2.3.206 Problems 20501 to 20600

Table 2.961: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20501	23152	\begin{align*} y^{\prime } x +y&=3 x \\ \end{align*}	✓	✓	✓	✓	5.464
20502	123	\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{3} \\ \end{align*}	✓	✓	✓	✓	5.466
20503	9930	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	5.468
20504	8828	\begin{align*} a y^{\prime \prime } y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	5.469
20505	13835	\begin{align*} \left (2 a x +x^{2}+b \right ) y^{\prime \prime }+\left (a +x \right ) y^{\prime }-m^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.471
20506	18524	\begin{align*} y^{\prime } t +4 y&=t^{2}-t +1 \\ y \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	5.471
20507	12642	\begin{align*} y^{\prime \prime }&=\frac {12 y}{\left (x +1\right )^{2} \left (x^{2}+2 x +3\right )} \\ \end{align*}	✓	✓	✓	✗	5.472
20508	5859	\begin{align*} a \csc \left (x \right )^{2} y+\left (2+\cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.473
20509	11628	\begin{align*} \sqrt {-1+y^{2}}\, y^{\prime }-\sqrt {x^{2}-1}&=0 \\ \end{align*}	✓	✓	✓	✓	5.473
20510	21463	\begin{align*} y^{\prime }&=1-y+y^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	5.473
20511	25871	\begin{align*} y y^{\prime }+\cot \left (x \right ) y^{2}&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.474
20512	8229	\begin{align*} \left (y^{3}+1\right ) y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	5.475
20513	11888	\begin{align*} y^{\prime }&=-\frac {y^{2} \left (2 x -F \left (-\frac {y x -2}{2 y}\right )\right )}{4 x} \\ \end{align*}	✓	✓	✓	✗	5.476
20514	24222	\begin{align*} x^{4} y^{\prime }&=-x^{3} y-\csc \left (y x \right ) \\ \end{align*}	✓	✓	✓	✗	5.476
20515	18541	\begin{align*} y^{\prime }-6 y&=t^{6} {\mathrm e}^{6 t} \\ \end{align*}	✓	✓	✓	✓	5.479
20516	14452	\begin{align*} \frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}}&=0 \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.480
20517	3603	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.481
20518	15379	\begin{align*} x^{2}+y+\left (x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.481
20519	21828	\begin{align*} y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	5.481
20520	6556	\begin{align*} y^{3} y^{\prime \prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	5.482
20521	9342	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.483
20522	5611	\begin{align*} {y^{\prime }}^{3}&=\left (y-a \right )^{2} \left (y-b \right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.485
20523	25056	\begin{align*} y^{\prime } t&=2 y-t \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✗	✓	✓	5.487
20524	11980	\begin{align*} y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \\ \end{align*}	✓	✓	✓	✗	5.489
20525	24138	\begin{align*} 1+\ln \left (x \right )+\left (1+\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.489
20526	26279	\begin{align*} \left (x^{2}+2 x -1\right ) y^{\prime }-\left (x +1\right ) y&=x -1 \\ \end{align*}	✓	✓	✓	✓	5.489
20527	24136	\begin{align*} y^{\prime } x +y+x y \left (1+y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.490
20528	9328	\begin{align*} y^{\prime \prime }&=\tan \left (x \right ) \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.496
20529	4715	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	5.498
20530	9929	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.500
20531	2992	\begin{align*} r^{\prime }+\left (r-\frac {1}{r}\right ) \theta &=0 \\ \end{align*}	✓	✓	✓	✓	5.503
20532	5754	\begin{align*} a \csc \left (x \right )^{2} y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.503
20533	20266	\begin{align*} \cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.503
20534	15961	\begin{align*} y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.505
20535	18848	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.507
20536	12019	\begin{align*} y^{\prime }&=\frac {x \left (-1+x -2 y x +2 x^{3}\right )}{x^{2}-y} \\ \end{align*}	✓	✓	✓	✗	5.509
20537	18010	\begin{align*} y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	5.509
20538	26221	\begin{align*} x y^{2}-y^{2}+x -1+\left (x^{2} y-2 y x +x^{2}+2 y-2 x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.509
20539	16333	\begin{align*} y^{\prime } x&=2 y^{2}-6 y \\ \end{align*}	✓	✓	✓	✓	5.510
20540	9139	\begin{align*} \ln \left (y\right ) x +y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.514
20541	11919	\begin{align*} y^{\prime }&=\left (-\ln \left (y\right )+x^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	5.515
20542	5134	\begin{align*} y y^{\prime } x +x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.516
20543	21373	\begin{align*} x \sin \left (y\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	5.516
20544	22380	\begin{align*} y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.519
20545	7872	\begin{align*} 1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.520
20546	10317	\begin{align*} {y^{\prime }}^{2}&=\frac {1}{x^{3} y^{4}} \\ \end{align*}	✓	✓	✓	✓	5.520
20547	4815	\begin{align*} y^{\prime } x&=\left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.521
20548	5011	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	5.521
20549	22566	\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.522
20550	19377	\begin{align*} y^{\prime } x +y&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	5.524
20551	9989	\begin{align*} y^{\prime }&=\frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \\ \end{align*}	✓	✓	✓	✓	5.526
20552	11859	\begin{align*} f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y&=0 \\ \end{align*}	✗	✓	✓	✗	5.532
20553	17209	\begin{align*} \frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.534
20554	7149	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.536
20555	5196	\begin{align*} 3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.537
20556	7704	\begin{align*} y^{\prime } x -2 y&=\cos \left (x \right ) x^{3} \\ \end{align*}	✓	✓	✓	✓	5.538
20557	4338	\begin{align*} y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.543
20558	17078	\begin{align*} \cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\ \end{align*}	✓	✓	✓	✓	5.545
20559	18582	\begin{align*} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.545
20560	15109	\begin{align*} y^{\prime \prime }&=2 y^{3} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.546
20561	11880	\begin{align*} y^{\prime }&=\frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )} \\ \end{align*}	✓	✓	✓	✗	5.547
20562	11958	\begin{align*} y^{\prime }&=\frac {y+x^{3} a \,{\mathrm e}^{x}+x^{4} a +a \,x^{3}-x y^{2} {\mathrm e}^{x}-y^{2} x^{2}-x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	5.547
20563	903	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	5.548
20564	7130	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.552
20565	8670	\begin{align*} {\mathrm e}^{x}-\left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.552
20566	15461	\begin{align*} y^{\prime }&=x +y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.553
20567	4654	\begin{align*} y^{\prime }+1-x&=y \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✗	5.554
20568	18480	\begin{align*} y^{\prime }&=\frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}} \\ \end{align*}	✓	✓	✓	✓	5.554
20569	21084	\begin{align*} x^{\prime }&=\frac {x+2 t}{t} \\ \end{align*}	✓	✓	✓	✓	5.554
20570	5483	\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	5.555
20571	9926	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.555
20572	11864	\begin{align*} y^{\prime }&=\frac {1+2 F \left (\frac {4 x^{2} y+1}{4 x^{2}}\right ) x}{2 x^{3}} \\ \end{align*}	✗	✓	✓	✗	5.557
20573	12105	\begin{align*} y^{\prime }&=\frac {y \left (x +y\right )}{x \left (x +y+y^{3}+y^{4}\right )} \\ \end{align*}	✓	✓	✓	✗	5.558
20574	21719	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.558
20575	1243	\begin{align*} y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\ \end{align*}	✓	✓	✓	✗	5.559
20576	24969	\begin{align*} 2 y y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	5.559
20577	12679	\begin{align*} y^{\prime \prime }&=-\frac {\left (2 n +1\right ) \cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\left (v +n +1\right ) \left (v -n \right ) y \\ \end{align*}	✗	✓	✓	✗	5.560
20578	6576	\begin{align*} 3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	5.561
20579	15491	\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	5.561
20580	11359	\begin{align*} y^{\prime }-a \sqrt {y}-b x&=0 \\ \end{align*}	✓	✓	✓	✗	5.564
20581	4300	\begin{align*} x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.565
20582	16252	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.566
20583	18957	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.566
20584	1648	\begin{align*} y^{\prime }&=\frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 y x} \\ \end{align*}	✓	✓	✓	✓	5.567
20585	21170	\begin{align*} t^{2} x^{\prime \prime }+a t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	5.567
20586	13308	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+\lambda y-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x} \\ \end{align*}	✓	✓	✓	✗	5.569
20587	15341	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	5.569
20588	3451	\begin{align*} y^{\prime } t&=-y+t^{3} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.572
20589	6009	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	5.572
20590	7875	\begin{align*} y^{\prime } x +2 y&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.573
20591	8666	\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}	✓	✓	✓	✓	5.573
20592	17205	\begin{align*} {\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.573
20593	19101	\begin{align*} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.573
20594	19918	\begin{align*} 2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.573
20595	21399	\begin{align*} y-x y^{2}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.574
20596	1688	\begin{align*} 3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.575
20597	15063	\begin{align*} 3 y^{\prime } y^{2} x +y^{3}-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.578
20598	23237	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.579
20599	11830	\begin{align*} x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	5.580
20600	2999	\begin{align*} y^{\prime }&=x \left (1-{\mathrm e}^{2 y-x^{2}}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.581