2.3.206 Problems 20501 to 20600

Table 2.943: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20501	7467	\begin{align*} y \,{\mathrm e}^{t}+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	3.500
20502	18475	\begin{align*} y^{\prime }+y^{3} \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.500
20503	18490	\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.500
20504	8282	\begin{align*} \left (-y x +1\right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.501
20505	15650	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	3.502
20506	8433	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	3.503
20507	9788	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.503
20508	2504	\begin{align*} y^{\prime }&=\frac {t +y}{t -y} \\ \end{align*}	✓	✓	✓	✓	3.504
20509	15884	\begin{align*} w^{\prime }&=\left (w^{2}-2\right ) \arctan \left (w\right ) \\ \end{align*}	✓	✓	✓	✓	3.504
20510	18492	\begin{align*} y^{\prime }&=x^{2} {\mathrm e}^{-3 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.505
20511	23186	\begin{align*} y+\cos \left (x \right )+\left (x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.505
20512	8180	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	3.507
20513	3636	\begin{align*} \left (3 x -y\right ) y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	3.508
20514	11700	\begin{align*} x {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.508
20515	22572	\begin{align*} y^{\prime } x +y \ln \left (x \right )&=y \ln \left (y\right )+y \\ \end{align*}	✓	✓	✓	✓	3.508
20516	5419	\begin{align*} {y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.509
20517	13005	\begin{align*} a y \left (y-1\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.509
20518	5258	\begin{align*} x \left (a +y\right )^{2} y^{\prime }&=b y^{2} \\ \end{align*}	✓	✓	✓	✓	3.510
20519	20410	\begin{align*} x&=y+a \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.510
20520	22366	\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.510
20521	5114	\begin{align*} \left (8+5 x -12 y\right ) y^{\prime }&=3+2 x -5 y \\ \end{align*}	✓	✓	✓	✓	3.513
20522	15455	\begin{align*} y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.513
20523	2997	\begin{align*} y^{\prime }+y \cos \left (x \right )&=y^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.514
20524	5008	\begin{align*} x^{n} y^{\prime }&=x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	3.514
20525	2501	\begin{align*} t y^{\prime }&=y+\sqrt {t^{2}+y^{2}} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.515
20526	21626	\begin{align*} L i^{\prime }+R i&=E_{0} \\ i \left (0\right ) &= i_{0} \\ \end{align*}	✓	✓	✓	✓	3.515
20527	18062	\begin{align*} \left (x -1\right ) \left (y^{2}-y+1\right )&=\left (y-1\right ) \left (x^{2}+x +1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.516
20528	25664	\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.517
20529	4695	\begin{align*} y^{\prime }&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	3.518
20530	20544	\begin{align*} y^{3} y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	3.519
20531	7710	\begin{align*} \cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	3.520
20532	11387	\begin{align*} y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	3.521
20533	17988	\begin{align*} x^{2}+y^{2}+1-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	3.521
20534	1655	\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}	✓	✓	✓	✓	3.522
20535	8667	\begin{align*} y^{\prime }-x y^{2}&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.523
20536	11611	\begin{align*} \left (2 x y^{3}+y x +x^{2}\right ) y^{\prime }-y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.524
20537	25794	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (1\right ) &= {\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	3.524
20538	3656	\begin{align*} y^{\prime }-\frac {y}{x}&=\frac {4 x^{2} \cos \left (x \right )}{y} \\ \end{align*}	✓	✓	✓	✓	3.526
20539	8691	\begin{align*} \left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.527
20540	14916	\begin{align*} x^{\prime }&=k x-x^{2} \\ \end{align*}	✓	✓	✓	✓	3.527
20541	15626	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.527
20542	58	\begin{align*} x^{2} y^{\prime }&=1-x^{2}+y^{2}-y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	3.529
20543	3662	\begin{align*} \left (x -a \right ) \left (-b +x \right ) \left (y^{\prime }-\sqrt {y}\right )&=2 \left (b -a \right ) y \\ \end{align*}	✓	✓	✓	✓	3.529
20544	5027	\begin{align*} y^{\prime } \left (4 x^{3}+a_{1} x +a_{0} \right )^{{2}/{3}}+\left (a_{0} +a_{1} y+4 y^{3}\right )^{{2}/{3}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.529
20545	6575	\begin{align*} \operatorname {f5} y^{2}+\operatorname {f4} y y^{\prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✗	✗	3.529
20546	17039	\begin{align*} y^{\prime }&=4 t^{2}-t y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.529
20547	11577	\begin{align*} 3 \left (y^{2}-x^{2}\right ) y^{\prime }+2 y^{3}-6 \left (x +1\right ) x y-3 \,{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	3.530
20548	17063	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.530
20549	7357	\begin{align*} -y+y^{\prime } x&=x^{2} \\ y \left (2\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	3.531
20550	23461	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.531
20551	11893	\begin{align*} y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right ) x^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	3.533
20552	14197	\begin{align*} x^{\prime }+2 x&=t^{2}+4 t +7 \\ \end{align*}	✓	✓	✓	✓	3.534
20553	1162	\begin{align*} y^{\prime }&=\frac {x +3 y}{x -y} \\ \end{align*}	✓	✓	✓	✗	3.535
20554	7726	\begin{align*} \left (y x +1\right ) y+x \left (1+y x +y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.535
20555	20563	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	3.535
20556	22609	\begin{align*} x^{2}+y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	3.535
20557	17936	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=\frac {1}{\cos \left (x \right )^{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.536
20558	719	\begin{align*} y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.537
20559	4845	\begin{align*} \left (x +a \right ) y^{\prime }&=b +c y \\ \end{align*}	✓	✓	✓	✓	3.539
20560	7919	\begin{align*} -3 y-\left (x -2\right ) {\mathrm e}^{x}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.539
20561	9191	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	3.539
20562	15627	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	3.539
20563	1581	\begin{align*} \left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	3.541
20564	7466	\begin{align*} y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.542
20565	2981	\begin{align*} 3 y^{2} y^{\prime }-x y^{3}&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.543
20566	21555	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.547
20567	17268	\begin{align*} 2 y-3 t +t y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.548
20568	8309	\begin{align*} y^{\prime } y&=-x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.549
20569	19066	\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.550
20570	20815	\begin{align*} y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.550
20571	13690	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.552
20572	15628	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.552
20573	4994	\begin{align*} x^{4} y^{\prime }+x^{3} y+\csc \left (y x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.554
20574	20817	\begin{align*} s^{\prime }+2 s&=s t^{2} \\ s \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.554
20575	4329	\begin{align*} x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.556
20576	5081	\begin{align*} \left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.556
20577	20547	\begin{align*} y^{\prime \prime }&=y^{3}-y \\ \end{align*}	✓	✓	✓	✗	3.559
20578	1243	\begin{align*} y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\ \end{align*}	✓	✓	✓	✗	3.560
20579	4083	\begin{align*} 6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\ y \left (\frac {1}{2}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.560
20580	20686	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\ \end{align*}	✓	✓	✓	✓	3.560
20581	15921	\begin{align*} y^{\prime }&=-\frac {y}{t +1}+2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.561
20582	4846	\begin{align*} \left (x +a \right ) y^{\prime }&=-b -c y \\ \end{align*}	✓	✓	✓	✓	3.562
20583	11882	\begin{align*} y^{\prime }&=\frac {-x +F \left (y^{2}+x^{2}\right )}{y} \\ \end{align*}	✓	✓	✓	✗	3.562
20584	18478	\begin{align*} y^{\prime } x&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.562
20585	22446	\begin{align*} y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.562
20586	5476	\begin{align*} x {y^{\prime }}^{2}+a y y^{\prime }+b x&=0 \\ \end{align*}	✓	✓	✓	✓	3.563
20587	4230	\begin{align*} y^{\prime } x&=2 y \left (y-1\right ) \\ y \left (\frac {1}{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.565
20588	23886	\begin{align*} 3 x^{2} {\mathrm e}^{x^{3}}+{\mathrm e}^{2 y}+\left (2 x \,{\mathrm e}^{2 y}-3\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.565
20589	17090	\begin{align*} y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \\ \end{align*}	✓	✓	✓	✓	3.566
20590	3051	\begin{align*} 4 x y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.567
20591	3640	\begin{align*} -y+y^{\prime } x&=\sqrt {9 x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.567
20592	7398	\begin{align*} \frac {y^{\prime }}{2}&=\sqrt {1+y}\, \cos \left (x \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.567
20593	19947	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.568
20594	1554	\begin{align*} y^{\prime } x +\left (2 x^{2}+1\right ) y&=x^{3} {\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.569
20595	12882	\begin{align*} y^{\prime \prime }&=a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	3.573
20596	23214	\begin{align*} y^{\prime }&=\frac {x -y}{x +y+2} \\ \end{align*}	✓	✓	✓	✓	3.574
20597	3663	\begin{align*} y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	3.575
20598	15652	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (1\right ) &= -{\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	3.576
20599	17130	\begin{align*} y^{\prime }&=\left (x +y-4\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.576
20600	17075	\begin{align*} y^{\prime }&=\frac {2+y}{2 t +1} \\ \end{align*}	✓	✓	✓	✓	3.580