2.3.62 Problems 6101 to 6200

Table 2.655: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
6101	10305	\begin{align*} {y^{\prime }}^{n}&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
6102	10530	\begin{align*} \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
6103	10599	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
6104	10614	\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
6105	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*}	✓	✓	✓	✗	0.316
6106	10908	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
6107	15093	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y&=1 \\ \end{align*}	✓	✓	✓	✗	0.316
6108	15418	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
6109	15972	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.316
6110	16185	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 16 \\ \end{align*}	✓	✓	✓	✓	0.316
6111	16760	\begin{align*} 3 y+y^{\prime }&=\operatorname {Heaviside}\left (t -4\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.316
6112	18350	\begin{align*} x^{\prime \prime }+x {x^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
6113	18796	\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.316
6114	20453	\begin{align*} y^{2}-2 x y^{\prime } y+{y^{\prime }}^{2} \left (x^{2}-1\right )&=m \\ \end{align*}	✓	✓	✓	✗	0.316
6115	21713	\begin{align*} y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.316
6116	22198	\begin{align*} y^{\prime \prime }-\left (x -1\right ) y^{\prime }&=x^{2}-2 x \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	0.316
6117	263	\begin{align*} y^{\prime \prime }-2 y^{\prime }-5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.317
6118	1641	\begin{align*} y^{\prime }-y&=x \sqrt {y} \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	0.317
6119	2444	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y&=0 \\ \end{align*} Series expansion around \(t=-1\).	✗	✗	✓	✗	0.317
6120	3335	\begin{align*} y^{\prime }&=y x -x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.317
6121	3337	\begin{align*} y^{\prime }&=3 x +\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.317
6122	5827	\begin{align*} -\left (-4 x^{2}+3\right ) y-4 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.317
6123	8010	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.317
6124	8909	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.317
6125	9332	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.317
6126	14148	\begin{align*} \left (-x^{2}+2\right ) y+4 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.317
6127	14404	\begin{align*} x^{\prime }&=5 x-4 y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.317
6128	14664	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.317
6129	15705	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=-2 \sin \left (3 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.317
6130	15767	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.317
6131	16186	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 20 \\ \end{align*}	✓	✓	✓	✓	0.317
6132	16613	\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.317
6133	17823	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.317
6134	20447	\begin{align*} \left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	0.317
6135	21911	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.317
6136	23439	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.317
6137	24567	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x \\ y \left (0\right ) &= -3 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.317
6138	456	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.318
6139	1011	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}+5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.318
6140	1717	\begin{align*} 27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.318
6141	3813	\begin{align*} x_{1}^{\prime }&=2 x_{2} \\ x_{2}^{\prime }&=-2 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.318
6142	3993	\begin{align*} \left (x^{2}-3\right ) y^{\prime \prime }-3 y^{\prime } x -5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.318
6143	4165	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\ \end{align*}	✓	✓	✓	✓	0.318
6144	5588	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-y \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.318
6145	6439	\begin{align*} y y^{\prime \prime }&=y^{3}-y f^{\prime }\left (x \right )+f \left (x \right ) y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✗	✗	✓	✗	0.318
6146	6854	\begin{align*} \frac {x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y}{y^{2}+x^{2}}-\frac {x y^{\prime }}{y^{2}+x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.318
6147	7993	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-2 x^{2}+2 x +2 \\ \end{align*}	✓	✓	✓	✓	0.318
6148	10645	\begin{align*} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.318
6149	20031	\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}	✓	✓	✓	✓	0.318
6150	22915	\begin{align*} x^{\prime }-2 x+4 y&=0 \\ 3 x+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.318
6151	23293	\begin{align*} 3 y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.318
6152	23564	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.318
6153	24870	\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\ y \left (2\right ) &= 5 \\ y^{\prime }\left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.318
6154	25684	\begin{align*} y^{\prime }&=y^{2}+2 y-3 \\ \end{align*}	✓	✓	✓	✓	0.318
6155	333	\begin{align*} y^{\prime }+y^{\prime \prime \prime }&=2-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.319
6156	2222	\begin{align*} 4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 y^{\prime } x +2 y&=30 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.319
6157	3513	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-z y^{\prime }+m^{2} y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.319
6158	3998	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.319
6159	6581	\begin{align*} h \left (x \right )+g \left (y\right ) y^{\prime }+f \left (y^{\prime }\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.319
6160	7574	\begin{align*} y^{\prime \prime }+6 y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.319
6161	8197	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=5 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.319
6162	9465	\begin{align*} x^{\prime }&=5 x+4 y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.319
6163	9747	\begin{align*} x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.319
6164	10508	\begin{align*} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.319
6165	10643	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.319
6166	10648	\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.319
6167	15427	\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.319
6168	15473	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.319
6169	16495	\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.319
6170	18129	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	0.319
6171	20489	\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\ \end{align*}	✓	✓	✓	✓	0.319
6172	585	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-9 x+6 y \\ \end{align*}	✓	✓	✓	✓	0.320
6173	1083	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.320
6174	4133	\begin{align*} y^{\prime \prime }+2 y&={\mathrm e}^{x}+2 \\ \end{align*}	✓	✓	✓	✓	0.320
6175	7078	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.320
6176	10564	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.320
6177	14385	\begin{align*} x^{\prime }&=-2 x-y \\ y^{\prime }&=-4 y \\ \end{align*}	✓	✓	✓	✓	0.320
6178	15261	\begin{align*} y^{\prime \prime }-3 y^{\prime }-7 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.320
6179	15970	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.320
6180	16191	\begin{align*} y^{\prime }&={\mathrm e}^{-9 x^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.320
6181	16483	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.320
6182	16641	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.320
6183	16854	\begin{align*} y^{\prime }-{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.320
6184	18317	\begin{align*} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✗	0.320
6185	18695	\begin{align*} x^{\prime }&=2 x+\frac {y}{2} \\ y^{\prime }&=-\frac {x}{2}+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.320
6186	19475	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.320
6187	21536	\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	0.320
6188	23437	\begin{align*} y^{\prime \prime }+\left (x +3\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.320
6189	23774	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.320
6190	24081	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +20 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.320
6191	3498	\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=A x \\ \end{align*}	✓	✓	✓	✓	0.321
6192	5804	\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.321
6193	6389	\begin{align*} a y \left (1-y^{n}\right )+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.321
6194	7089	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.321
6195	7299	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=16 x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.321
6196	7657	\begin{align*} w^{\prime }+w x&={\mathrm e}^{x} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.321
6197	8815	\begin{align*} 4 y+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.321
6198	9289	\begin{align*} y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.321
6199	16651	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.321
6200	18343	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.321