2.3.188 Problems 18701 to 18800

Table 2.949: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18701	27218	\begin{align*} x y^{\prime }+y&=y^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.440
18702	11434	\begin{align*} x^{2} y^{\prime }-\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.441
18703	12019	\begin{align*} y^{\prime }&=\frac {x \left (-1+x -2 y x +2 x^{3}\right )}{x^{2}-y} \\ \end{align*}	✓	✓	✓	✗	3.441
18704	20271	\begin{align*} \left (x y^{2}+1+x \right ) y^{\prime }+y+y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.441
18705	27688	\begin{align*} y^{\prime \prime }+y&=1 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	3.441
18706	12909	\begin{align*} 2 \left (-x^{k}+4 x^{3}\right ) \left (y y^{\prime }+y^{\prime \prime }-y^{3}\right )-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+a x y+b&=0 \\ \end{align*}	✗	✗	✗	✗	3.443
18707	17656	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.444
18708	18812	\begin{align*} y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.444
18709	19087	\begin{align*} y^{\prime }&=\frac {y^{2}}{3}+\frac {2}{3 x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.444
18710	794	\begin{align*} 9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.445
18711	7033	\begin{align*} \left (y x -1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.445
18712	13944	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+c \left (a \,{\mathrm e}^{\lambda x}+b -c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.446
18713	14075	\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.446
18714	4096	\begin{align*} y^{\prime }&=\frac {y-2 x}{x} \\ \end{align*}	✓	✓	✓	✓	3.447
18715	5929	\begin{align*} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.447
18716	26285	\begin{align*} y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.447
18717	26332	\begin{align*} x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.447
18718	12649	\begin{align*} y^{\prime \prime }&=\frac {18 y}{\left (2 x +1\right )^{2} \left (x^{2}+x +1\right )} \\ \end{align*}	✓	✓	✓	✗	3.449
18719	26220	\begin{align*} \left (1+y^{2}\right ) {\mathrm e}^{2 x}-\left (1+y^{2}\right ) {\mathrm e}^{y} y^{\prime }-\left (y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.449
18720	2529	\begin{align*} y^{\prime }&={\mathrm e}^{\left (y-t \right )^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.450
18721	5651	\begin{align*} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.451
18722	20773	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.451
18723	24251	\begin{align*} 2 x \left (y-x^{2}\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.451
18724	1539	\begin{align*} x y^{\prime }+y \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.453
18725	18543	\begin{align*} 2 y+t y^{\prime }&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.453
18726	3330	\begin{align*} y&=x y^{\prime }+{\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	3.454
18727	25451	\begin{align*} y^{\prime }-\sqrt {3}\, y&=\sin \left (t \right )+\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.454
18728	25301	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <5 \\ 0 & 5\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.455
18729	11664	\begin{align*} {y^{\prime }}^{2}+a^{2} y^{2} \left (\ln \left (y\right )^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.456
18730	23185	\begin{align*} \cos \left (y\right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.456
18731	26633	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y+1&=0 \\ \end{align*}	✓	✓	✓	✗	3.456
18732	26464	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	3.457
18733	2489	\begin{align*} y^{\prime }&=\left (t +1\right ) \left (1+y\right ) \\ \end{align*}	✓	✓	✓	✓	3.459
18734	15538	\begin{align*} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.459
18735	4521	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.460
18736	9127	\begin{align*} y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.460
18737	14558	\begin{align*} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	3.460
18738	15786	\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}	✓	✓	✓	✓	3.460
18739	19334	\begin{align*} y-x y^{2}+\left (x^{2} y^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.460
18740	7022	\begin{align*} \left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	3.461
18741	16273	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.461
18742	19969	\begin{align*} \left (x -y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	3.461
18743	25476	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.461
18744	8348	\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.463
18745	16145	\begin{align*} y^{\prime \prime }+y^{\prime }+5 y&=\operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.463
18746	16230	\begin{align*} y y^{\prime }&=x y^{2}-9 x \\ \end{align*}	✓	✓	✓	✓	3.463
18747	22818	\begin{align*} y^{\prime }+2 y&=5 \delta \left (t -1\right ) \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.463
18748	4093	\begin{align*} x^{2}+x -1+\left (2 y x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.465
18749	20920	\begin{align*} y^{\prime \prime }+6 y^{\prime }+18 y&=2 \operatorname {Heaviside}\left (\pi -t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.465
18750	16334	\begin{align*} 4 y^{2}-x^{2} y^{2}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.467
18751	7750	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✓	3.468
18752	8738	\begin{align*} 2 x^{2} y^{\prime }&=y^{3}+y x \\ \end{align*}	✓	✓	✓	✓	3.468
18753	26240	\begin{align*} y^{\prime }+y \tan \left (x \right )&=x \tan \left (x \right )+1 \\ \end{align*}	✓	✓	✓	✓	3.468
18754	27204	\begin{align*} x y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	3.468
18755	9988	\begin{align*} y^{\prime }&=x \left (\cos \left (y\right )+y\right ) \\ \end{align*}	✓	✓	✓	✓	3.469
18756	14256	\begin{align*} R^{\prime }+\frac {R}{t}&=\frac {2}{t^{2}+1} \\ R \left (1\right ) &= 3 \ln \left (2\right ) \\ \end{align*}	✓	✓	✓	✓	3.471
18757	1131	\begin{align*} \sin \left (x \right ) y^{2}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.473
18758	19953	\begin{align*} y^{\prime }&=x^{3} y^{3}-y x \\ \end{align*}	✓	✓	✓	✓	3.473
18759	2062	\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.474
18760	10020	\begin{align*} y^{2}+\frac {2}{x}+2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.474
18761	14427	\begin{align*} {y^{\prime }}^{2}-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.474
18762	16751	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=\frac {1}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	3.474
18763	25665	\begin{align*} x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \\ \end{align*}	✓	✓	✓	✓	3.474
18764	8238	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.476
18765	24994	\begin{align*} y^{\prime }+a y&={\mathrm e}^{b t} \\ \end{align*}	✓	✓	✓	✓	3.476
18766	3450	\begin{align*} y^{\prime }&=\frac {2 y}{t +1} \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	3.477
18767	4430	\begin{align*} 2 x +y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.477
18768	5363	\begin{align*} {y^{\prime }}^{2}&=a^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.477
18769	24844	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4&=0 \\ \end{align*}	✓	✓	✓	✗	3.478
18770	9974	\begin{align*} x^{\prime } t +2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.479
18771	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*}	✓	✓	✓	✓	3.479
18772	7115	\begin{align*} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.480
18773	4027	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.481
18774	16964	\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.482
18775	25457	\begin{align*} y^{\prime }&=y-t^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.482
18776	6004	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.483
18777	20573	\begin{align*} a y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.483
18778	4190	\begin{align*} y^{\prime }-y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	3.484
18779	3521	\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}	✓	✓	✓	✓	3.485
18780	674	\begin{align*} y y^{\prime }&=x -1 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.486
18781	11613	\begin{align*} \left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.486
18782	18926	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.486
18783	20114	\begin{align*} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y&=n^{2} x^{m} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.486
18784	24219	\begin{align*} x y \left (1+y^{2}\right )+\left (x^{2} y^{2}-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.487
18785	23942	\begin{align*} y \cos \left (y x \right )+y-x +\left (x \cos \left (y x \right )+x -y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.488
18786	33	\begin{align*} y y^{\prime }&=x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.489
18787	2099	\begin{align*} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.490
18788	9055	\begin{align*} x y^{\prime }&=y+x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.490
18789	10161	\begin{align*} y^{\prime }&=2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✗	3.490
18790	15596	\begin{align*} y^{\prime }&=y x +2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.490
18791	20795	\begin{align*} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.491
18792	2298	\begin{align*} \cos \left (t \right ) y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.493
18793	9596	\begin{align*} x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.493
18794	16251	\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.493
18795	17083	\begin{align*} y^{\prime }&={\mathrm e}^{3 y+2 t} \\ \end{align*}	✓	✓	✓	✓	3.493
18796	24275	\begin{align*} \cos \left (x \right ) y^{\prime }&=1-y-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.493
18797	15957	\begin{align*} y^{\prime }&=t^{2} y^{3}+y^{3} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.494
18798	23861	\begin{align*} y^{\prime }&=3 x^{2} y-3 x^{4}+2 x^{2}-2 y+2 x \\ \end{align*}	✓	✓	✓	✓	3.494
18799	25904	\begin{align*} x y^{\prime }+\left (x +1\right ) y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	3.494
18800	5399	\begin{align*} {y^{\prime }}^{2}-\left (2 x +1\right ) y^{\prime }-x \left (1-x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.496