2.3.52 Problems 5101 to 5200

Table 2.647: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5101	24538	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=-6 x^{2}-8 x +4 \\ \end{align*}	✓	✓	✓	✓	0.336
5102	25940	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.336
5103	26133	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=-2 x-y \\ \end{align*}	✓	✓	✓	✓	0.336
5104	6251	\begin{align*} -2 y-x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
5105	6945	\begin{align*} x^{2}+\cos \left (x \right ) y+\left (y^{3}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
5106	8035	\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
5107	8044	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (9 x^{2}+6\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
5108	9036	\begin{align*} y y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
5109	10471	\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
5110	10726	\begin{align*} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.337
5111	12837	\begin{align*} y^{\prime \prime }-6 y^{2}-x&=0 \\ \end{align*}	✗	✗	✗	✗	0.337
5112	15809	\begin{align*} y^{\prime }&=t^{2}+t \\ \end{align*}	✓	✓	✓	✓	0.337
5113	18228	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.337
5114	18395	\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
5115	21931	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.337
5116	22248	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.337
5117	24924	\begin{align*} y^{\prime }&=t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.337
5118	855	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.338
5119	1273	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
5120	1276	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
5121	1366	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338
5122	6509	\begin{align*} a y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
5123	10026	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
5124	11190	\begin{align*} x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
5125	15228	\begin{align*} y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.338
5126	18859	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.338
5127	19647	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.338
5128	22245	\begin{align*} y^{\prime \prime }-y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.338
5129	22793	\begin{align*} y^{\left (5\right )}-5 y^{\prime \prime }+4 y^{\prime }&=x^{2}-x +{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.338
5130	23998	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&={\mathrm e}^{x}+1 \\ \end{align*}	✓	✓	✓	✓	0.338
5131	24781	\begin{align*} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.338
5132	25193	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.338
5133	867	\begin{align*} 2 x^{\prime \prime }+16 x^{\prime }+40 x&=0 \\ x \left (0\right ) &= 5 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.339
5134	897	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.339
5135	971	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-5 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.339
5136	1069	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
5137	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*}	✓	✓	✓	✓	0.339
5138	6847	\begin{align*} x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
5139	12600	\begin{align*} y^{\prime \prime }&=-\frac {\left (3 x +a +2 b \right ) y^{\prime }}{2 \left (a +x \right ) \left (x +b \right )}-\frac {\left (a -b \right ) y}{4 \left (a +x \right )^{2} \left (x +b \right )} \\ \end{align*}	✓	✓	✓	✗	0.339
5140	15767	\begin{align*} x^{\prime }&=-x+2 y \\ y^{\prime }&=-2 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.339
5141	17420	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.339
5142	18159	\begin{align*} y^{\prime \prime }-4 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.339
5143	18321	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.339
5144	18684	\begin{align*} x^{\prime }&=3 x-4 y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.339
5145	19634	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.339
5146	21541	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.339
5147	21643	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
5148	22241	\begin{align*} y^{\prime }+2 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.339
5149	22684	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.339
5150	25242	\begin{align*} t y^{\prime \prime }+\left (2+2 t \right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.339
5151	26033	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
5152	26245	\begin{align*} \ln \left (y^{\prime }\right )&=x \\ \end{align*}	✓	✓	✓	✓	0.339
5153	634	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.340
5154	2254	\begin{align*} y_{1}^{\prime }&=-y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.340
5155	4125	\begin{align*} 4 y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
5156	7074	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.340
5157	8021	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.340
5158	8494	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.340
5159	8795	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=1+3 x \\ \end{align*}	✓	✓	✓	✓	0.340
5160	16640	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=100 \\ \end{align*}	✓	✓	✓	✓	0.340
5161	16801	\begin{align*} y^{\prime }&=3 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.340
5162	17731	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
5163	24877	\begin{align*} y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.340
5164	25621	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=12 \\ \end{align*}	✓	✓	✓	✓	0.340
5165	25948	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x^{2}+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.340
5166	899	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.341
5167	900	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.341
5168	6533	\begin{align*} a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	0.341
5169	6534	\begin{align*} y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=b x +a \\ \end{align*}	✗	✗	✗	✗	0.341
5170	9467	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	0.341
5171	9819	\begin{align*} x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
5172	12415	\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
5173	15988	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+4 y \\ \end{align*}	✓	✓	✓	✓	0.341
5174	16314	\begin{align*} {\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
5175	16649	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.341
5176	16788	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.341
5177	18375	\begin{align*} y^{\prime \prime }-\sin \left (x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.341
5178	18390	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
5179	18398	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\pi ^{2}-x^{2} \\ \end{align*}	✓	✓	✓	✓	0.341
5180	18909	\begin{align*} y^{\prime \prime \prime \prime }-9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.341
5181	19633	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=4 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.341
5182	20620	\begin{align*} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
5183	22795	\begin{align*} x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }&=\frac {\ln \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	0.341
5184	26109	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.341
5185	796	\begin{align*} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	0.342
5186	894	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.342
5187	1261	\begin{align*} y^{\prime \prime }+5 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.342
5188	1634	\begin{align*} y^{\prime }-\frac {\left (x +1\right ) y}{3 x}&=y^{4} \\ \end{align*}	✓	✓	✓	✓	0.342
5189	2176	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&={\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (1+6 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.342
5190	2236	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.342
5191	2418	\begin{align*} y^{\prime \prime }-y t^{3}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.342
5192	3423	\begin{align*} y^{\prime }&=\frac {t}{\sqrt {t}+1} \\ \end{align*}	✓	✓	✓	✓	0.342
5193	3854	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=-x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.342
5194	3883	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.342
5195	3925	\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-4 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.342
5196	4379	\begin{align*} 2 x^{3}-y^{4}+x y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
5197	5983	\begin{align*} -\left (i x^{2}+p^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
5198	6497	\begin{align*} x y y^{\prime \prime }&=-y y^{\prime }+x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.342
5199	8004	\begin{align*} y^{\prime \prime }+2 y&={\mathrm e}^{x}+2 \\ \end{align*}	✓	✓	✓	✓	0.342
5200	9719	\begin{align*} y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.342