2.3.53 Problems 5201 to 5300

Table 2.637: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5201	10612	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.407
5202	16835	\begin{align*} y^{\prime \prime }-3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.407
5203	23784	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.407
5204	24783	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.407
5205	434	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5206	613	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.408
5207	1364	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5208	1447	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.408
5209	4026	\begin{align*} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.408
5210	8746	\begin{align*} \left (1+y^{2} x^{2}\right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.408
5211	9457	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.408
5212	13027	\begin{align*} \left (-y+y^{\prime } x \right ) y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	0.408
5213	15724	\begin{align*} y^{\prime }-3 y&=\delta \left (x -1\right )+2 \operatorname {Heaviside}\left (x -2\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.408
5214	21642	\begin{align*} x^{\prime \prime }-s x&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	0.408
5215	21722	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=10 \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.408
5216	24097	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.408
5217	3273	\begin{align*} y^{\prime \prime }&=y^{3} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= \frac {\sqrt {2}}{2} \\ \end{align*}	✓	✓	✓	✗	0.409
5218	8576	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.409
5219	9363	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.409
5220	14379	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.409
5221	18026	\begin{align*} {y^{\prime }}^{2}-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.409
5222	21748	\begin{align*} y^{\prime }&=y-3 z \\ z^{\prime }&=2 y-4 z \\ \end{align*}	✓	✓	✓	✓	0.409
5223	25364	\begin{align*} y_{1}^{\prime }&=5 y_{1}-2 y_{2} \\ y_{2}^{\prime }&=4 y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.409
5224	3943	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12-6 \,{\mathrm e}^{t} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.410
5225	5522	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.410
5226	14398	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.410
5227	15468	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=3 x-y \\ \end{align*}	✓	✓	✓	✓	0.410
5228	15886	\begin{align*} y^{\prime }&=y^{2}-4 y+2 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	0.410
5229	23718	\begin{align*} 6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.410
5230	25366	\begin{align*} y_{1}^{\prime }&=2 y_{1}-y_{2} \\ y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.410
5231	446	\begin{align*} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.411
5232	631	\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.411
5233	634	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.411
5234	1380	\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
5235	2798	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.411
5236	3945	\begin{align*} y^{\prime \prime }-9 y&=13 \sin \left (2 t \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.411
5237	10650	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.411
5238	12964	\begin{align*} 3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \\ \end{align*}	✗	✓	✓	✗	0.411
5239	14203	\begin{align*} x^{\prime }&=t \cos \left (t^{2}\right ) \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.411
5240	15982	\begin{align*} x^{\prime }&=-2 x-3 y \\ y^{\prime }&=3 x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.411
5241	16980	\begin{align*} y^{\prime }&=\left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.411
5242	18228	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.411
5243	18451	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.411
5244	21945	\begin{align*} y^{\prime \prime }+4 y&=2 t -8 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.411
5245	22222	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411
5246	23810	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.411
5247	24054	\begin{align*} y^{\prime \prime }+9 y&=3 x -6 \\ y \left (0\right ) &= {\frac {1}{3}} \\ y^{\prime }\left (0\right ) &= {\frac {4}{3}} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.411
5248	25372	\begin{align*} y_{1}^{\prime }&=2 y_{1}-y_{2} \\ y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.411
5249	626	\begin{align*} x_{1}^{\prime }&=9 x_{1}+5 x_{2} \\ x_{2}^{\prime }&=-6 x_{1}-2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.412
5250	1365	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412
5251	6436	\begin{align*} y y^{\prime \prime }&=-2 y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.412
5252	7646	\begin{align*} y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.412
5253	15388	\begin{align*} y&=2 y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.412
5254	16185	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 16 \\ \end{align*}	✓	✓	✓	✓	0.412
5255	17044	\begin{align*} y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.412
5256	25371	\begin{align*} y_{1}^{\prime }&=-y_{1}+2 y_{2} \\ y_{2}^{\prime }&=-2 y_{1}-y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.412
5257	582	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=6 x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.413
5258	9612	\begin{align*} -y+y^{\prime }&=1+{\mathrm e}^{t} t \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.413
5259	11812	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.413
5260	12898	\begin{align*} x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right )&=0 \\ \end{align*}	✗	✗	✗	✗	0.413
5261	15858	\begin{align*} y^{\prime }&=\frac {1}{\left (2+y\right )^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.413
5262	19589	\begin{align*} n^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.413
5263	19654	\begin{align*} x^{\prime }&=5 x+2 y \\ y^{\prime }&=-17 x-5 y \\ \end{align*}	✓	✓	✓	✓	0.413
5264	20508	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{2}+\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.413
5265	21917	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.413
5266	23661	\begin{align*} y^{\prime \prime \prime }+y&=18 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 13 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.413
5267	25327	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.413
5268	6389	\begin{align*} a y \left (1-y^{n}\right )+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.414
5269	6854	\begin{align*} \frac {x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.414
5270	9072	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.414
5271	9820	\begin{align*} {y^{\prime }}^{3}-2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✗	✗	0.414
5272	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*}	✓	✓	✓	✗	0.414
5273	10626	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.414
5274	13191	\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ -6 & 11 & 2 \\ 6 & -15 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.414
5275	16277	\begin{align*} y^{\prime }-3 y&=6 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.414
5276	21315	\begin{align*} x_{1}^{\prime }&=-x_{1} \\ x_{2}^{\prime }&=-2 x_{2} \\ x_{3}^{\prime }&=x_{3} \\ \end{align*}	✓	✓	✓	✓	0.414
5277	24140	\begin{align*} x +\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.414
5278	24710	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.414
5279	25243	\begin{align*} -t y^{\prime \prime }+\left (-2+t \right ) y^{\prime }+y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.414
5280	25385	\begin{align*} y_{1}^{\prime }&=-2 y_{1}+y_{2} \\ y_{2}^{\prime }&=-4 y_{1}+3 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.414
5281	589	\begin{align*} x^{\prime }&=-3 x+2 y \\ y^{\prime }&=-3 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.415
5282	623	\begin{align*} x_{1}^{\prime }&=3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=3 x_{1}+2 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.415
5283	1018	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-4 x_{3} \\ x_{2}^{\prime }&=-x_{1}-x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.415
5284	2288	\begin{align*} y_{1}^{\prime }&=5 y_{1}-6 y_{2} \\ y_{2}^{\prime }&=3 y_{1}-y_{2} \\ \end{align*}	✓	✓	✓	✓	0.415
5285	3506	\begin{align*} y^{\prime \prime }-2 z y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.415
5286	3989	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.415
5287	4049	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.415
5288	4592	\begin{align*} y^{\prime \prime }-2 x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.415
5289	7370	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.415
5290	9747	\begin{align*} x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.415
5291	9996	\begin{align*} y^{\prime }&=1+\frac {\sec \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	0.415
5292	13292	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\mu x} y^{2}+\lambda y-a \,b^{2} {\mathrm e}^{\left (2 \lambda +\mu \right ) x} \\ \end{align*}	✓	✓	✓	✗	0.415
5293	15769	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=5 x+y \\ \end{align*}	✓	✓	✓	✓	0.415
5294	16193	\begin{align*} y^{\prime } x&=\sin \left (x^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.415
5295	19038	\begin{align*} x_{1}^{\prime }&=x_{2}-x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.415
5296	23600	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.415
5297	23605	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.415
5298	25386	\begin{align*} y_{1}^{\prime }&=5 y_{1}-3 y_{2} \\ y_{2}^{\prime }&=2 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.415
5299	1442	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.416
5300	2286	\begin{align*} y_{1}^{\prime }&=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-26 y_{1}+9 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.416