2.3.167 Problems 16601 to 16700

Table 2.883: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16601	20953	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	2.645
16602	22873	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.645
16603	8472	\begin{align*} y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	2.647
16604	12396	\begin{align*} a y+y^{\prime }+2 y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.647
16605	24917	\begin{align*} y^{\prime }&=y^{2}-y \\ \end{align*}	✓	✓	✓	✓	2.648
16606	26108	\begin{align*} y^{\prime \prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	2.648
16607	1538	\begin{align*} y^{\prime }+3 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.649
16608	18365	\begin{align*} y^{\prime \prime }+\lambda ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.649
16609	19631	\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.649
16610	17194	\begin{align*} y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.650
16611	21670	\begin{align*} y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.650
16612	25673	\begin{align*} y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.650
16613	603	\begin{align*} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }&=5 x-y-t^{2} \\ \end{align*}	✓	✓	✓	✓	2.651
16614	11689	\begin{align*} 2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	2.651
16615	19979	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✗	✓	2.651
16616	22037	\begin{align*} y-x y^{2}+\left (y^{2} x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.651
16617	26420	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.652
16618	1133	\begin{align*} y^{\prime }&=\cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.653
16619	25048	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.653
16620	20674	\begin{align*} -y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	2.654
16621	22549	\begin{align*} \left (\sin \left (y\right )-x \right ) y^{\prime }&=2 x +y \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✗	2.654
16622	23962	\begin{align*} y^{\prime }&=z \\ z^{\prime }&=w \\ w^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	2.654
16623	20437	\begin{align*} \left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.655
16624	776	\begin{align*} 2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.656
16625	8248	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.656
16626	88	\begin{align*} y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\ y \left (\pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.657
16627	18354	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.657
16628	21612	\begin{align*} \left (2+x \right ) y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	2.657
16629	1169	\begin{align*} 2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\ y \left (-3\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.658
16630	10330	\begin{align*} 2 x^{\prime }+y^{\prime }-x&=y+t \\ x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.658
16631	15501	\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.658
16632	16359	\begin{align*} \ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.658
16633	20710	\begin{align*} y^{\prime \prime }+a^{2} y&=\cos \left (a x \right ) \\ \end{align*}	✓	✓	✓	✓	2.658
16634	66	\begin{align*} y^{\prime }&=2 x y^{2}+3 y^{2} x^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.659
16635	5246	\begin{align*} \left (x -6 y\right )^{2} y^{\prime }+a +2 y x -6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.659
16636	12562	\begin{align*} \left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.659
16637	20420	\begin{align*} x {y^{\prime }}^{2}-y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	2.659
16638	23384	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.660
16639	3627	\begin{align*} y-{\mathrm e}^{x}+y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.661
16640	15519	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (2\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.661
16641	17190	\begin{align*} \frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	2.661
16642	22608	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	2.661
16643	3271	\begin{align*} y^{\prime \prime }&=\sec \left (x \right ) \tan \left (x \right ) \\ y \left (0\right ) &= \frac {\pi }{4} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.662
16644	19105	\begin{align*} y^{\prime }&=2 y x -x^{3}+x \\ \end{align*}	✓	✓	✓	✓	2.662
16645	20184	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \\ \end{align*}	✓	✓	✓	✗	2.662
16646	22028	\begin{align*} y+2 x y^{3}+\left (1+3 y^{2} x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.662
16647	18926	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.663
16648	22606	\begin{align*} y^{\prime }+y x&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	2.663
16649	15316	\begin{align*} y^{\prime \prime }+\alpha ^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.664
16650	17182	\begin{align*} 3 y+y^{\prime }&=27 t^{2}+9 \\ \end{align*}	✓	✓	✓	✓	2.664
16651	23201	\begin{align*} 2 x^{2}+2 y^{2}+x +\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.664
16652	11329	\begin{align*} y^{\prime }+a y \left (-x +y\right )-1&=0 \\ \end{align*}	✓	✓	✓	✗	2.665
16653	13790	\begin{align*} \left (a \left (1+a \right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.665
16654	14982	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.665
16655	17848	\begin{align*} y^{\prime } x +y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.665
16656	22861	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.665
16657	5219	\begin{align*} \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	2.666
16658	9242	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.667
16659	22219	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (2 x^{2}+4 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.667
16660	23396	\begin{align*} y^{\prime \prime }-\frac {5 y^{\prime }}{x}+\frac {5 y}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.667
16661	8247	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.668
16662	17615	\begin{align*} 2 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.668
16663	695	\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.669
16664	19341	\begin{align*} y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\ \end{align*}	✓	✓	✓	✓	2.669
16665	5549	\begin{align*} y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.670
16666	12498	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +2&=0 \\ \end{align*}	✓	✓	✓	✓	2.670
16667	16964	\begin{align*} y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.670
16668	8802	\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	2.671
16669	10091	\begin{align*} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	2.671
16670	17616	\begin{align*} 2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.672
16671	5587	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.673
16672	715	\begin{align*} y^{\prime } x +3 y&=2 x^{5} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.674
16673	6124	\begin{align*} 6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.674
16674	2481	\begin{align*} y^{\prime }-2 t y&=t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.675
16675	20842	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.675
16676	14967	\begin{align*} x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z&=0 \\ z \left (1\right ) &= 0 \\ z^{\prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.677
16677	21257	\begin{align*} x^{\prime \prime }&=x^{3}-x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	2.677
16678	18808	\begin{align*} -3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.678
16679	19597	\begin{align*} x^{2} y^{\prime \prime }+\sin \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.678
16680	21022	\begin{align*} x^{\prime }-2 x&=2 t \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.678
16681	2637	\begin{align*} t \left (-2+t \right )^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	2.679
16682	17458	\begin{align*} y^{\prime \prime }-y&=4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.679
16683	20725	\begin{align*} y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.679
16684	1572	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-2 y x&=x \left (x^{2}-1\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.680
16685	775	\begin{align*} 3 y+x^{4} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	2.681
16686	14226	\begin{align*} x^{\prime }&=\left (4 t -x\right )^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.681
16687	14425	\begin{align*} 2 y+y^{\prime }&=6 \,{\mathrm e}^{x}+4 \,{\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	2.681
16688	17177	\begin{align*} -y+y^{\prime }&=\sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.681
16689	22871	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (3 x^{2}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.681
16690	8611	\begin{align*} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.682
16691	14690	\begin{align*} x^{2} y^{\prime \prime }-6 y^{\prime } x +10 y&=3 x^{4}+6 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.682
16692	24721	\begin{align*} y^{\prime \prime }+y&=3 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.682
16693	1625	\begin{align*} y^{\prime }-y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	2.683
16694	2476	\begin{align*} t^{2} y+y^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	2.683
16695	19172	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.683
16696	22004	\begin{align*} x \,{\mathrm e}^{x}+\left (y^{5}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.684
16697	25711	\begin{align*} \left (4-y^{2}\right ) y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.684
16698	15054	\begin{align*} x^{2}-y+\left (y^{2} x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.685
16699	16894	\begin{align*} \left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.685
16700	11400	\begin{align*} y^{\prime } x +a +x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.686