2.3.187 Problems 18601 to 18700

Table 2.947: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18601	12005	\begin{align*} y^{\prime }&=\frac {2 a}{y+2 y^{4} a -16 a^{2} x y^{2}+32 a^{3} x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.381
18602	5010	\begin{align*} \sqrt {x^{2}+1}\, y^{\prime }&=2 x -y \\ \end{align*}	✓	✓	✓	✓	3.383
18603	11617	\begin{align*} \left (a x y^{3}+c \right ) x y^{\prime }+\left (b \,x^{3} y+c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.383
18604	13945	\begin{align*} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	3.383
18605	23969	\begin{align*} y^{\prime }+\frac {3 y}{2}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	3.383
18606	4345	\begin{align*} x^{2}+y+y^{2}-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.385
18607	8029	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=\ln \left (x +1\right )^{2}+x -1 \\ \end{align*}	✓	✓	✓	✗	3.385
18608	8759	\begin{align*} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.385
18609	4192	\begin{align*} y^{\prime }+y \cot \left (x \right )&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.386
18610	13784	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	3.386
18611	18929	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right . \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.387
18612	23910	\begin{align*} y^{\prime }+\frac {y}{x}&=\ln \left (x \right )-2 \\ \end{align*}	✓	✓	✓	✓	3.387
18613	6485	\begin{align*} 2 y y^{\prime \prime }&={y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	3.388
18614	8677	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	3.388
18615	8886	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	3.388
18616	2965	\begin{align*} 1&=\left (x +{\mathrm e}^{y}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.389
18617	9718	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.389
18618	13813	\begin{align*} n^{2} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.390
18619	17669	\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.390
18620	7525	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x +y}}{-1+y} \\ \end{align*}	✓	✓	✓	✓	3.391
18621	21510	\begin{align*} y^{\prime }-y&=3 x^{2}+x \\ \end{align*}	✓	✓	✓	✓	3.392
18622	11722	\begin{align*} \left (x y^{\prime }+y+2 x \right )^{2}-4 y x -4 x^{2}-4 a&=0 \\ \end{align*}	✓	✓	✓	✗	3.394
18623	14782	\begin{align*} x^{\prime }+y^{\prime }-x+5 y&=t^{2} \\ x^{\prime }+2 y^{\prime }-2 x+4 y&=2 t +1 \\ \end{align*}	✓	✓	✓	✓	3.394
18624	24243	\begin{align*} y^{\prime }&=-2 y x +x \\ \end{align*}	✓	✓	✓	✓	3.394
18625	27280	\begin{align*} x y y^{\prime }&=x +y^{2} \\ \end{align*}	✓	✓	✓	✓	3.394
18626	2497	\begin{align*} \cos \left (y\right ) y^{\prime }&=-\frac {t \sin \left (y\right )}{t^{2}+1} \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	3.395
18627	17800	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	3.395
18628	18290	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.395
18629	15023	\begin{align*} x^{\prime }&=x+\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.396
18630	17783	\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.397
18631	11426	\begin{align*} x y^{\prime }-y f \left (x^{a} y^{b}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.398
18632	12578	\begin{align*} x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+a \,x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.398
18633	21617	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.398
18634	24817	\begin{align*} y&=x y^{\prime }+{y^{\prime }}^{n} \\ \end{align*}	✓	✓	✓	✗	3.398
18635	8544	\begin{align*} x y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.401
18636	1699	\begin{align*} \sin \left (x \right )-y \sin \left (x \right )-2 \cos \left (x \right )+\cos \left (x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.402
18637	7818	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.402
18638	8525	\begin{align*} x y^{\prime \prime }-x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.402
18639	11919	\begin{align*} y^{\prime }&=\left (-\ln \left (y\right )+x^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	3.403
18640	1152	\begin{align*} y^{\prime }&=\frac {2-{\mathrm e}^{x}}{3+2 y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.404
18641	10089	\begin{align*} y^{\prime \prime }-a x y^{\prime }-b x y-c x&=0 \\ \end{align*}	✗	✓	✓	✗	3.404
18642	26304	\begin{align*} \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=x +1 \\ \end{align*}	✓	✓	✓	✓	3.404
18643	26687	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	3.404
18644	7736	\begin{align*} y^{\prime }-y \tan \left (x \right )&=\cos \left (x \right )-2 x \sin \left (x \right ) \\ y \left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.405
18645	22939	\begin{align*} x^{\prime }&=-12 x-7 y \\ y^{\prime }&=19 x+11 y \\ \end{align*}	✓	✓	✓	✓	3.405
18646	11331	\begin{align*} y^{\prime }-x y^{2}-3 y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.406
18647	24998	\begin{align*} y^{\prime }-\frac {n y}{t}&={\mathrm e}^{t} t^{n} \\ \end{align*}	✓	✓	✓	✓	3.407
18648	67	\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.409
18649	18799	\begin{align*} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✓	3.410
18650	8778	\begin{align*} y^{\prime }&=\frac {x^{2}}{1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.411
18651	22356	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2} x&=1 \\ \end{align*}	✓	✓	✓	✗	3.411
18652	24938	\begin{align*} y^{\prime }&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.411
18653	3664	\begin{align*} y^{\prime }+4 y x&=4 x^{3} \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	3.412
18654	4218	\begin{align*} x y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.412
18655	7434	\begin{align*} y^{\prime }-\frac {y}{x}&=x \,{\mathrm e}^{x} \\ y \left (1\right ) &= {\mathrm e}-1 \\ \end{align*}	✓	✓	✓	✓	3.412
18656	5364	\begin{align*} {y^{\prime }}^{2}&=y^{2} a^{2} \\ \end{align*}	✓	✓	✓	✓	3.414
18657	81	\begin{align*} x y^{\prime }-y&=x \\ y \left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	3.415
18658	18791	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{3}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{3}\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	3.415
18659	26179	\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.415
18660	2104	\begin{align*} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }-x \left (x^{2}+3\right ) y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.417
18661	8546	\begin{align*} x y^{\prime \prime }-y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.417
18662	19940	\begin{align*} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}&=1 \\ \end{align*}	✓	✓	✓	✓	3.418
18663	9745	\begin{align*} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	3.419
18664	1540	\begin{align*} x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.420
18665	8146	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.420
18666	1602	\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )}{\sin \left (y\right )} \\ y \left (\pi \right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	3.421
18667	5554	\begin{align*} y {y^{\prime }}^{2}+y&=a \\ \end{align*}	✓	✓	✓	✓	3.421
18668	9881	\begin{align*} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.421
18669	18539	\begin{align*} -y+y^{\prime }&=1+3 \sin \left (t \right ) \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	3.421
18670	23897	\begin{align*} y+6 x y^{3}-4 y^{4}-\left (2 x +4 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.421
18671	24879	\begin{align*} y^{\prime \prime }+\beta ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	3.421
18672	696	\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.423
18673	9345	\begin{align*} y^{\prime \prime }&=-3 y \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.424
18674	13223	\begin{align*} a \,x^{2} \left (x -1\right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s&=0 \\ \end{align*}	✓	✓	✗	✗	3.424
18675	15925	\begin{align*} y^{\prime }-\frac {2 y}{t}&=2 t^{2} \\ y \left (-2\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.424
18676	17889	\begin{align*} y^{\prime }&=\sin \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	3.424
18677	21404	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	3.425
18678	23205	\begin{align*} x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.425
18679	16906	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.426
18680	26234	\begin{align*} y x +2 x y \ln \left (y\right )^{2}+\ln \left (y\right ) y+\left (2 x^{2} \ln \left (y\right )+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.426
18681	1547	\begin{align*} y^{\prime }+\tan \left (k x \right ) y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.428
18682	2322	\begin{align*} t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.428
18683	5067	\begin{align*} \left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.428
18684	1241	\begin{align*} 2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.429
18685	16928	\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.430
18686	1600	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.433
18687	96	\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.434
18688	1669	\begin{align*} 3 x y^{2} y^{\prime }&=y^{3}+x \\ \end{align*}	✓	✓	✓	✓	3.434
18689	6132	\begin{align*} 6 y-4 \left (x +a \right ) y^{\prime }+\left (x +a \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.434
18690	26425	\begin{align*} y^{\prime \prime } {\mathrm e}^{y^{\prime }} \left (y^{\prime }+2\right )&=1 \\ \end{align*}	✓	✓	✓	✓	3.434
18691	8879	\begin{align*} y^{\prime }-y \tan \left (x \right )&={\mathrm e}^{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	3.435
18692	12307	\begin{align*} y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.435
18693	8094	\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.436
18694	694	\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x} \\ y \left (0\right ) &= 2 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✓	3.437
18695	11659	\begin{align*} f \left (x^{2}+a y^{2}\right ) \left (a y y^{\prime }+x \right )-y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.437
18696	3680	\begin{align*} \frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right )&=q \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	3.438
18697	6804	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=3 y^{\prime } {y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.439
18698	15539	\begin{align*} y^{\prime }&=y^{2}-3 y \\ \end{align*}	✓	✓	✓	✓	3.439
18699	17812	\begin{align*} x^{\prime \prime }+x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.440
18700	21607	\begin{align*} y^{\prime }&=\sin \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	3.440