2.3.189 Problems 18801 to 18900

Table 2.909: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18801	4367	\begin{align*} y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.440
18802	25753	\begin{align*} y^{\prime }+y \sin \left (x \right )&=x \\ \end{align*}	✓	✓	✓	✓	2.440
18803	780	\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	2.441
18804	17313	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\ \end{align*}	✓	✓	✓	✓	2.441
18805	25466	\begin{align*} y^{\prime }&=\sin \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.441
18806	7444	\begin{align*} x^{\prime }&=\alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \\ x \left (0\right ) &= x_{0} \\ \end{align*}	✓	✓	✓	✓	2.442
18807	19791	\begin{align*} y^{\prime }&=x -y \\ \end{align*}	✓	✓	✓	✓	2.442
18808	14030	\begin{align*} 5 y x -3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.443
18809	1533	\begin{align*} y^{\prime }&=-\frac {y \left (1+y\right )}{x} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.444
18810	1700	\begin{align*} \left (2 x -1\right ) \left (y-1\right )+\left (2+x \right ) \left (x -3\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.444
18811	15948	\begin{align*} y^{\prime }&=\frac {t y}{t^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.445
18812	17170	\begin{align*} \left (t^{2}+4\right ) y^{\prime }+2 t y&=2 t \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	2.445
18813	2321	\begin{align*} \cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.446
18814	15124	\begin{align*} x \left (1+y\right )^{2}&=\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.447
18815	15857	\begin{align*} y^{\prime }&=\frac {1}{\left (1+y\right ) \left (t -2\right )} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.447
18816	24236	\begin{align*} 3 y x +3 y-4+\left (x +1\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.447
18817	4624	\begin{align*} y^{\prime }&={\mathrm e}^{-\sin \left (x \right )}-y \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.448
18818	24186	\begin{align*} y^{2}-2 y x +6 x -\left (x^{2}-2 y x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.448
18819	22469	\begin{align*} x^{2} y+y^{3}-x +\left (x^{3}-y+x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.449
18820	52	\begin{align*} y^{\prime } y&=x \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.450
18821	2989	\begin{align*} \csc \left (y\right ) \cot \left (y\right ) y^{\prime }&=\csc \left (y\right )+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.450
18822	15790	\begin{align*} y^{\prime }&=\frac {1}{t y+t +y+1} \\ \end{align*}	✓	✓	✓	✓	2.450
18823	1227	\begin{align*} \frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{y-2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.451
18824	13012	\begin{align*} y^{3} y^{\prime \prime }-a&=0 \\ \end{align*}	✓	✓	✓	✓	2.451
18825	16320	\begin{align*} 1+\ln \left (y x \right )+\frac {x y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	2.451
18826	17955	\begin{align*} \left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime }&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.451
18827	4613	\begin{align*} y^{\prime }&=a \sin \left (b x +c \right )+k y \\ \end{align*}	✓	✓	✓	✓	2.452
18828	8172	\begin{align*} y^{\prime }+4 y x&=8 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.453
18829	7409	\begin{align*} y^{\prime }&=2 y-2 t y \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.454
18830	12345	\begin{align*} b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.454
18831	4782	\begin{align*} y^{\prime } x&=\left (-y x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.455
18832	17349	\begin{align*} y^{\prime }&=-\frac {y}{t -2} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.456
18833	9932	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.457
18834	23761	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=\ln \left (x \right ) \\ y \left (1\right ) &= A \\ y \left (2\right ) &= B \\ \end{align*}	✓	✓	✓	✓	2.458
18835	17973	\begin{align*} 3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.459
18836	90	\begin{align*} y^{\prime } x&=2 y+\cos \left (x \right ) x^{3} \\ \end{align*}	✓	✓	✓	✓	2.462
18837	8302	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.463
18838	6	\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \\ y \left (-4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.464
18839	3430	\begin{align*} y^{\prime }&=\frac {y}{t} \\ \end{align*}	✓	✓	✓	✓	2.464
18840	17305	\begin{align*} y&=t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \\ \end{align*}	✓	✓	✓	✓	2.464
18841	17341	\begin{align*} {\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.464
18842	16349	\begin{align*} y^{\prime }&=\frac {3 y}{x +1}-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.465
18843	2485	\begin{align*} t y+\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✓	2.466
18844	19483	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.466
18845	21441	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.466
18846	7753	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.467
18847	8688	\begin{align*} y^{\prime }&=2 \sqrt {2 x +y+1} \\ \end{align*}	✓	✓	✓	✓	2.467
18848	9161	\begin{align*} y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	2.467
18849	7039	\begin{align*} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✓	2.468
18850	20218	\begin{align*} \sin \left (x \right ) y^{\prime }-y \cos \left (x \right )+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.468
18851	7750	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✓	2.469
18852	22016	\begin{align*} y^{\prime }&=\frac {y^{2}+2 x}{y x} \\ \end{align*}	✓	✓	✓	✓	2.469
18853	2554	\begin{align*} t^{2} y^{\prime \prime }+5 t y^{\prime }-2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.470
18854	11600	\begin{align*} \left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.470
18855	11684	\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.470
18856	1617	\begin{align*} y^{\prime }&=x \left (y^{2}-1\right )^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	2.471
18857	2480	\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.471
18858	2849	\begin{align*} y+3+\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.472
18859	15382	\begin{align*} \frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.472
18860	25019	\begin{align*} y+y^{\prime }&=t y^{3} \\ \end{align*}	✓	✓	✓	✓	2.472
18861	4696	\begin{align*} y^{\prime }+y \left (1-x y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.473
18862	17056	\begin{align*} y^{\prime }+y \sec \left (t \right )&=t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.473
18863	17856	\begin{align*} y^{\prime }&=\left (y-1\right ) x \\ \end{align*}	✓	✓	✓	✓	2.473
18864	700	\begin{align*} -y+y^{\prime } x&=2 x^{2} y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.474
18865	4636	\begin{align*} y^{\prime }&=y \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.474
18866	8348	\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.474
18867	16217	\begin{align*} y^{\prime } y&={\mathrm e}^{x -3 y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.474
18868	5370	\begin{align*} {y^{\prime }}^{2}&=a^{2} \left (1-\ln \left (y\right )^{2}\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	2.475
18869	14669	\begin{align*} y^{\prime \prime \prime \prime }+16 y&=x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right ) \\ \end{align*}	✓	✓	✓	✓	2.475
18870	17273	\begin{align*} t -y+t y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.475
18871	4786	\begin{align*} y^{\prime } x&=y \left (2 y x +1\right ) \\ \end{align*}	✓	✓	✓	✓	2.476
18872	7429	\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-4 x}-4 y \\ \end{align*}	✓	✓	✓	✓	2.476
18873	19691	\begin{align*} x^{\prime \prime }+3 x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.476
18874	11820	\begin{align*} 4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.477
18875	12428	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (-v^{2}+x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.477
18876	17234	\begin{align*} \frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✗	✗	✗	2.478
18877	23189	\begin{align*} 2 x -y \sin \left (y x \right )+\left (6 y^{2}-x \sin \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.478
18878	4529	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (-1+t \right ) \\ y \left (0\right ) &= 15 \\ y^{\prime }\left (0\right ) &= -6 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.479
18879	13775	\begin{align*} x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+2 a b x +b^{2}-b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.479
18880	2994	\begin{align*} 3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.480
18881	7936	\begin{align*} L i^{\prime }+R i&=E \sin \left (2 t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.480
18882	9924	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.480
18883	12314	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	2.480
18884	12923	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	2.480
18885	25034	\begin{align*} 2 t y+2 t^{3}+\left (t^{2}-y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.480
18886	3436	\begin{align*} y^{\prime }&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.481
18887	19101	\begin{align*} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.481
18888	83	\begin{align*} y^{\prime } x +y&=3 y x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.482
18889	3294	\begin{align*} y&=y^{\prime } x \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	2.483
18890	9200	\begin{align*} -y+y^{\prime } x&=2 x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.483
18891	9528	\begin{align*} x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.483
18892	15018	\begin{align*} y^{\prime } x +y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	2.483
18893	16287	\begin{align*} \cos \left (-4 y+8 x -3\right ) y^{\prime }&=2+2 \cos \left (-4 y+8 x -3\right ) \\ \end{align*}	✓	✓	✓	✓	2.483
18894	3625	\begin{align*} \sin \left (x \right ) y^{\prime }-y \cos \left (x \right )&=\sin \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	2.485
18895	9160	\begin{align*} 2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.485
18896	2340	\begin{align*} \frac {y^{2}}{2}-2 y \,{\mathrm e}^{t}+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.486
18897	25820	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.486
18898	5434	\begin{align*} {y^{\prime }}^{2}&={\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right ) \\ \end{align*}	✓	✓	✓	✗	2.487
18899	18473	\begin{align*} y^{\prime }&=\frac {x^{4}}{y} \\ \end{align*}	✓	✓	✓	✓	2.487
18900	6990	\begin{align*} 2 x y^{\prime } y+\left (x +1\right ) y^{2}&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.488