2.3.149 Problems 14801 to 14900

Table 2.829: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14801	21006	\begin{align*} x^{\prime }&=-2 x+3 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.119
14802	6379	\begin{align*} y^{\prime \prime } x&=\left (1-y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.120
14803	10030	\begin{align*} y&=x {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.120
14804	11858	\begin{align*} f \left (x {y^{\prime }}^{2}\right )+2 y^{\prime } x -y&=0 \\ \end{align*}	✗	✓	✓	✗	1.120
14805	14780	\begin{align*} x^{\prime }-y^{\prime }-2 x+4 y&=t \\ x^{\prime }+y^{\prime }-x-y&=1 \\ \end{align*}	✓	✓	✓	✓	1.120
14806	20787	\begin{align*} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.120
14807	3781	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+25 y&=0 \\ y \left (1\right ) &= \frac {3 \sqrt {3}}{2} \\ y^{\prime }\left (1\right ) &= {\frac {15}{2}} \\ \end{align*}	✓	✓	✓	✓	1.121
14808	5424	\begin{align*} {y^{\prime }}^{2}-x y^{\prime } y+y^{2} \ln \left (a y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.121
14809	5944	\begin{align*} -y-\left (2+x \right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.121
14810	4267	\begin{align*} y^{\prime } x&=y+x^{2}+9 y^{2} \\ \end{align*}	✓	✓	✓	✓	1.122
14811	12991	\begin{align*} x \left (x +1\right )^{2} y y^{\prime \prime }-x \left (x +1\right )^{2} {y^{\prime }}^{2}+2 \left (x +1\right )^{2} y y^{\prime }-a \left (2+x \right ) y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	1.122
14812	13933	\begin{align*} y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.122
14813	18957	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.122
14814	22926	\begin{align*} 3 x-y^{\prime }-2 y&=8 t \\ x^{\prime }-2 x+y&=16 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.122
14815	25674	\begin{align*} y^{\prime }+2 y x&=1 \\ \end{align*}	✓	✓	✓	✓	1.122
14816	563	\begin{align*} x^{\prime \prime }+4 x^{\prime }+13 x&=f \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.123
14817	15759	\begin{align*} y_{1}^{\prime }&=y_{1}+2 y_{2}-3 y_{3} \\ y_{2}^{\prime }&=-3 y_{1}+4 y_{2}-2 y_{3} \\ y_{3}^{\prime }&=2 y_{1}+y_{3} \\ \end{align*}	✓	✓	✓	✓	1.123
14818	15824	\begin{align*} y^{\prime }&=y^{2}+y \\ \end{align*}	✓	✓	✓	✓	1.123
14819	20096	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	1.124
14820	20727	\begin{align*} x^{2} \left (y-y^{\prime } x \right )&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.124
14821	5299	\begin{align*} \left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.125
14822	5491	\begin{align*} 4 x {y^{\prime }}^{2}+4 y^{\prime } y-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	1.125
14823	9762	\begin{align*} y&=y^{\prime } x +x^{3} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.125
14824	12979	\begin{align*} a y y^{\prime }+2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.125
14825	17162	\begin{align*} v^{\prime }+v&={\mathrm e}^{-s} \\ \end{align*}	✓	✓	✓	✓	1.125
14826	20635	\begin{align*} y^{\prime \prime }+\left (\tan \left (x \right )-1\right )^{2} y^{\prime }-n \left (n -1\right ) y \sec \left (x \right )^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	1.125
14827	149	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.126
14828	6124	\begin{align*} 6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.126
14829	7553	\begin{align*} y^{\prime }&=\left (x +y+1\right )^{2}-\left (x +y-1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.126
14830	17482	\begin{align*} y^{\prime \prime }+16 y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	1.126
14831	20804	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✗	1.126
14832	21144	\begin{align*} x^{\prime \prime }-x^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	1.126
14833	9629	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.127
14834	4768	\begin{align*} y^{\prime } x +\left (b x +a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.128
14835	5290	\begin{align*} \left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.128
14836	13017	\begin{align*} \left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.128
14837	20503	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x \\ \end{align*}	✓	✓	✓	✓	1.128
14838	25427	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.128
14839	3591	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	1.129
14840	6877	\begin{align*} {y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1&=0 \\ \end{align*}	✓	✓	✓	✓	1.129
14841	7815	\begin{align*} y^{\prime \prime }-7 y^{\prime }&=-3 \\ \end{align*}	✓	✓	✓	✓	1.129
14842	13790	\begin{align*} \left (a \left (a +1\right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.129
14843	15271	\begin{align*} x^{\prime }&=-\frac {x}{2}+2 y-3 z \\ y^{\prime }&=y-\frac {z}{2} \\ z^{\prime }&=-2 x+z \\ \end{align*}	✓	✓	✓	✓	1.129
14844	20437	\begin{align*} \left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.129
14845	1189	\begin{align*} y^{\prime }&=y \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.132
14846	12883	\begin{align*} y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	1.132
14847	17387	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.132
14848	20444	\begin{align*} y&=a y^{\prime }+b {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.132
14849	23274	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.132
14850	4245	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.133
14851	5591	\begin{align*} 3 y^{2} {y^{\prime }}^{2}-2 x y^{\prime } y-x^{2}+4 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.133
14852	15154	\begin{align*} y^{\prime \prime } x +2 x^{2} y^{\prime }+y \sin \left (x \right )&=\sinh \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	1.133
14853	16154	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.133
14854	17455	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	1.133
14855	25479	\begin{align*} y^{\prime }&=y \left (1-y\right ) \left (2-y\right ) \\ \end{align*}	✓	✓	✓	✓	1.133
14856	25726	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.133
14857	14922	\begin{align*} \theta ^{\prime \prime }+4 \theta &=0 \\ \theta \left (0\right ) &= 0 \\ \theta ^{\prime }\left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	1.134
14858	15094	\begin{align*} m x^{\prime \prime }&=f \left (x\right ) \\ \end{align*}	✓	✓	✓	✗	1.134
14859	16180	\begin{align*} y^{\prime \prime } x +2&=\sqrt {x} \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	1.134
14860	20135	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	1.134
14861	6064	\begin{align*} a^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.135
14862	7137	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.135
14863	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*}	✓	✓	✓	✗	1.135
14864	13227	\begin{align*} \left (a \,x^{n}+b \,x^{m}+c \right ) \left (y^{\prime }-y^{2}\right )+a n \left (n -1\right ) x^{-2+n}+b m \left (m -1\right ) x^{m -2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.135
14865	17533	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y&=t^{3}+2 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	1.135
14866	24937	\begin{align*} y^{\prime }&=y \left (t +y\right ) \\ \end{align*}	✓	✓	✓	✓	1.135
14867	9441	\begin{align*} p \left (1+p \right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✓	✓	✓	✓	1.136
14868	10233	\begin{align*} x^{\prime }&=x+2 y+2 t +1 \\ y^{\prime }&=5 x+y+3 t -1 \\ \end{align*}	✓	✓	✓	✓	1.136
14869	14707	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.136
14870	21757	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.136
14871	8762	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.137
14872	19385	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	1.137
14873	10005	\begin{align*} y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \\ \end{align*}	✗	✗	✗	✗	1.138
14874	14268	\begin{align*} x^{\prime }&=x \left (1+{\mathrm e}^{t} x\right ) \\ \end{align*}	✓	✓	✓	✓	1.138
14875	809	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	1.139
14876	14585	\begin{align*} 4 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.139
14877	16202	\begin{align*} y^{3}-25 y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.139
14878	20198	\begin{align*} -y+y^{\prime } x +y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.140
14879	1119	\begin{align*} -y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.141
14880	7151	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.141
14881	8457	\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.141
14882	18122	\begin{align*} y^{\prime \prime }&={\mathrm e}^{2 y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.141
14883	21673	\begin{align*} -y+\left (x +1\right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.141
14884	22620	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	1.141
14885	3424	\begin{align*} y^{\prime }&=2 y-4 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.142
14886	15034	\begin{align*} y^{\prime }&=\frac {2 y-x -4}{2 x -y+5} \\ \end{align*}	✓	✓	✓	✓	1.142
14887	19488	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.142
14888	12573	\begin{align*} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+y x -1&=0 \\ \end{align*}	✓	✓	✓	✓	1.143
14889	16216	\begin{align*} y^{\prime }&=\sin \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	1.143
14890	16048	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=-2 y+3 z \\ z^{\prime }&=-x+3 y-z \\ \end{align*}	✓	✓	✓	✓	1.144
14891	5047	\begin{align*} y^{\prime } y&=\sqrt {y^{2}+a^{2}} \\ \end{align*}	✓	✓	✓	✓	1.145
14892	13051	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-3 y^{\prime } {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.145
14893	13726	\begin{align*} y^{\prime \prime } x +n y^{\prime }+b \,x^{1-2 n} y&=0 \\ \end{align*}	✓	✓	✓	✗	1.145
14894	13762	\begin{align*} y^{\prime \prime } x +\left (a \,x^{n}+b x \right ) y^{\prime }+\left (a b \,x^{n}+x^{n -1} a n -b \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	1.145
14895	15370	\begin{align*} y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\ \end{align*}	✓	✓	✓	✗	1.145
14896	17381	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.145
14897	18029	\begin{align*} y^{\prime }&=y^{{2}/{3}}+a \\ \end{align*}	✓	✓	✓	✓	1.145
14898	22288	\begin{align*} y^{\prime \prime }+y&=x \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	1.145
14899	6067	\begin{align*} a -2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.146
14900	3328	\begin{align*} y&=y^{\prime } x +\frac {3}{{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.147