2.3.198 Problems 19701 to 19800

Table 2.969: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19701	24967	\begin{align*} t y y^{\prime }+t^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	4.097
19702	1557	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=\frac {\sin \left (x \right )}{x +1} \\ \end{align*}	✓	✓	✓	✓	4.099
19703	3625	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	4.100
19704	7739	\begin{align*} x y^{\prime }+2 y&=3 x -1 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.101
19705	15959	\begin{align*} y^{\prime }&=2 y t +3 t \,{\mathrm e}^{t^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.101
19706	2840	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.102
19707	11410	\begin{align*} x y^{\prime }+f \left (x \right ) \left (y^{2}-x^{2}\right )-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.102
19708	5971	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.104
19709	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*}	✓	✓	✓	✓	4.105
19710	27330	\begin{align*} \left (x^{2}+1\right ) \left (2 x +\cos \left (y\right ) y^{\prime }\right )&=2 \sin \left (y\right ) x \\ \end{align*}	✓	✓	✓	✓	4.105
19711	1163	\begin{align*} x^{2}+3 y x +y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.106
19712	10110	\begin{align*} y^{\prime \prime }-y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.106
19713	724	\begin{align*} x y^{\prime }&=3 y+x^{4} \cos \left (x \right ) \\ y \left (2 \pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.108
19714	19937	\begin{align*} x y^{\prime }-y&=x \sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	4.108
19715	23193	\begin{align*} y^{\prime }&=\frac {y-x +1}{3-x +y} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.108
19716	5944	\begin{align*} -y-\left (x +2\right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.109
19717	8389	\begin{align*} y^{\prime }&=y-y^{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	4.109
19718	10130	\begin{align*} y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	4.109
19719	18038	\begin{align*} 3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.109
19720	189	\begin{align*} x^{2} y^{\prime }&=y x +3 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.110
19721	17024	\begin{align*} y \cos \left (y x \right )+\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.111
19722	773	\begin{align*} y x +y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.112
19723	25429	\begin{align*} y^{\prime }-a y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	4.114
19724	8539	\begin{align*} y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.115
19725	8535	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.116
19726	15231	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.116
19727	7482	\begin{align*} 2 y^{2}+2 y+4 x^{2}+\left (2 y x +x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.119
19728	21970	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.119
19729	25352	\begin{align*} t y^{\prime \prime }-4 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	4.119
19730	4654	\begin{align*} y^{\prime }+1-x&=y \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✗	4.121
19731	11500	\begin{align*} 2 f \left (x \right ) y^{\prime }+2 f \left (x \right ) y^{2}-f^{\prime }\left (x \right ) y-2 f \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.121
19732	7559	\begin{align*} 2 \cos \left (2 x +y\right )-x^{2}+\left (\cos \left (2 x +y\right )+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.122
19733	11577	\begin{align*} 3 \left (y^{2}-x^{2}\right ) y^{\prime }+2 y^{3}-6 \left (x +1\right ) x y-3 \,{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	4.122
19734	16312	\begin{align*} y^{\prime }&=x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \\ \end{align*}	✓	✓	✓	✓	4.122
19735	7726	\begin{align*} \left (y x +1\right ) y+x \left (1+y x +x^{2} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.123
19736	7507	\begin{align*} y^{\prime }&=\left (x -y+5\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.124
19737	21049	\begin{align*} x^{\prime }&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	4.125
19738	25273	\begin{align*} t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=t^{4} \\ \end{align*}	✓	✓	✓	✓	4.125
19739	12052	\begin{align*} y^{\prime }&=\frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \\ \end{align*}	✓	✓	✓	✗	4.126
19740	26403	\begin{align*} 2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.127
19741	4202	\begin{align*} \tan \left (x \right ) y^{\prime }+y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.128
19742	21399	\begin{align*} y-x y^{2}+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.128
19743	3577	\begin{align*} y^{\prime }&=\frac {1-y^{2}}{2 y x +2} \\ \end{align*}	✓	✓	✓	✓	4.129
19744	15968	\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}	✓	✓	✓	✓	4.130
19745	25479	\begin{align*} y^{\prime }&=y \left (1-y\right ) \left (2-y\right ) \\ \end{align*}	✓	✓	✓	✓	4.130
19746	25613	\begin{align*} y^{\prime }-a y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	4.131
19747	14900	\begin{align*} z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \\ \end{align*}	✓	✓	✓	✓	4.133
19748	4115	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.135
19749	13939	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{\mu x} \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+\mu \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	4.135
19750	19270	\begin{align*} x y y^{\prime }&=\left (x +1\right ) \left (y+1\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.135
19751	10278	\begin{align*} c y^{\prime }&=\frac {a x +b y^{2}}{r} \\ \end{align*}	✓	✓	✓	✗	4.136
19752	18078	\begin{align*} y^{\prime }+{y^{\prime }}^{2} x -y&=0 \\ \end{align*}	✓	✓	✓	✗	4.136
19753	22616	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-y&=1 \\ \end{align*}	✓	✓	✗	✓	4.137
19754	18544	\begin{align*} y+2 y^{\prime }&=3 t^{2} \\ \end{align*}	✓	✓	✓	✓	4.141
19755	2810	\begin{align*} x^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	4.142
19756	5541	\begin{align*} x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.142
19757	2870	\begin{align*} x +y&=x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.143
19758	3039	\begin{align*} x \sqrt {1-y}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.143
19759	17071	\begin{align*} 6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.144
19760	17918	\begin{align*} x +y-2+\left (1-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.144
19761	19895	\begin{align*} y^{\prime \prime }-k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.145
19762	8643	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	4.148
19763	10317	\begin{align*} {y^{\prime }}^{2}&=\frac {1}{x^{3} y^{4}} \\ \end{align*}	✓	✓	✓	✓	4.148
19764	7356	\begin{align*} 3 x^{2} y+x^{3} y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.151
19765	18015	\begin{align*} y&=\frac {3 x y^{\prime }}{2}+{\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	4.151
19766	27253	\begin{align*} 2 x^{2} y^{\prime }&=y^{3}+y x \\ \end{align*}	✓	✓	✓	✓	4.151
19767	22981	\begin{align*} y^{\prime }-6 y&={\mathrm e}^{6 t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.153
19768	15839	\begin{align*} y^{\prime }&=t -y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.154
19769	8311	\begin{align*} y^{\prime }&=\frac {1}{y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.155
19770	17470	\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.155
19771	26385	\begin{align*} y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.155
19772	13995	\begin{align*} 4 x y^{\prime }+3 y+{\mathrm e}^{x} x^{4} y^{5}&=0 \\ \end{align*}	✓	✓	✓	✓	4.156
19773	21373	\begin{align*} \sin \left (y\right ) x +\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	4.157
19774	1619	\begin{align*} y^{\prime }&=\sqrt {x +y} \\ \end{align*}	✓	✓	✓	✓	4.158
19775	8428	\begin{align*} x y^{\prime }-y&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.159
19776	8205	\begin{align*} y^{\prime }&=4+y^{2} \\ \end{align*}	✓	✓	✓	✓	4.160
19777	755	\begin{align*} 3 x y^{2} y^{\prime }&=3 x^{4}+y^{3} \\ \end{align*}	✓	✓	✓	✓	4.161
19778	1536	\begin{align*} y^{\prime }&=-\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \\ \end{align*}	✓	✓	✓	✓	4.161
19779	19093	\begin{align*} y^{\prime }&=\frac {x -y^{2}}{2 y \left (x +y^{2}\right )} \\ \end{align*}	✓	✓	✓	✓	4.161
19780	7855	\begin{align*} 4 y+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.162
19781	7516	\begin{align*} y^{\prime }+x y^{3}+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.164
19782	9013	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (x_{0} \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.164
19783	11402	\begin{align*} x y^{\prime }+x y^{2}-y-a \,x^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	4.166
19784	20811	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\ \end{align*}	✓	✓	✓	✓	4.166
19785	1588	\begin{align*} y^{\prime }+x \left (y^{2}+y\right )&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.167
19786	22453	\begin{align*} y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.167
19787	24855	\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	4.167
19788	1573	\begin{align*} x y^{\prime }-2 y&=-1 \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	4.168
19789	16143	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=\delta \left (t -1\right )-3 \delta \left (-4+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.168
19790	17170	\begin{align*} \left (t^{2}+4\right ) y^{\prime }+2 y t&=2 t \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	4.168
19791	5810	\begin{align*} b y+a y^{\prime }+y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.169
19792	24146	\begin{align*} x y^{2}+{\mathrm e}^{x} y^{\prime }&=0 \\ y \left (\infty \right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	4.170
19793	752	\begin{align*} 2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x}&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.172
19794	13358	\begin{align*} y^{\prime }&=a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	4.173
19795	15412	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.173
19796	4031	\begin{align*} x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.174
19797	6455	\begin{align*} g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+a {y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	4.174
19798	10129	\begin{align*} y^{\prime \prime }-x^{3} y^{\prime }-y x -x^{3}-x^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	4.174
19799	11454	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1&=0 \\ \end{align*}	✓	✓	✓	✓	4.174
19800	4300	\begin{align*} x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.175