2.3.216 Problems 21501 to 21600

Table 2.1005: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21501	9807	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4&=0 \\ \end{align*}	✓	✓	✓	✗	12.319
21502	7333	\begin{align*} x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	12.320
21503	7033	\begin{align*} \left (y x -1\right )^{2} x y^{\prime }+\left (y^{2} x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	12.323
21504	25220	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	12.328
21505	14534	\begin{align*} y^{2} {\mathrm e}^{2 x}-2 x +y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	12.333
21506	9012	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✗	12.339
21507	25436	\begin{align*} y^{\prime }&=a \left (t \right ) y+q \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	12.339
21508	24939	\begin{align*} y^{\prime }&=y-t \\ \end{align*}	✓	✓	✓	✓	12.345
21509	19961	\begin{align*} y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	12.346
21510	24250	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	12.346
21511	11641	\begin{align*} \sin \left (y\right )+\cos \left (x \right ) y+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	12.349
21512	15564	\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (x \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	12.351
21513	24244	\begin{align*} y-\cos \left (x \right )^{2}+\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.355
21514	7022	\begin{align*} \left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	12.359
21515	15342	\begin{align*} 1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.360
21516	5596	\begin{align*} \left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	12.362
21517	14192	\begin{align*} x^{\prime }&=\frac {2 x}{t} \\ \end{align*}	✓	✓	✓	✓	12.362
21518	11951	\begin{align*} y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 x}}{{\mathrm e}^{-x} y+1} \\ \end{align*}	✓	✓	✓	✓	12.364
21519	1592	\begin{align*} y^{\prime }&=2 x y \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	12.365
21520	14770	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	12.368
21521	14892	\begin{align*} y^{\prime } x&=k y \\ \end{align*}	✓	✓	✓	✓	12.369
21522	18814	\begin{align*} m y^{\prime \prime }+k y&=0 \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}	✓	✓	✓	✓	12.369
21523	21438	\begin{align*} y^{\prime }+\frac {y}{x}&=3 x \\ \end{align*}	✓	✓	✓	✓	12.371
21524	13320	\begin{align*} y^{\prime }&=y^{2}-a^{2}+a \lambda \sinh \left (\lambda x \right )-a^{2} \sinh \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	12.373
21525	12156	\begin{align*} y^{\prime }&=-\frac {y^{2} \left (x^{2} y-2 x -2 y x +y\right )}{2 \left (-2+y x -2 y\right ) x} \\ \end{align*}	✓	✓	✓	✗	12.385
21526	5272	\begin{align*} x \left (x +6 y^{2}\right ) y^{\prime }+y x -3 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	12.388
21527	25582	\begin{align*} y^{\prime \prime }+2 p y^{\prime }+\omega _{n}^{2} y&=\omega _{n}^{2} t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	12.388
21528	27736	\begin{align*} 2 y^{\prime \prime } x +y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	12.392
21529	5089	\begin{align*} \left (6 x -2 y\right ) y^{\prime }&=2+3 x -y \\ \end{align*}	✓	✓	✓	✓	12.394
21530	22439	\begin{align*} i^{\prime }&=\frac {t -i t}{t^{2}+1} \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	12.396
21531	11924	\begin{align*} y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{4}}{2 x^{3}} \\ \end{align*}	✗	✓	✓	✗	12.399
21532	21050	\begin{align*} x^{\prime }&=x^{2}-1 \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	12.405
21533	5586	\begin{align*} \left (x^{2} \left (-a^{2}+1\right )+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	12.412
21534	8155	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	12.412
21535	18115	\begin{align*} 2 y^{\prime \prime }&=3 y^{2} \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	12.413
21536	22326	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ y \left (\pi \right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	12.415
21537	24917	\begin{align*} y^{\prime }&=y^{2}-y \\ \end{align*}	✓	✓	✓	✓	12.415
21538	5094	\begin{align*} 3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	12.422
21539	23229	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	12.427
21540	3636	\begin{align*} \left (3 x -y\right ) y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	12.441
21541	19306	\begin{align*} \frac {y^{\prime } x +y}{1-y^{2} x^{2}}+x&=0 \\ \end{align*}	✓	✓	✓	✓	12.441
21542	11877	\begin{align*} y^{\prime }&=\frac {F \left (-\frac {-y^{2}+b}{x^{2}}\right ) x}{y} \\ \end{align*}	✓	✓	✓	✗	12.454
21543	5007	\begin{align*} x^{n} y^{\prime }&=a^{2} x^{2 n -2}+b^{2} y^{2} \\ \end{align*}	✓	✓	✓	✗	12.456
21544	25440	\begin{align*} y^{\prime }-4 y&=\cos \left (3 t \right )+\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	12.456
21545	22354	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+4 y^{2}} \\ \end{align*}	✓	✓	✗	✗	12.457
21546	9971	\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	12.458
21547	14826	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	12.460
21548	11622	\begin{align*} a \,x^{2} y^{n} y^{\prime }-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	12.461
21549	14418	\begin{align*} y^{\prime } x +y&=x^{3} y^{3} \\ \end{align*}	✓	✓	✓	✓	12.462
21550	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*}	✓	✓	✓	✗	12.464
21551	13222	\begin{align*} x^{4} y^{\prime }&=-y^{2} x^{4}-a^{2} \\ \end{align*}	✓	✓	✓	✓	12.470
21552	25494	\begin{align*} y^{\prime }&=y+t \\ \end{align*}	✓	✓	✓	✓	12.470
21553	20241	\begin{align*} -y^{\prime } x +y&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	12.471
21554	19337	\begin{align*} 2 x y^{2}-y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	12.475
21555	22450	\begin{align*} y^{2}+y y^{\prime } x&=\left (2 y^{2}+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	12.476
21556	25583	\begin{align*} y^{\prime \prime }+y&=4 \\ \end{align*}	✓	✓	✓	✓	12.476
21557	15946	\begin{align*} y^{\prime }&=t y \\ \end{align*}	✓	✓	✓	✓	12.481
21558	3677	\begin{align*} y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2}&=r \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	12.489
21559	9395	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	12.490
21560	22583	\begin{align*} r^{3} r^{\prime }&=\sqrt {a^{8}-r^{8}} \\ \end{align*}	✓	✓	✓	✓	12.490
21561	26620	\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	12.491
21562	25404	\begin{align*} y^{\prime }-9 y&=90 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	12.492
21563	20822	\begin{align*} x +y^{2}-2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	12.494
21564	9209	\begin{align*} y^{\prime \prime } x&=y^{\prime }-2 {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	12.497
21565	10429	\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	12.497
21566	17891	\begin{align*} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	12.498
21567	25808	\begin{align*} y^{\prime }&=y^{2} \left (4-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	12.500
21568	12196	\begin{align*} y^{\prime }&=\frac {y \left (\ln \left (y\right ) x +\ln \left (y\right )-x -1+x \ln \left (x \right )+\ln \left (x \right )+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✗	12.510
21569	24231	\begin{align*} y \left (3 x^{3}-x +y\right )+x^{2} \left (-x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.511
21570	19915	\begin{align*} y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.520
21571	13305	\begin{align*} y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,x^{n} {\mathrm e}^{\lambda x} y-a \,x^{n} \\ \end{align*}	✓	✓	✓	✗	12.523
21572	15954	\begin{align*} x^{\prime }&=-t x \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	12.524
21573	24278	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	12.525
21574	3642	\begin{align*} y^{\prime } x +y \ln \left (x \right )&=y \ln \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	12.527
21575	13642	\begin{align*} y^{\prime }&=a y^{3}+3 y^{2} a b x -b -2 a \,b^{3} x^{3} \\ \end{align*}	✓	✓	✓	✗	12.529
21576	13665	\begin{align*} y^{\prime \prime }-\left (a \,x^{2}+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	12.537
21577	7630	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	12.539
21578	13380	\begin{align*} y^{\prime }&=y^{2}+a \cos \left (\beta x \right ) y+a b \cos \left (\beta x \right )-b^{2} \\ \end{align*}	✓	✓	✓	✗	12.540
21579	25803	\begin{align*} y^{\prime }&=y^{2}-y^{4} \\ \end{align*}	✓	✓	✓	✓	12.543
21580	20287	\begin{align*} 1+4 y x +2 y^{2}+\left (1+4 y x +2 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	12.544
21581	12835	\begin{align*} y^{\prime \prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	12.549
21582	17902	\begin{align*} x^{2} \cos \left (y\right ) y^{\prime }+1&=0 \\ y \left (\infty \right ) &= \frac {16 \pi }{3} \\ \end{align*}	✓	✓	✗	✗	12.553
21583	17959	\begin{align*} 2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	12.553
21584	7908	\begin{align*} 1+y^{2}&=\left (x^{2}+x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	12.556
21585	16235	\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}	✓	✓	✓	✓	12.556
21586	14765	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	12.565
21587	5178	\begin{align*} x \left (a +b y\right ) y^{\prime }&=c y \\ \end{align*}	✓	✓	✓	✓	12.566
21588	5093	\begin{align*} \left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime }&=2 \,{\mathrm e}^{-2 x} x -\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \\ \end{align*}	✓	✓	✓	✗	12.573
21589	25699	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	12.576
21590	4806	\begin{align*} y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	12.579
21591	3030	\begin{align*} y^{\prime } x +y \left (1+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	12.581
21592	16318	\begin{align*} 1+3 y^{2} x^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.584
21593	27337	\begin{align*} y^{\prime }&=y+{\mathrm e}^{y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	12.585
21594	9817	\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	12.586
21595	25458	\begin{align*} y^{\prime }&=-{\mathrm e}^{t}+y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	12.586
21596	25427	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	12.588
21597	25657	\begin{align*} 2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	12.588
21598	8777	\begin{align*} y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	12.589
21599	1725	\begin{align*} \sin \left (y\right ) y+x \left (\sin \left (y\right )-y \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	12.591
21600	12697	\begin{align*} y^{\prime \prime }&=-\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	12.597