2.3.43 Problems 4201 to 4300

Table 2.629: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4201	7235	\begin{align*} \left ({\mathrm e}^{x}+1\right ) y^{\prime }+2 \,{\mathrm e}^{x} y&=\left ({\mathrm e}^{x}+1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.283
4202	7993	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-2 x^{2}+2 x +2 \\ \end{align*}	✓	✓	✓	✓	0.283
4203	8074	\begin{align*} y^{\prime \prime }-y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.283
4204	8891	\begin{align*} y^{\prime \prime }+2 i y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
4205	15689	\begin{align*} y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y&={\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.283
4206	15713	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2} \\ y \left (0\right ) &= {\frac {11}{4}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.283
4207	16395	\begin{align*} \left (y-3\right ) y^{\prime \prime }&=2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.283
4208	16725	\begin{align*} y^{\prime \prime }-8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
4209	16772	\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 9 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.283
4210	20412	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) x&=1 \\ \end{align*}	✓	✓	✓	✓	0.283
4211	23423	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.283
4212	23427	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.283
4213	24433	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= {\mathrm e}^{3} \\ \end{align*}	✓	✓	✓	✓	0.283
4214	24512	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
4215	25990	\begin{align*} y^{\prime }&=-y+2 z \\ z^{\prime }&=4 y+z \\ \end{align*}	✓	✓	✓	✓	0.283
4216	452	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.284
4217	1011	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.284
4218	2557	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
4219	4063	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.284
4220	6091	\begin{align*} -12 y-8 y^{\prime } x +\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
4221	6765	\begin{align*} x^{2} y^{\prime \prime \prime \prime }&=2 y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✓	0.284
4222	11094	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
4223	14568	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
4224	15432	\begin{align*} y^{\prime \prime }+6 y^{\prime }+5 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.284
4225	16852	\begin{align*} y^{\prime \prime }-y^{2}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.284
4226	18429	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.284
4227	20924	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.284
4228	23406	\begin{align*} x^{3} y^{\prime \prime }+\left (5 x^{3}-x^{2}\right ) y^{\prime }+2 \left (3 x^{3}-x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.284
4229	24473	\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
4230	24774	\begin{align*} x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.284
4231	25639	\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\delta \left (t \right ) \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.284
4232	5	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {2+x}} \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.285
4233	406	\begin{align*} \left (2 x -1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.285
4234	547	\begin{align*} x^{\prime \prime \prime \prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.285
4235	5759	\begin{align*} -\left (a^{2}-b \,{\mathrm e}^{x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.285
4236	6636	\begin{align*} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=3 x^{2}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.285
4237	9213	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.285
4238	10050	\begin{align*} y^{2} y^{\prime \prime }&=x \\ \end{align*}	✗	✓	✗	✗	0.285
4239	18380	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.285
4240	19037	\begin{align*} x_{1}^{\prime }&=-x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.285
4241	25076	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.285
4242	1488	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.286
4243	3199	\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{3}-\frac {\cos \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	0.286
4244	8612	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
4245	10560	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
4246	10722	\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {y^{\prime } x}{2}-\frac {3 y x}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
4247	10869	\begin{align*} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+y t^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
4248	15702	\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.286
4249	17384	\begin{align*} y^{\prime \prime }+5 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
4250	20882	\begin{align*} y^{\prime }&=2 y x -x^{3} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286
4251	22579	\begin{align*} x^{4} y^{\prime \prime \prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
4252	22664	\begin{align*} y a^{2} b^{2}+\left (a^{2}+b^{2}\right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=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*}	✓	✓	✓	✓	0.286
4253	23409	\begin{align*} y^{\prime \prime } x +\left (x -1\right ) y^{\prime }+\left (3-12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
4254	23411	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {9 y}{x^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.286
4255	23428	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.286
4256	901	\begin{align*} y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.287
4257	2726	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=t^{3} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.287
4258	3615	\begin{align*} 2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	0.287
4259	6650	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.287
4260	9221	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
4261	9610	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.287
4262	10860	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.287
4263	18892	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.287
4264	22335	\begin{align*} \left (y^{\prime }-2 x \right ) \left (y^{\prime }-3 x^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
4265	23519	\begin{align*} e i u^{\prime \prime \prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.287
4266	24072	\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.287
4267	24775	\begin{align*} x^{2} {y^{\prime }}^{2}-7 y y^{\prime } x +12 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.287
4268	26132	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.287
4269	2185	\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y&={\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.288
4270	9617	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.288
4271	13195	\(\left [\begin {array}{ccc} 3 & -2 & 1 \\ 1 & 0 & 1 \\ -1 & 1 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.288
4272	13626	\begin{align*} \left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+B y x +\left (A b +k \right ) y+B b x +b k \\ \end{align*}	✓	✓	✓	✓	0.288
4273	14273	\begin{align*} x^{3}+3 t x^{2} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.288
4274	15047	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.288
4275	16758	\begin{align*} y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.288
4276	18136	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.288
4277	20154	\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y&=2 x \\ \end{align*}	✓	✓	✓	✗	0.288
4278	23521	\begin{align*} e i u^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.288
4279	24469	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.288
4280	562	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.289
4281	1377	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.289
4282	3171	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.289
4283	3210	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.289
4284	3929	\begin{align*} 3 y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.289
4285	9222	\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.289
4286	13194	\(\left [\begin {array}{ccc} -2 & 4 & -1 \\ -3 & 5 & -1 \\ -1 & 1 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.289
4287	14996	\(\left [\begin {array}{cc} 6 & 0 \\ 0 & -13 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.289
4288	16778	\begin{align*} y^{\prime \prime }+8 y^{\prime }+17 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.289
4289	18908	\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 ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.289
4290	25629	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.289
4291	25977	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x -2\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.289
4292	7	\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.290
4293	467	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.290
4294	893	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.290
4295	1076	\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.290
4296	1333	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.290
4297	3189	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}-8 \\ \end{align*}	✓	✓	✓	✓	0.290
4298	3422	\begin{align*} y^{\prime }&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.290
4299	7213	\begin{align*} y^{\prime \prime }+\frac {y}{4 x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.290
4300	8339	\begin{align*} y^{\prime }&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.290