
14320	9961	\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.011
14321	13298	\begin{align*} y^{\prime }&={\mathrm e}^{\mu x} \left (y-b \,{\mathrm e}^{\lambda x}\right )^{2}+b \lambda \,{\mathrm e}^{\lambda x} \\ \end{align*}	✓	✓	✓	✗	1.011
14322	18125	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.011
14323	20478	\begin{align*} 8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \\ \end{align*}	✓	✓	✓	✗	1.011
14324	13789	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (a^{2} x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.012
14325	15255	\begin{align*} t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y&=\ln \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	1.012
14326	17020	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.012
14327	23375	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.012
14328	229	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 7 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.013
14329	5599	\begin{align*} x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✗	1.013
14330	13783	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2 n} \left (b \,x^{n}+c \right )^{m}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.013
14331	15162	\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+4 y x&=2 x \\ \end{align*}	✓	✓	✓	✗	1.013
14332	17448	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=-32 t^{2} \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.013
14333	22942	\begin{align*} x^{\prime }-2 x+y&={\mathrm e}^{-t} \\ y^{\prime }-3 x+2 y&=t \\ \end{align*}	✓	✓	✓	✓	1.013
14334	5469	\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime } y+a&=0 \\ \end{align*}	✓	✓	✓	✗	1.014
14335	5930	\begin{align*} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=4 x^{3} {\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✗	1.014
14336	7971	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.014
14337	16568	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.014
14338	19207	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✗	✗	1.014
14339	20211	\begin{align*} 4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\ \end{align*}	✓	✓	✓	✓	1.014
14340	22134	\begin{align*} y^{\prime }-5 y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.014
14341	6282	\begin{align*} A y+\left (c \,x^{2}+b x +a \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.015
14342	9910	\begin{align*} y^{\prime \prime } x -\left (x +3\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.015
14343	12694	\begin{align*} y^{\prime \prime }&=\frac {\cos \left (2 x \right ) y^{\prime }}{\sin \left (2 x \right )}-2 y \\ \end{align*}	✓	✓	✓	✗	1.015
14344	15773	\begin{align*} x^{\prime }&=3 x-2 y-6 \\ y^{\prime }&=4 x-y+2 \\ \end{align*}	✓	✓	✓	✓	1.015
14345	22803	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.015
14346	2434	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.016
14347	3918	\begin{align*} x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}+t \\ x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3}+1 \\ \end{align*}	✓	✓	✓	✓	1.016
14348	5868	\begin{align*} -y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.016
14349	8856	\begin{align*} y^{\prime \prime }&=2+x \\ \end{align*}	✓	✓	✓	✓	1.016
14350	9867	\begin{align*} 2 x \left (x +3\right ) y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.016
14351	20587	\begin{align*} x^{4} y^{\prime \prime }-x^{3} y^{\prime }&=x^{2} {y^{\prime }}^{2}-4 y^{2} \\ \end{align*}	✗	✓	✓	✗	1.016
14352	1350	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=g \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.017
14353	2808	\begin{align*} x^{\prime }&=x \left (1-x\right ) \\ \end{align*}	✓	✓	✓	✓	1.017
14354	3566	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.017
14355	6001	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.017
14356	6784	\begin{align*} y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )}&=a x +b \cos \left (x \right )+c \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.017
14357	8529	\begin{align*} y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.017
14358	13711	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.017
14359	23155	\begin{align*} -y+y^{\prime } x&=2 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.017
14360	23190	\begin{align*} x -y+\left (y-x +2\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.017
14361	25030	\begin{align*} 2 t^{2}-y+\left (t +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	1.017
14362	23233	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.018
14363	3243	\begin{align*} y^{\prime \prime }&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.019
14364	5389	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x +x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.019
14365	16492	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.019
14366	18301	\begin{align*} x^{2} y^{\prime \prime }-2 y&=\sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.019
14367	2565	\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.020
14368	16267	\begin{align*} 2 y+y^{\prime }&=20 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	1.020
14369	20647	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=-4 x^{3} \\ \end{align*}	✓	✓	✓	✗	1.020
14370	22338	\begin{align*} {| y^{\prime }|}+{| y|}&=0 \\ \end{align*}	✓	✓	✓	✗	1.020
14371	5744	\begin{align*} \left (x^{2}+a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.021
14372	9277	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.021
14373	17135	\begin{align*} y^{\prime }&=16 y-8 y^{2} \\ \end{align*}	✓	✓	✓	✓	1.021
14374	20535	\begin{align*} y^{\prime \prime }&=x +\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.021
14375	18769	\begin{align*} 4 y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.022
14376	21678	\begin{align*} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.022
14377	647	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ x_{3}^{\prime }&=3 x_{2}+3 x_{3} \\ x_{4}^{\prime }&=4 x_{3}+4 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.023
14378	2399	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.023
14379	5712	\begin{align*} y^{\prime \prime }&=\operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right ) \\ \end{align*}	✓	✓	✓	✓	1.023
14380	5810	\begin{align*} b y+a y^{\prime }+y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.023
14381	10224	\begin{align*} x^{2} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.023
14382	17666	\begin{align*} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.023
14383	18646	\begin{align*} x^{\prime }&=-5 x+4 y-35 \\ y^{\prime }&=-2 x+y-11 \\ \end{align*}	✓	✓	✓	✓	1.023
14384	121	\begin{align*} y^{\prime }&=\left (4 x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.024
14385	1332	\begin{align*} t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.024
14386	17621	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.024
14387	6275	\begin{align*} -y-2 \left (a -x \right )^{3} y^{\prime }+\left (a -x \right )^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.025
14388	8224	\begin{align*} y^{\prime }&=y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	1.025
14389	19611	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.025
14390	1114	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.026
14391	3697	\begin{align*} y^{\prime \prime }-36 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.026
14392	7369	\begin{align*} y^{\prime \prime }&=y \\ \end{align*}	✓	✓	✓	✓	1.026
14393	13716	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.026
14394	15842	\begin{align*} w^{\prime }&=\left (3-w\right ) \left (w+1\right ) \\ w \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✗	✗	1.026
14395	16561	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +10 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.026
14396	16974	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.026
14397	25481	\begin{align*} y^{\prime }&=2 \left (1-y\right ) \left (1-{\mathrm e}^{y}\right ) \\ \end{align*}	✓	✓	✓	✓	1.026
14398	2443	\begin{align*} \left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	1.027
14399	8724	\begin{align*} y^{\prime }&=\frac {2 y-x +5}{2 x -y-4} \\ \end{align*}	✓	✓	✓	✓	1.027
14400	17518	\begin{align*} y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \tan \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.027