2.3.153 Problems 15201 to 15300

Table 2.849: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15201	6466	\begin{align*} \left (x -y\right ) y^{\prime \prime }&=f \left (y^{\prime }\right ) \\ \end{align*}	✗	✓	✓	✗	1.894
15202	15366	\begin{align*} \left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.894
15203	21320	\begin{align*} x^{\prime \prime }+6 x^{5}&=0 \\ x \left (0\right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.895
15204	12391	\begin{align*} y^{\prime \prime } x +\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	1.896
15205	12937	\begin{align*} y y^{\prime \prime }+a \left (1+{y^{\prime }}^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.896
15206	22353	\begin{align*} y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	1.896
15207	22805	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \left (2+y^{\prime } x -4 y^{2} y^{\prime }\right ) \\ \end{align*}	✓	✓	✗	✗	1.896
15208	9755	\begin{align*} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✗	✗	1.898
15209	12629	\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	1.899
15210	11434	\begin{align*} x^{2} y^{\prime }-\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.901
15211	15043	\begin{align*} y^{\prime }&=\left (x -5 y\right )^{{1}/{3}}+2 \\ \end{align*}	✓	✓	✓	✓	1.901
15212	26223	\begin{align*} y^{\prime }&=a x +b y+c \\ \end{align*}	✓	✓	✓	✓	1.902
15213	11699	\begin{align*} x {y^{\prime }}^{2}+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.903
15214	2809	\begin{align*} x^{\prime }&=-x \left (1-x\right ) \\ \end{align*}	✓	✓	✓	✓	1.904
15215	8738	\begin{align*} 2 x^{2} y^{\prime }&=y^{3}+y x \\ \end{align*}	✓	✓	✓	✓	1.904
15216	19345	\begin{align*} 2 y-x^{3}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	1.904
15217	21029	\begin{align*} x^{\prime }&=\frac {3 x^{{1}/{3}}}{2} \\ x \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✗	1.904
15218	23920	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.904
15219	25685	\begin{align*} \left (-1+y\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.904
15220	20747	\begin{align*} x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	1.905
15221	6305	\begin{align*} y^{\prime \prime }&=f \left (x \right )+g \left (x \right ) y+2 y^{3} \\ \end{align*}	✗	✗	✗	✗	1.906
15222	8544	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.906
15223	13694	\begin{align*} y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.906
15224	25309	\begin{align*} y+y^{\prime }&=\delta \left (t -1\right )-\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.906
15225	3436	\begin{align*} y^{\prime }&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.907
15226	6420	\begin{align*} y y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✗	1.907
15227	8980	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.907
15228	20978	\begin{align*} x y^{2}-y^{3}+\left (1-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.907
15229	3257	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.908
15230	9846	\begin{align*} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.908
15231	11751	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.908
15232	7306	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.909
15233	15375	\begin{align*} 3 y^{2} y^{\prime }-a y^{3}-x -1&=0 \\ \end{align*}	✓	✓	✓	✓	1.909
15234	23619	\begin{align*} x^{\prime }&=x+2 y+z-w \\ y^{\prime }&=-y+2 z+2 w \\ z^{\prime }&=2 y+2 z+2 w \\ w^{\prime }&=-3 y-6 z-6 w \\ \end{align*}	✓	✓	✓	✓	1.909
15235	7643	\begin{align*} y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	1.911
15236	13853	\begin{align*} x^{2} \left (a x +b \right ) y^{\prime \prime }-2 x \left (a x +2 b \right ) y^{\prime }+2 \left (a x +3 b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.911
15237	18584	\begin{align*} y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.911
15238	21170	\begin{align*} t^{2} x^{\prime \prime }+a t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	1.911
15239	24941	\begin{align*} y^{\prime }&=y-t^{2} \\ \end{align*}	✓	✓	✓	✓	1.911
15240	5525	\begin{align*} \left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +b +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.912
15241	11825	\begin{align*} {y^{\prime }}^{3} \sin \left (x \right )-\left (\sin \left (x \right ) y-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+\sin \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.912
15242	19271	\begin{align*} y^{\prime }&=2 y x +1 \\ \end{align*}	✓	✓	✓	✓	1.912
15243	3984	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.913
15244	26077	\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}	✓	✓	✓	✓	1.916
15245	15881	\begin{align*} y^{\prime }&=1+\cos \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.917
15246	18542	\begin{align*} \frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.917
15247	1244	\begin{align*} y^{\prime }&=\frac {x}{x^{2}+y^{3}+y} \\ \end{align*}	✓	✓	✓	✓	1.918
15248	11392	\begin{align*} y^{\prime } x -y-x^{2} \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.918
15249	15116	\begin{align*} x^{2} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	1.918
15250	9329	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\ln \left (x \right ) \\ y \left (1\right ) &= {\mathrm e} \\ y^{\prime }\left (1\right ) &= {\mathrm e}^{-1} \\ \end{align*}	✓	✓	✓	✓	1.919
15251	15120	\begin{align*} y^{\prime } x +y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	1.919
15252	16698	\begin{align*} y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	1.919
15253	15719	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.920
15254	2604	\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=t^{2}+\left (2 t +3\right ) \left (1+\cos \left (t \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.921
15255	17456	\begin{align*} y^{\prime \prime }&=t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.921
15256	24885	\begin{align*} y^{\prime \prime }+{\mathrm e}^{-2 y}&=0 \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	1.921
15257	6347	\begin{align*} y^{\prime \prime }&=\left (a -x \right ) {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	1.922
15258	14603	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	1.922
15259	5362	\begin{align*} {y^{\prime }}^{2}&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.924
15260	14767	\begin{align*} y^{\prime \prime } x +y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.924
15261	3588	\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.925
15262	8642	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=\left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.925
15263	11672	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.925
15264	21834	\begin{align*} 2+3 x -5 y+7 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.925
15265	23734	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{3}+x^{2}+x \right ) y^{\prime }+\left (4 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.925
15266	3557	\begin{align*} y^{\prime \prime }-25 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.926
15267	17386	\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.926
15268	23377	\begin{align*} x^{2} y^{\prime \prime }+\frac {7 y^{\prime } x}{2}-\frac {3 y}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.926
15269	1240	\begin{align*} \left (1+t \right ) y+y^{\prime } t&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	1.927
15270	21262	\begin{align*} x^{\prime \prime }+x+\frac {x^{2}}{3}&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.927
15271	25315	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=3 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.928
15272	4740	\begin{align*} y^{\prime }&=f \left (a +b x +c y\right ) \\ \end{align*}	✓	✓	✓	✓	1.930
15273	14839	\begin{align*} \frac {\left (1+t \right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	1.930
15274	25404	\begin{align*} y^{\prime }-9 y&=90 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.930
15275	18324	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \\ \end{align*}	✓	✓	✓	✗	1.931
15276	24290	\begin{align*} 3 \left (-1+y\right ) x +y+2+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.931
15277	19889	\begin{align*} z^{\prime }+5 y-2 z&=x \\ y^{\prime }+4 y+z&=x \\ \end{align*}	✓	✓	✓	✓	1.932
15278	25461	\begin{align*} y^{\prime }&=t +2 y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.932
15279	1229	\begin{align*} y^{\prime }+y&=\frac {1}{{\mathrm e}^{x}+1} \\ \end{align*}	✓	✓	✓	✓	1.933
15280	692	\begin{align*} y^{\prime }&=1+x +y+y x \\ \end{align*}	✓	✓	✓	✓	1.935
15281	3446	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.935
15282	6312	\begin{align*} y^{\prime \prime }&=f \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	1.936
15283	21869	\begin{align*} y-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.936
15284	22315	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.936
15285	6070	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=\left (-x^{2}+1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.937
15286	3537	\begin{align*} t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.938
15287	19095	\begin{align*} y^{\prime }&=k y+f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.938
15288	11583	\begin{align*} \left (6 y-x \right )^{2} y^{\prime }-6 y^{2}+2 y x +a&=0 \\ \end{align*}	✓	✓	✓	✓	1.939
15289	762	\begin{align*} 2 x y^{2}+3 x^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.940
15290	26235	\begin{align*} -y^{\prime } x +y&=a \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	1.940
15291	8883	\begin{align*} 2 y+y^{\prime }&=b \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.941
15292	20497	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	1.941
15293	19055	\begin{align*} x_{1}^{\prime }&=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\ x_{2}^{\prime }&=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\ x_{3}^{\prime }&=-2 x_{1}-2 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.942
15294	25561	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.942
15295	3411	\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.943
15296	6499	\begin{align*} 2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.943
15297	8525	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.943
15298	21728	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{4}\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	1.943
15299	18509	\begin{align*} y^{\prime }&=\frac {a y+b}{d +c y} \\ \end{align*}	✓	✓	✓	✓	1.944
15300	21125	\begin{align*} x^{\prime \prime }-x&=0 \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.944