2.3.42 Problems 4101 to 4200

Table 2.627: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4101	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*}	✓	✓	✓	✓	0.276
4102	4119	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
4103	5760	\begin{align*} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
4104	7044	\begin{align*} y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
4105	8716	\begin{align*} x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
4106	9652	\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.276
4107	9711	\begin{align*} x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
4108	10464	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
4109	10750	\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
4110	10929	\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*}	✓	✓	✓	✗	0.276
4111	12336	\begin{align*} y^{\prime \prime }+\sqrt {x}\, y^{\prime }+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
4112	16515	\begin{align*} y^{\prime \prime }-4 y^{\prime }+29 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
4113	20993	\begin{align*} x^{\prime }&=2 x-4 y \\ y^{\prime }&=-x+2 y \\ \end{align*}	✓	✓	✓	✓	0.276
4114	21727	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.276
4115	23405	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}-x \right ) y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.276
4116	24430	\begin{align*} y^{\prime \prime }-4 a y^{\prime }+3 a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.276
4117	843	\begin{align*} y^{\prime \prime }+2 y&=6 x \\ \end{align*}	✓	✓	✓	✓	0.277
4118	1397	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.277
4119	2212	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.277
4120	2567	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.277
4121	6243	\begin{align*} -\left (x +1\right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.277
4122	7822	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.277
4123	15082	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-\frac {1}{25}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.277
4124	15708	\begin{align*} y^{\prime }-2 y&=6 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.277
4125	19462	\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.277
4126	22252	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.277
4127	23019	\begin{align*} y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi \sqrt {3}}{6}\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.277
4128	23760	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.277
4129	515	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
4130	8128	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.278
4131	9216	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
4132	9315	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
4133	9462	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.278
4134	14342	\begin{align*} x^{\prime \prime }-\frac {\left (t +2\right ) x^{\prime }}{t}+\frac {\left (t +2\right ) x}{t^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
4135	15164	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
4136	18761	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
4137	18770	\begin{align*} 25 y^{\prime \prime }-20 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
4138	18777	\begin{align*} 9 y^{\prime \prime }-24 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.278
4139	20122	\begin{align*} x^{2} y y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2}-3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.278
4140	20146	\begin{align*} x^{4} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.278
4141	20454	\begin{align*} y&=y^{\prime } x -{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.278
4142	21913	\begin{align*} y^{\prime \prime }+n^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= k \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.278
4143	24923	\begin{align*} y^{\prime }&={\mathrm e}^{2 t}-1 \\ \end{align*}	✓	✓	✓	✓	0.278
4144	151	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.279
4145	1051	\begin{align*} 2 \left (x -1\right ) y^{\prime }&=3 y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.279
4146	2365	\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.279
4147	4493	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=12 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.279
4148	6681	\begin{align*} 4 y^{\prime }+5 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.279
4149	19628	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.279
4150	443	\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 \(x=1\).	✓	✓	✓	✓	0.280
4151	844	\begin{align*} y^{\prime \prime }+2 y&=6 x +4 \\ \end{align*}	✓	✓	✓	✓	0.280
4152	1259	\begin{align*} 6 y^{\prime \prime }-5 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.280
4153	2186	\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y&={\mathrm e}^{-x} \left (\left (4-x \right ) \cos \left (x \right )-\left (x +5\right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.280
4154	3403	\begin{align*} y^{\prime }&=2 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.280
4155	8067	\begin{align*} \left (1-x \right ) y^{\prime }&=x^{2}-y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.280
4156	8930	\begin{align*} y^{\prime \prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.280
4157	9109	\begin{align*} y-x +x y \cot \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
4158	10243	\begin{align*} y^{\prime }+y&=\frac {1}{x^{2}} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.280
4159	11144	\begin{align*} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.280
4160	12760	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-6 x^{3} \left (x -1\right ) \ln \left (x \right )+x^{3} \left (8+x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
4161	16516	\begin{align*} 9 y^{\prime \prime }+18 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
4162	20215	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{r}&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
4163	22237	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.280
4164	24777	\begin{align*} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.280
4165	26184	\begin{align*} y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.280
4166	1075	\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.281
4167	2175	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.281
4168	3792	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 x} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.281
4169	7899	\begin{align*} -y-3 \left (x^{2}+y^{2}\right ) x^{2}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
4170	10740	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
4171	11069	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
4172	16799	\begin{align*} y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
4173	18199	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.281
4174	19640	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.281
4175	20396	\begin{align*} {y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.281
4176	21288	\begin{align*} x^{\prime \prime }+x&=g \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
4177	21716	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \\ y \left (0\right ) &= -3 \\ y \left (1\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
4178	23408	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.281
4179	25058	\begin{align*} y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
4180	25318	\begin{align*} y^{\prime \prime }-y&=\delta \left (t -1\right )-\delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
4181	25630	\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
4182	25640	\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.281
4183	3228	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	0.282
4184	3686	\begin{align*} 2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.282
4185	3791	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=15 \,{\mathrm e}^{3 x} \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.282
4186	5782	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.282
4187	5872	\begin{align*} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
4188	9808	\begin{align*} 6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.282
4189	11323	\begin{align*} y^{\prime }-y^{2}+\sin \left (x \right ) y-\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.282
4190	22109	\begin{align*} y^{\prime \prime }-3 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.282
4191	24139	\begin{align*} x -\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.282
4192	26036	\begin{align*} y^{\prime \prime } x +y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.282
4193	26070	\begin{align*} y^{\prime }&=3 y-z \\ z^{\prime }&=y+3 z \\ \end{align*}	✓	✓	✓	✓	0.282
4194	1045	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.283
4195	1071	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.283
4196	3113	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.283
4197	3175	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.283
4198	3398	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=6 \left (-x^{2}+1\right )^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.283
4199	3413	\begin{align*} {y^{\prime }}^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.283
4200	3418	\begin{align*} y^{\prime }&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.283