2.3.153 Problems 15201 to 15300

Table 2.837: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15201	15113	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.225
15202	25790	\begin{align*} y^{\prime }&=\frac {1}{y} \\ y \left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.225
15203	15816	\begin{align*} y^{\prime }&=2 y-t \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	1.226
15204	16232	\begin{align*} y^{\prime }&={\mathrm e}^{x +y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.226
15205	18161	\begin{align*} y^{\prime \prime }+k^{2} y&=k \sin \left (k x +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	1.226
15206	21331	\begin{align*} y^{\prime }&=6 y \\ \end{align*}	✓	✓	✓	✓	1.226
15207	15483	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.227
15208	15867	\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✗	✗	1.228
15209	19592	\begin{align*} x^{2} \left (x^{2}-1\right )^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.228
15210	25108	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.228
15211	25211	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=\frac {t^{2}+1}{-t^{2}+1} \\ y \left (2\right ) &= y_{1} \\ y^{\prime }\left (2\right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✗	1.228
15212	5970	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.229
15213	12571	\begin{align*} x^{3} y^{\prime \prime }-x^{2} y^{\prime }+y x -\ln \left (x \right )^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.229
15214	227	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.230
15215	710	\begin{align*} 2 y^{\prime } x +y&=10 \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	1.230
15216	1437	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\ x_{2}^{\prime }&=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.230
15217	2553	\begin{align*} t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y&=0 \\ \end{align*}	✓	✓	✓	✓	1.230
15218	17453	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	1.230
15219	1916	\begin{align*} \left (\beta \,x^{2}+x \alpha +1\right ) y^{\prime \prime }+\left (\delta x +\gamma \right ) y^{\prime }+\epsilon y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.231
15220	16237	\begin{align*} y^{\prime }&=\tan \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.231
15221	16473	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.231
15222	16999	\begin{align*} t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.231
15223	18531	\begin{align*} -y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.231
15224	18848	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.231
15225	8986	\begin{align*} y^{\prime \prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.232
15226	9780	\begin{align*} y^{\prime \prime }&=-{\mathrm e}^{-2 y} \\ y \left (3\right ) &= 0 \\ y^{\prime }\left (3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	1.232
15227	22873	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.232
15228	24005	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.234
15229	5967	\begin{align*} x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.235
15230	21174	\begin{align*} x^{\prime \prime }-t x^{\prime }+3 x&=0 \\ \end{align*}	✓	✓	✓	✗	1.235
15231	6057	\begin{align*} -y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.236
15232	13901	\begin{align*} x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y&=0 \\ \end{align*}	✗	✗	✗	✗	1.236
15233	23967	\begin{align*} x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.236
15234	4058	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.237
15235	5990	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.237
15236	7325	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=2 x \\ \end{align*}	✓	✓	✓	✓	1.237
15237	7956	\begin{align*} y {y^{\prime }}^{2}-y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.237
15238	8299	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.237
15239	15881	\begin{align*} y^{\prime }&=1+\cos \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.237
15240	20137	\begin{align*} 2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.237
15241	21968	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (\frac {\pi }{8}\right ) &= 0 \\ y \left (\frac {\pi }{6}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.237
15242	23567	\begin{align*} x_{1}^{\prime }&=x_{2}-x_{3}+x_{4} \\ x_{2}^{\prime }&=-x_{2}+x_{4} \\ x_{3}^{\prime }&=x_{3}-x_{4} \\ x_{4}^{\prime }&=2 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.237
15243	5103	\begin{align*} \left (5+2 x -4 y\right ) y^{\prime }&=x -2 y+3 \\ \end{align*}	✓	✓	✓	✓	1.238
15244	15504	\begin{align*} {y^{\prime }}^{2}-9 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.238
15245	16601	\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.238
15246	18361	\begin{align*} y^{\prime \prime }+\alpha y^{\prime }&=0 \\ y \left (0\right ) &= {\mathrm e}^{\alpha } \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.238
15247	19603	\begin{align*} 2 y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.238
15248	22342	\begin{align*} y^{\prime }+y x&=x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.238
15249	2087	\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.239
15250	5418	\begin{align*} {y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.239
15251	15815	\begin{align*} y^{\prime }&=3 y \left (1-y\right ) \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	1.239
15252	17355	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	1.239
15253	165	\begin{align*} y^{\prime }&=\sin \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	1.240
15254	3778	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\frac {x^{2}}{\ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	1.240
15255	17524	\begin{align*} y^{\prime \prime }+4 y&=\sec \left (2 t \right )+\tan \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.240
15256	20184	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \\ \end{align*}	✓	✓	✓	✗	1.240
15257	819	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.241
15258	23278	\begin{align*} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\ \end{align*}	✗	✗	✗	✗	1.241
15259	21618	\begin{align*} y^{\prime \prime }+2 b y^{\prime }+y&=k \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.242
15260	25701	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.242
15261	1302	\begin{align*} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.243
15262	1355	\begin{align*} u^{\prime \prime }+2 u&=0 \\ \end{align*}	✓	✓	✓	✓	1.243
15263	19237	\begin{align*} y^{\prime } x +y&=x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.243
15264	23628	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.243
15265	130	\begin{align*} 3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.244
15266	15295	\begin{align*} x^{\prime }&=x+5 y+10 \sinh \left (t \right ) \\ y^{\prime }&=19 x-13 y+24 \sinh \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.244
15267	15868	\begin{align*} y^{\prime }&=\cos \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.244
15268	16604	\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=4 x^{2}+2 x +3 \\ \end{align*}	✓	✓	✓	✓	1.244
15269	24263	\begin{align*} L i^{\prime }+R i&=e \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.244
15270	4662	\begin{align*} y^{\prime }&=\cos \left (2 x \right )+\left (\sin \left (2 x \right )+y\right ) y \\ \end{align*}	✓	✓	✓	✗	1.245
15271	17750	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=-3 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.246
15272	9385	\begin{align*} x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.247
15273	14746	\begin{align*} \left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.247
15274	18001	\begin{align*} x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	1.247
15275	23678	\begin{align*} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.247
15276	6150	\begin{align*} y-\left (x +1\right ) y^{\prime }+2 \left (x +1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.248
15277	15543	\begin{align*} y^{\prime }&=\ln \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	1.248
15278	20844	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.248
15279	6559	\begin{align*} \left (-\left (1-y\right ) \left (-y+a \right )+y \left (1-y\right )+\left (-y+a \right ) y\right ) {y^{\prime }}^{2}+2 \left (1-y\right ) \left (-y+a \right ) y y^{\prime \prime }&=\operatorname {a3} \left (1-y\right )^{2} \left (-y+a \right )^{2}+\operatorname {a1} \left (1-y\right )^{2} y^{2}+\operatorname {a2} \left (-y+a \right )^{2} y^{2}+\operatorname {a0} \left (-y+a \right )^{2} y^{2} \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	1.249
15280	17804	\begin{align*} x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= {\frac {1}{3}} \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.249
15281	2767	\begin{align*} x_{1}^{\prime }&=x_{1}+3 x_{2}+2 x_{3}+\sin \left (t \right ) \\ x_{2}^{\prime }&=-x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }&=4 x_{1}-x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	1.250
15282	2668	\begin{align*} t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.251
15283	4011	\begin{align*} 4 y^{\prime \prime } x -y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.251
15284	14508	\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	1.251
15285	15897	\begin{align*} y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.251
15286	3779	\begin{align*} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y&=x^{m} \ln \left (x \right )^{k} \\ \end{align*}	✓	✓	✓	✓	1.253
15287	19602	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.253
15288	18735	\begin{align*} \left (x -2\right ) y^{\prime \prime }+y^{\prime }+\left (x -2\right ) \tan \left (x \right ) y&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= 2 \\ \end{align*}	✗	✗	✗	✗	1.254
15289	7606	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.255
15290	17444	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.255
15291	21	\begin{align*} y^{\prime }&=y-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.256
15292	5361	\begin{align*} {y^{\prime }}^{2}&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	1.256
15293	660	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.257
15294	5893	\begin{align*} -a^{2} x^{3} y-y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.257
15295	8867	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.257
15296	8979	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=1 \\ \end{align*}	✓	✓	✓	✓	1.257
15297	15762	\begin{align*} y_{1}^{\prime }&=2 y_{1}+y_{2} \\ y_{2}^{\prime }&=-y_{1}+2 y_{2} \\ y_{3}^{\prime }&=3 y_{3}-4 y_{4} \\ y_{4}^{\prime }&=4 y_{3}+3 y_{4} \\ \end{align*}	✓	✓	✓	✓	1.257
15298	716	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.258
15299	5547	\begin{align*} y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	1.258
15300	7006	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.258