2.3.198 Problems 19701 to 19800

Table 2.927: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19701	21930	\begin{align*} x y^{2}&=-y^{\prime } x +y \\ \end{align*}	✓	✓	✓	✓	7.444
19702	24127	\begin{align*} y \,{\mathrm e}^{2 x}-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.444
19703	13761	\begin{align*} y^{\prime \prime } x +\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{-2+n} y&=0 \\ \end{align*}	✗	✓	✗	✗	7.445
19704	4800	\begin{align*} y^{\prime } x&=a y+b \left (x^{2}+1\right ) y^{3} \\ \end{align*}	✓	✓	✓	✓	7.446
19705	24043	\begin{align*} y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	7.450
19706	17878	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.452
19707	23374	\begin{align*} -3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.452
19708	24128	\begin{align*} 1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	7.452
19709	4805	\begin{align*} y^{\prime } x +2 y&=-\sqrt {1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.455
19710	12276	\begin{align*} y^{\prime }&=\frac {\left (y-\operatorname {Si}\left (x \right )\right )^{2}+\sin \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	7.456
19711	20736	\begin{align*} \sin \left (y^{\prime } x \right ) \cos \left (y\right )&=\cos \left (y^{\prime } x \right ) \sin \left (y\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	7.457
19712	20690	\begin{align*} y^{\prime }+x \sin \left (2 y\right )&=x^{3} \cos \left (y\right )^{2} \\ \end{align*}	✗	✓	✓	✗	7.458
19713	20595	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	7.460
19714	10430	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{3}-x^{2} \\ \end{align*}	✓	✓	✓	✓	7.463
19715	5321	\begin{align*} 2 \left (x -y^{4}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	7.464
19716	10055	\begin{align*} a y^{2} y^{\prime \prime }+b y^{2}&=c \\ \end{align*}	✓	✓	✓	✓	7.470
19717	22015	\begin{align*} y^{\prime }&=\frac {x^{2}+2 y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✓	7.473
19718	1306	\begin{align*} 4 y^{\prime \prime }+12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.474
19719	9774	\begin{align*} y^{\prime \prime }+\beta ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	7.483
19720	17792	\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	7.484
19721	19821	\begin{align*} \left (5 x -2 y+7\right ) y^{\prime }&=10 x -4 y+6 \\ \end{align*}	✓	✓	✓	✓	7.487
19722	15303	\begin{align*} x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.488
19723	11437	\begin{align*} x^{2} y^{\prime }-y^{2}-y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.489
19724	24853	\begin{align*} {y^{\prime }}^{4}+y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✗	✗	7.490
19725	21962	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.491
19726	20813	\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}}{x} \\ \end{align*}	✓	✓	✓	✓	7.496
19727	8705	\begin{align*} -y+y^{\prime } x&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.509
19728	24164	\begin{align*} x +\sin \left (\frac {y}{x}\right )^{2} \left (-y^{\prime } x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	7.509
19729	1310	\begin{align*} 16 y^{\prime \prime }+24 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.510
19730	18560	\begin{align*} y^{\prime }&=2 t y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	7.510
19731	20960	\begin{align*} x^{\prime }&=x-\frac {\mu x}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	7.519
19732	20753	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	7.520
19733	3020	\begin{align*} \left (3 x +4 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}	✓	✓	✓	✓	7.521
19734	22420	\begin{align*} y^{\prime }&=\frac {y-2 x}{-x +2 y} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.525
19735	18808	\begin{align*} -3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.527
19736	24410	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.527
19737	12239	\begin{align*} y^{\prime }&=\frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \\ \end{align*}	✓	✓	✓	✗	7.529
19738	22398	\begin{align*} 2 x +3 y+4&=\left (4 x +6 y+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	7.530
19739	20828	\begin{align*} y&=2 y^{\prime } x +\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	7.532
19740	2517	\begin{align*} 3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.533
19741	16979	\begin{align*} \frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.533
19742	19329	\begin{align*} \left (x +y\right ) y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	7.534
19743	23163	\begin{align*} y y^{\prime }-7 y&=6 x \\ \end{align*}	✓	✓	✓	✗	7.534
19744	13342	\begin{align*} y^{\prime }&=y^{2}+a x \coth \left (b x \right )^{m} y+a \coth \left (b x \right )^{m} \\ \end{align*}	✓	✓	✓	✗	7.538
19745	17911	\begin{align*} x -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	7.538
19746	17635	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	7.542
19747	13391	\begin{align*} y^{\prime }&=a y^{2}+b \tan \left (x \right ) y+c \\ \end{align*}	✓	✓	✓	✗	7.543
19748	6079	\begin{align*} -\left (x^{2}+1\right ) y-4 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.544
19749	20794	\begin{align*} y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y&={\mathrm e}^{6 x} \\ \end{align*}	✓	✓	✓	✗	7.545
19750	3456	\begin{align*} y^{\prime }-x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	7.547
19751	16678	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=\frac {5}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	7.547
19752	6919	\begin{align*} x +y+\left (3 x +3 y-4\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	7.549
19753	17731	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.557
19754	21398	\begin{align*} y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	7.558
19755	5328	\begin{align*} x \left (x^{3}+y^{5}\right ) y^{\prime }&=\left (x^{3}-y^{5}\right ) y \\ \end{align*}	✓	✓	✓	✗	7.559
19756	15562	\begin{align*} y^{\prime }&=y x +\frac {1}{x^{2}+1} \\ y \left (-5\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.562
19757	23123	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	7.564
19758	21997	\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	7.566
19759	13958	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b \,{\mathrm e}^{\mu x}-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+c \,{\mathrm e}^{2 \lambda x}+{\mathrm e}^{2 \mu x} b^{2}+b \left (\mu -\lambda \right ) {\mathrm e}^{\mu x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	7.568
19760	11660	\begin{align*} {y^{\prime }}^{2}+a y+b \,x^{2}&=0 \\ \end{align*}	✓	✗	✓	✗	7.569
19761	22387	\begin{align*} x^{3}+y^{3}-y^{\prime } y^{2} x&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.569
19762	21863	\begin{align*} 2 {y^{\prime }}^{2}+y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	7.570
19763	21428	\begin{align*} y^{\prime }&=\frac {x -2 y}{2 x -y} \\ \end{align*}	✓	✓	✓	✓	7.571
19764	11880	\begin{align*} y^{\prime }&=\frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )} \\ \end{align*}	✓	✓	✓	✗	7.572
19765	16524	\begin{align*} y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	7.573
19766	4920	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	7.575
19767	24329	\begin{align*} y^{\prime } x&=y-y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.576
19768	15966	\begin{align*} y^{\prime }&=\left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \\ \end{align*}	✗	✗	✗	✗	7.580
19769	16423	\begin{align*} 2 x y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= \sqrt {3} \\ \end{align*}	✓	✓	✓	✓	7.588
19770	13743	\begin{align*} y^{\prime \prime } x +\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (2 a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	7.591
19771	19075	\begin{align*} \left (x +2 y+1\right ) y^{\prime }&=3+2 x +4 y \\ \end{align*}	✓	✓	✓	✓	7.591
19772	18305	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=2 \ln \left (x \right )^{2}+12 x \\ \end{align*}	✓	✓	✓	✓	7.592
19773	21555	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.592
19774	8310	\begin{align*} y y^{\prime }&=-x \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	7.593
19775	18777	\begin{align*} 9 y^{\prime \prime }-24 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.593
19776	3268	\begin{align*} y^{\prime \prime }+2 {y^{\prime }}^{2}&=2 \\ \end{align*}	✓	✓	✓	✗	7.599
19777	9098	\begin{align*} \frac {y^{\prime \prime }}{y^{\prime }}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	7.599
19778	11891	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )} \\ \end{align*}	✓	✓	✓	✗	7.599
19779	8808	\begin{align*} x x^{\prime \prime }-{x^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	7.600
19780	12188	\begin{align*} y^{\prime }&=\frac {4 x \left (-1+a \right ) \left (1+a \right )}{4 y+y^{4} a^{2}-2 a^{4} y^{2} x^{2}+4 y^{2} a^{2} x^{2}+a^{6} x^{4}-3 a^{4} x^{4}+3 a^{2} x^{4}-y^{4}-2 y^{2} x^{2}-x^{4}} \\ \end{align*}	✓	✓	✓	✗	7.602
19781	23873	\begin{align*} y^{\prime }&=\frac {x^{2} {\mathrm e}^{\frac {y}{x}}+y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✗	7.602
19782	8797	\begin{align*} y^{\prime \prime }+y&=4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	7.606
19783	1356	\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u&=0 \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.607
19784	5037	\begin{align*} y y^{\prime }+x^{3}+y&=0 \\ \end{align*}	✗	✗	✗	✗	7.607
19785	12215	\begin{align*} y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 y x +\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 y^{2} x^{2}}{4}-3 x y^{2}+\frac {3 x^{4} y}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \\ \end{align*}	✓	✓	✓	✓	7.610
19786	17359	\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.615
19787	15385	\begin{align*} \frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	7.622
19788	19377	\begin{align*} y^{\prime } x +y&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	7.622
19789	9221	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.625
19790	13640	\begin{align*} y^{\prime }&=-y^{3}+\frac {y^{2}}{\left (a x +b \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	7.625
19791	18770	\begin{align*} 25 y^{\prime \prime }-20 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.632
19792	4875	\begin{align*} x^{2} y^{\prime }&=\left (x +a y\right ) y \\ \end{align*}	✓	✓	✓	✓	7.641
19793	23126	\begin{align*} y^{\prime } x +\frac {y}{2 x +3}&=\ln \left (x -2\right ) \\ \end{align*}	✓	✓	✓	✓	7.642
19794	5197	\begin{align*} x^{2} \left (4 x -3 y\right ) y^{\prime }&=\left (6 x^{2}-3 y x +2 y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	7.644
19795	6038	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.645
19796	11331	\begin{align*} y^{\prime }-x y^{2}-3 y x&=0 \\ \end{align*}	✓	✓	✓	✓	7.645
19797	12223	\begin{align*} y^{\prime }&=\frac {-128 y x -24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 y^{2} x^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \\ \end{align*}	✓	✓	✓	✗	7.649
19798	17905	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}	✓	✓	✗	✗	7.649
19799	2503	\begin{align*} \left (t -\sqrt {t y}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	7.656
19800	2875	\begin{align*} y y^{\prime }+x&=2 y \\ \end{align*}	✓	✓	✓	✗	7.657