2.3.187 Problems 18601 to 18700

Table 2.905: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18601	14032	\begin{align*} y+x y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.349
18602	17183	\begin{align*} -\frac {y}{2}+y^{\prime }&=5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.349
18603	22422	\begin{align*} y^{\prime }&=\frac {2 x -\sin \left (y\right )}{x \cos \left (y\right )} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.349
18604	6915	\begin{align*} 7 y-3+\left (2 x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.350
18605	11115	\begin{align*} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.350
18606	14443	\begin{align*} 6 y x +2 y^{2}-5+\left (3 x^{2}+4 y x -6\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.350
18607	18075	\begin{align*} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.350
18608	23159	\begin{align*} y^{\prime }+\frac {y}{\sin \left (x \right )}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.350
18609	16312	\begin{align*} y^{\prime }&=x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \\ \end{align*}	✓	✓	✓	✓	2.352
18610	17889	\begin{align*} y^{\prime }&=\sin \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	2.352
18611	8419	\begin{align*} y^{\prime }&=\frac {x \left (1-x \right )}{y \left (y-2\right )} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.353
18612	8441	\begin{align*} p^{\prime }+2 t p&=p+4 t -2 \\ \end{align*}	✓	✓	✓	✓	2.353
18613	17951	\begin{align*} \sin \left (x \right ) y^{\prime }+y \cos \left (x \right )&=1 \\ \end{align*}	✓	✓	✓	✓	2.353
18614	19079	\begin{align*} \cos \left (x \right ) y^{\prime }&=y \sin \left (x \right )+\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.353
18615	3283	\begin{align*} \left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }&={\mathrm e}^{x} y^{\prime } \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.354
18616	25470	\begin{align*} m y^{\prime \prime }+k y&=F \\ \end{align*}	✓	✓	✓	✓	2.354
18617	75	\begin{align*} y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	2.355
18618	927	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{3}+1 \\ x_{2}^{\prime }&=x_{3}+x_{4}+t \\ x_{3}^{\prime }&=x_{1}+x_{4}+t^{2} \\ x_{4}^{\prime }&=x_{1}+x_{2}+t^{3} \\ \end{align*}	✓	✓	✓	✓	2.355
18619	1210	\begin{align*} 2 y x +3 x^{2} y+y^{3}+\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.355
18620	7117	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	2.355
18621	12371	\begin{align*} b x y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	2.355
18622	23057	\begin{align*} \left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	2.355
18623	13776	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.357
18624	10020	\begin{align*} y^{2}+\frac {2}{x}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	2.360
18625	14429	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.360
18626	22434	\begin{align*} \left (x +x^{3} \sin \left (2 y\right )\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.360
18627	2478	\begin{align*} \sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\ y \left (0\right ) &= \sqrt {5} \\ \end{align*}	✓	✓	✓	✓	2.361
18628	15934	\begin{align*} y^{\prime }&=t^{r} y+4 \\ \end{align*}	✓	✓	✓	✗	2.362
18629	21918	\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ y^{\prime \prime \prime }\left (0\right ) &= -5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.362
18630	8680	\begin{align*} z^{\prime }&=10^{x +z} \\ \end{align*}	✓	✓	✓	✓	2.363
18631	24215	\begin{align*} x^{3}+x y^{2}+y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.364
18632	4348	\begin{align*} y^{2}-\left (y x +x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.365
18633	15588	\begin{align*} x \,{\mathrm e}^{y}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.365
18634	19157	\begin{align*} a^{2} y^{\prime \prime }&=2 x \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✗	✓	✗	2.365
18635	23838	\begin{align*} y^{\prime }&=1-\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	2.365
18636	14764	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.366
18637	5952	\begin{align*} y-y^{\prime } x +\left (-x \cot \left (x \right )+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.367
18638	16321	\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.367
18639	1690	\begin{align*} \frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.368
18640	4777	\begin{align*} y^{\prime } x&=a \,x^{2 n}+\left (n +b y\right ) y \\ \end{align*}	✓	✓	✓	✗	2.368
18641	7435	\begin{align*} y^{\prime }+4 y-{\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= {\frac {4}{3}} \\ \end{align*}	✓	✓	✓	✓	2.368
18642	8466	\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=10 \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.368
18643	11813	\begin{align*} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	2.368
18644	13924	\begin{align*} \left (a \,x^{n}+b \right )^{m +1} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }-a n m \,x^{n -1} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.368
18645	14906	\begin{align*} T^{\prime }&=-k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \\ \end{align*}	✓	✓	✓	✓	2.368
18646	13004	\begin{align*} \left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.369
18647	18110	\begin{align*} 3 y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	2.369
18648	14763	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.370
18649	17137	\begin{align*} y^{\prime }&=y f \left (t \right ) \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.370
18650	57	\begin{align*} y^{\prime }&=1+x +y+y x \\ \end{align*}	✓	✓	✓	✓	2.371
18651	1209	\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.371
18652	8659	\begin{align*} y^{\prime }&=y \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.371
18653	189	\begin{align*} x^{2} y^{\prime }&=y x +3 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.372
18654	2317	\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.372
18655	8645	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 2 \,{\mathrm e}^{-\pi }-2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.372
18656	2305	\begin{align*} \sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\ y \left (0\right ) &= \sqrt {5} \\ \end{align*}	✓	✓	✓	✓	2.373
18657	3524	\begin{align*} \left (x -a \right ) \left (-b +x \right ) y^{\prime }-y+c&=0 \\ \end{align*}	✓	✓	✓	✓	2.373
18658	15365	\begin{align*} y^{\prime }-\frac {a y}{x}&=\frac {x +1}{x} \\ \end{align*}	✓	✓	✓	✓	2.373
18659	19232	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.373
18660	23124	\begin{align*} y^{\prime }&=y^{{2}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.373
18661	16279	\begin{align*} y^{\prime } x +3 y&=20 x^{2} \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.374
18662	23849	\begin{align*} 2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.374
18663	188	\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	2.375
18664	3675	\begin{align*} y^{\prime }&=2 x \left (x +y\right )^{2}-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.375
18665	4427	\begin{align*} y+2 y^{3} y^{\prime }&=\left (x +4 y \ln \left (y\right )\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.375
18666	12430	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (l \,x^{2}-v^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.375
18667	14512	\begin{align*} y^{\prime }+y&=2 \sin \left (x \right )+5 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.375
18668	17095	\begin{align*} \frac {\sqrt {\ln \left (x \right )}}{x}&=\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \\ \end{align*}	✓	✓	✓	✓	2.375
18669	25488	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.375
18670	25500	\begin{align*} y^{\prime }&=\left (y+4\right ) \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.375
18671	7155	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.376
18672	9967	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.376
18673	15829	\begin{align*} y^{\prime }&=t^{2}+t^{2} y \\ \end{align*}	✓	✓	✓	✓	2.376
18674	5124	\begin{align*} x y^{\prime } y&=x +y^{2} \\ \end{align*}	✓	✓	✓	✓	2.377
18675	669	\begin{align*} y^{\prime }&=2 y^{2} x^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.378
18676	4618	\begin{align*} y^{\prime }&=a \,x^{n} y \\ \end{align*}	✓	✓	✓	✓	2.378
18677	19087	\begin{align*} y^{\prime }&=\frac {y^{2}}{3}+\frac {2}{3 x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.378
18678	1213	\begin{align*} y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.379
18679	5042	\begin{align*} y^{\prime } y&=a x +b y^{2} \\ \end{align*}	✓	✓	✓	✓	2.379
18680	5283	\begin{align*} \left (1-x^{3}+6 y^{2} x^{2}\right ) y^{\prime }&=\left (6+3 y x -4 y^{3}\right ) x \\ \end{align*}	✓	✓	✓	✗	2.379
18681	24219	\begin{align*} x y \left (1+y^{2}\right )+\left (y^{2} x^{2}-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.379
18682	7791	\begin{align*} y^{\prime }-5 y&=\sin \left (x \right ) \left (x -1\right )+\left (x +1\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.381
18683	20799	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\ \end{align*}	✓	✓	✓	✗	2.381
18684	22955	\begin{align*} x \cos \left (y\right ) y^{\prime }-\left (x^{2}+1\right ) \sin \left (y\right )&=0 \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	2.381
18685	1703	\begin{align*} y^{4} x^{3}+x +\left (y^{3} x^{4}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.382
18686	5483	\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.382
18687	10313	\begin{align*} {y^{\prime }}^{2}&=\frac {1}{y x} \\ \end{align*}	✓	✓	✓	✓	2.382
18688	160	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	2.383
18689	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*}	✓	✓	✓	✓	2.383
18690	24074	\begin{align*} y^{\left (6\right )}+y&=x^{7}+2 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.383
18691	24242	\begin{align*} 2 y x +x^{2}+x^{4}-\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.383
18692	11381	\begin{align*} y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1&=0 \\ \end{align*}	✗	✓	✓	✗	2.385
18693	15589	\begin{align*} y-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.385
18694	781	\begin{align*} x^{2} y^{\prime }&=y x +3 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.386
18695	4335	\begin{align*} 4 y x +3 y^{2}-x +x \left (x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.387
18696	17213	\begin{align*} 2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.387
18697	22055	\begin{align*} x^{3} y^{2}-y+\left (x^{2} y^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.387
18698	24953	\begin{align*} y^{\prime }&=t y^{2}-y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	2.387
18699	14501	\begin{align*} {\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.388
18700	3525	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.389