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	736	\begin{align*} x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✗	5.803
21502	5747	\begin{align*} \left (b^{2} x^{2}+a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.803
21503	10068	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.803
21504	14520	\begin{align*} y-1+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.804
21505	5292	\begin{align*} \left (a^{2} x +y \left (x^{2}-y^{2}\right )\right ) y^{\prime }+x \left (x^{2}-y^{2}\right )&=a^{2} y \\ \end{align*}	✓	✓	✓	✗	5.805
21506	5537	\begin{align*} x^{2} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	5.805
21507	14845	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.805
21508	24214	\begin{align*} \left (-y^{2}+x^{2}+1\right ) y-x \left (x^{2}-y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.805
21509	13837	\begin{align*} \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (k x +d \right ) y^{\prime }-k y&=0 \\ \end{align*}	✓	✓	✓	✗	5.809
21510	15313	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	5.809
21511	16756	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{\left (x +1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	5.812
21512	20902	\begin{align*} x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✓	✓	✓	✓	5.812
21513	5270	\begin{align*} x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime }&=6 y^{3} \\ \end{align*}	✓	✓	✓	✓	5.813
21514	18880	\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y&=t \\ \end{align*}	✓	✓	✓	✓	5.813
21515	19412	\begin{align*} x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	5.813
21516	2855	\begin{align*} x y^{\prime }+y&=x y \left (y^{\prime }-1\right ) \\ \end{align*}	✓	✓	✓	✓	5.814
21517	15399	\begin{align*} y^{\prime \prime }&=\frac {1}{2 y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	5.814
21518	27240	\begin{align*} x y^{\prime }-y&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	5.814
21519	18040	\begin{align*} y^{\prime }&=\left (x -y\right )^{2}+1 \\ \end{align*}	✓	✓	✓	✓	5.815
21520	5000	\begin{align*} \left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\ \end{align*}	✓	✓	✓	✗	5.817
21521	5836	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	5.818
21522	13490	\begin{align*} y^{\prime }&=y^{2}+a^{2} f \left (a x +b \right ) \\ \end{align*}	✗	✗	✗	✗	5.818
21523	26476	\begin{align*} y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	5.820
21524	14931	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.821
21525	2936	\begin{align*} x y^{\prime }+\ln \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.822
21526	13222	\begin{align*} x^{4} y^{\prime }&=-y^{2} x^{4}-a^{2} \\ \end{align*}	✓	✓	✓	✓	5.822
21527	13272	\begin{align*} \left (a \,x^{2}+b x +e \right ) \left (x y^{\prime }-y\right )-y^{2}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.822
21528	7314	\begin{align*} {y^{\prime \prime }}^{2}&=k^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	5.823
21529	18928	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.823
21530	1193	\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.824
21531	19102	\begin{align*} \left (x^{2} y^{2}-1\right ) y^{\prime }+2 x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.824
21532	15545	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {15-x^{2}-y^{2}}} \\ \end{align*}	✗	✗	✗	✗	5.828
21533	15546	\begin{align*} y^{\prime }&=\frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	5.828
21534	19377	\begin{align*} x y^{\prime }+y&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	5.831
21535	21012	\begin{align*} t^{2} x^{\prime }-2 x t&=t^{5} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.832
21536	21995	\begin{align*} {\mathrm e}^{x}-y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.832
21537	2856	\begin{align*} y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.833
21538	14482	\begin{align*} x^{4} y^{\prime }+2 x^{3} y&=1 \\ \end{align*}	✓	✓	✓	✓	5.833
21539	18589	\begin{align*} y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.834
21540	7127	\begin{align*} y^{\prime \prime }&=2 k y^{3} \\ \end{align*}	✓	✓	✓	✓	5.840
21541	18624	\begin{align*} \left (2-x \right ) y^{\prime }&=y+2 \left (2-x \right )^{5} \\ \end{align*}	✓	✓	✓	✓	5.840
21542	24978	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{t} \\ y \left (1\right ) &= \sqrt {3} \\ \end{align*}	✓	✓	✓	✓	5.843
21543	23873	\begin{align*} y^{\prime }&=\frac {x^{2} {\mathrm e}^{\frac {y}{x}}+y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✗	5.846
21544	25773	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= -4 \\ \end{align*}	✗	✗	✗	✗	5.846
21545	2480	\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.847
21546	15388	\begin{align*} y&=2 x y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.847
21547	10000	\begin{align*} y^{\prime }&=\frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	5.849
21548	21081	\begin{align*} x +2 y+\left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.849
21549	15542	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	5.851
21550	5687	\begin{align*} \sqrt {1+{y^{\prime }}^{2}}&=x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.854
21551	14261	\begin{align*} x^{\prime }&=2 x t \\ \end{align*}	✓	✓	✓	✓	5.854
21552	20969	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-y^{2}}}{y \left (x^{2}+2 x \right )} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.855
21553	18850	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.858
21554	27537	\begin{align*} {y^{\prime \prime }}^{3}+x y^{\prime \prime }&=2 y^{\prime } \\ \end{align*}	✓	✓	✗	✗	5.858
21555	16978	\begin{align*} \cos \left (t \right ) y+\left (2 y+\sin \left (t \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.861
21556	25774	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (8\right ) &= -4 \\ \end{align*}	✗	✗	✗	✗	5.863
21557	1176	\begin{align*} y^{3}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.864
21558	25721	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.864
21559	6429	\begin{align*} y y^{\prime \prime }&=y y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.865
21560	12398	\begin{align*} 2 x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+a y&=0 \\ \end{align*}	✗	✓	✓	✗	5.865
21561	14456	\begin{align*} y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.866
21562	18564	\begin{align*} y^{\prime }&=y \left (3-y t \right ) \\ \end{align*}	✓	✓	✓	✓	5.870
21563	24369	\begin{align*} y x +1+x \left (x +4 y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.871
21564	12480	\begin{align*} x^{2} y^{\prime \prime }+\left (-x^{4}+\left (2 n +2 a +1\right ) x^{2}+\left (-1\right )^{n} a -a^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.874
21565	14266	\begin{align*} x^{\prime }+p \left (t \right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	5.874
21566	3277	\begin{align*} y y^{\prime \prime }&=y^{3}+{y^{\prime }}^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	5.875
21567	19228	\begin{align*} x y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	5.875
21568	21056	\begin{align*} x^{\prime }&={\mathrm e}^{t} \left (x^{2}+1\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.875
21569	10021	\begin{align*} f^{\prime } x -f&=\frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}} \\ \end{align*}	✓	✓	✓	✗	5.876
21570	11466	\begin{align*} 3 x^{2} y^{\prime }-7 y^{2}-3 y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.877
21571	13449	\begin{align*} y^{\prime }&=y^{2}+f \left (x \right ) y-a^{2}-a f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.877
21572	8740	\begin{align*} 2 y^{\prime }+x&=4 \sqrt {y} \\ \end{align*}	✓	✓	✓	✗	5.882
21573	19910	\begin{align*} \left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✗	5.884
21574	7218	\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	5.885
21575	8325	\begin{align*} y^{\prime }&=y-y^{3} \\ \end{align*}	✓	✓	✓	✓	5.885
21576	24189	\begin{align*} \cos \left (2 y\right )-3 x^{2} y^{2}+\left (\cos \left (2 y\right )-2 x \sin \left (2 y\right )-2 x^{3} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.885
21577	1533	\begin{align*} y^{\prime }&=-\frac {y \left (y+1\right )}{x} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	5.891
21578	5884	\begin{align*} \left (-x^{2}+4 a +2\right ) y+4 y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	5.891
21579	25855	\begin{align*} 3-2 y+\left (x^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.894
21580	5042	\begin{align*} y y^{\prime }&=a x +b y^{2} \\ \end{align*}	✓	✓	✓	✓	5.895
21581	5284	\begin{align*} x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	5.895
21582	64	\begin{align*} \tan \left (x \right ) y^{\prime }&=y \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	5.896
21583	27511	\begin{align*} 2 x y^{\prime }+1&=y+\frac {x^{2}}{-1+y} \\ \end{align*}	✓	✓	✓	✓	5.898
21584	5867	\begin{align*} \left (\cos \left (x \right )^{2} a -\sec \left (x \right )^{2}\right ) y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.901
21585	20481	\begin{align*} -x y^{\prime }+y&=a \left (y^{\prime }+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	5.903
21586	5471	\begin{align*} {y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✗	✓	5.905
21587	16219	\begin{align*} y^{\prime }&=y^{2}+9 \\ \end{align*}	✓	✓	✓	✓	5.905
21588	3644	\begin{align*} 2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.908
21589	2997	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.909
21590	214	\begin{align*} y^{\prime }&=\frac {\sqrt {y}-y}{\tan \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	5.911
21591	27257	\begin{align*} y^{\prime }&=y^{2}-\frac {2}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.911
21592	18055	\begin{align*} y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.913
21593	4857	\begin{align*} \left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \\ \end{align*}	✓	✓	✓	✓	5.914
21594	14472	\begin{align*} 8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime }&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✗	5.914
21595	16859	\begin{align*} {\mathrm e}^{3 x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\frac {2 y}{x^{2}+4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.914
21596	1148	\begin{align*} \sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.916
21597	7541	\begin{align*} y^{\prime }&=\left (2 x +y-1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.918
21598	12220	\begin{align*} y^{\prime }&=\frac {x y \ln \left (x \right )+x^{2} \ln \left (x \right )-2 y x -x^{2}-y^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x \left (-y+x \ln \left (x \right )-x \right )} \\ \end{align*}	✓	✓	✓	✗	5.922
21599	14691	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=1 \\ \end{align*}	✓	✓	✓	✗	5.922
21600	21355	\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	5.922