2.3.196 Problems 19501 to 19600

Table 2.935: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19501	10022	\begin{align*} y^{\prime } x -2 y+b y^{2}&=c \,x^{4} \\ \end{align*}	✓	✓	✓	✗	4.604
19502	21844	\begin{align*} 4 x^{2} y^{2} y^{\prime }-3 x y^{3}&=x^{2} y^{3}+2 x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.606
19503	14846	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.609
19504	21560	\begin{align*} y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.609
19505	21873	\begin{align*} x {y^{\prime }}^{2}&=y \\ \end{align*}	✓	✓	✓	✓	4.609
19506	22171	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	4.609
19507	22207	\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.611
19508	23337	\begin{align*} y^{\prime \prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.611
19509	14249	\begin{align*} y+y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	4.615
19510	5992	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.618
19511	22218	\begin{align*} y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.619
19512	14425	\begin{align*} 2 y+y^{\prime }&=6 \,{\mathrm e}^{x}+4 \,{\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	4.621
19513	24216	\begin{align*} y \left (x^{2}+y^{2}-1\right )+x \left (1+x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.621
19514	4306	\begin{align*} \cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.622
19515	17227	\begin{align*} 1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.623
19516	19004	\begin{align*} x_{1}^{\prime }&=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5} \\ x_{2}^{\prime }&=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5} \\ x_{3}^{\prime }&=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5} \\ x_{4}^{\prime }&=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5} \\ x_{5}^{\prime }&=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5} \\ \end{align*}	✓	✓	✓	✓	4.623
19517	3551	\begin{align*} 2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.625
19518	17644	\begin{align*} 2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.625
19519	20963	\begin{align*} y^{\prime }&=\frac {1+y}{2+x}+{\mathrm e}^{\frac {1+y}{2+x}} \\ \end{align*}	✓	✓	✓	✗	4.626
19520	1201	\begin{align*} 2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.628
19521	7149	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.629
19522	17796	\begin{align*} 4 x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.629
19523	11958	\begin{align*} y^{\prime }&=\frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-y^{2} x^{2}-x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	4.630
19524	12160	\begin{align*} y^{\prime }&=-\frac {2 a}{-y-2 a -2 a y^{4}+16 a^{2} x y^{2}-32 a^{3} x^{2}-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \\ \end{align*}	✓	✓	✓	✗	4.630
19525	24028	\begin{align*} y^{\left (8\right )}+y&=x^{15} \\ \end{align*}	✓	✓	✓	✗	4.630
19526	9365	\begin{align*} y^{\prime }+\frac {y}{x}&=x \\ \end{align*}	✓	✓	✓	✓	4.632
19527	13901	\begin{align*} x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y&=0 \\ \end{align*}	✗	✗	✗	✗	4.633
19528	7738	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (1+y\right ) \\ \end{align*}	✓	✓	✓	✓	4.634
19529	14491	\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.634
19530	4076	\begin{align*} 5 y x +4 y^{2}+1+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.636
19531	8688	\begin{align*} y^{\prime }&=2 \sqrt {2 x +y+1} \\ \end{align*}	✓	✓	✓	✓	4.636
19532	15874	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (3\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	4.638
19533	7753	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.642
19534	17156	\begin{align*} y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✓	4.642
19535	17245	\begin{align*} 2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.642
19536	20543	\begin{align*} y^{\prime \prime }&=y \\ \end{align*}	✓	✓	✓	✓	4.642
19537	24267	\begin{align*} \left (t^{2}+1\right ) s^{\prime }+2 t \left (s t^{2}-3 \left (t^{2}+1\right )^{2}\right )&=0 \\ s \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.642
19538	5293	\begin{align*} \left (a +x^{2}+y^{2}\right ) y y^{\prime }&=x \left (a -x^{2}-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	4.644
19539	22379	\begin{align*} y^{\prime }&=1+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	4.644
19540	22752	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.644
19541	10376	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	4.645
19542	15876	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✗	✓	4.645
19543	23351	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.646
19544	20586	\begin{align*} x^{4} y^{\prime \prime }&=\left (x^{3}+2 y x \right ) y^{\prime }-4 y^{2} \\ \end{align*}	✗	✓	✓	✗	4.647
19545	5488	\begin{align*} 4 x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.648
19546	17148	\begin{align*} y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \\ \end{align*}	✓	✓	✓	✓	4.649
19547	5458	\begin{align*} x {y^{\prime }}^{2}-y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	4.650
19548	22760	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=\sqrt {x}+\frac {1}{\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	4.654
19549	23322	\begin{align*} 2 y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.654
19550	1535	\begin{align*} y^{\prime }&={| y|}+1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.655
19551	2848	\begin{align*} \tan \left (x \right ) y^{\prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	4.656
19552	6576	\begin{align*} 3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	4.657
19553	1540	\begin{align*} y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.658
19554	19676	\begin{align*} 2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✗	4.658
19555	2984	\begin{align*} \sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t}&=0 \\ \end{align*}	✓	✓	✓	✓	4.664
19556	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*}	✓	✓	✓	✗	4.664
19557	15605	\begin{align*} x y \left (1-y\right )-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.664
19558	8365	\begin{align*} \left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.667
19559	15056	\begin{align*} y \left (x -y\right )-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.668
19560	14257	\begin{align*} N^{\prime }&=N-9 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	4.670
19561	18074	\begin{align*} x +y+1+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.673
19562	13251	\begin{align*} 2 x^{2} y^{\prime }&=2 y^{2}+3 y x -2 a^{2} x \\ \end{align*}	✓	✓	✓	✗	4.674
19563	17812	\begin{align*} x^{\prime \prime }+x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.676
19564	1619	\begin{align*} y^{\prime }&=\sqrt {x +y} \\ \end{align*}	✓	✓	✓	✓	4.677
19565	5316	\begin{align*} x \left (1-2 x^{2} y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.677
19566	2968	\begin{align*} x^{2} y^{\prime }+y-2 y x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.679
19567	7536	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.679
19568	9011	\begin{align*} y^{\prime }&=y^{2} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	4.679
19569	60	\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.681
19570	19673	\begin{align*} x^{\prime }&=\cos \left (\frac {x}{t}\right ) \\ \end{align*}	✓	✓	✓	✓	4.681
19571	13988	\begin{align*} y^{\prime } x +\left (x +1\right ) y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	4.683
19572	10216	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.684
19573	10429	\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	4.686
19574	6323	\begin{align*} y^{\prime \prime }&=g \left (x \right )+f \left (x \right ) y^{2}+\left (f \left (x \right )-2 y\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	4.688
19575	15786	\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}	✓	✓	✓	✓	4.690
19576	17890	\begin{align*} y^{\prime }&=a x +b y+c \\ \end{align*}	✓	✓	✓	✓	4.691
19577	8322	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	4.693
19578	12154	\begin{align*} y^{\prime }&=\frac {\left (-256 a \,x^{2}+512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512} \\ \end{align*}	✓	✓	✓	✗	4.693
19579	16888	\begin{align*} x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{x -2}+\frac {2 y}{2+x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	4.694
19580	21991	\begin{align*} x -y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.694
19581	17106	\begin{align*} y^{\prime }&=y^{3}+y \\ \end{align*}	✓	✓	✓	✓	4.699
19582	9759	\begin{align*} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.700
19583	12071	\begin{align*} y^{\prime }&=-\frac {\ln \left (x -1\right )-x^{2} \coth \left (x +1\right )-2 \coth \left (x +1\right ) x y-\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )} \\ \end{align*}	✓	✗	✓	✗	4.700
19584	19316	\begin{align*} y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.700
19585	12422	\begin{align*} x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right )&=0 \\ \end{align*}	✗	✓	✓	✗	4.701
19586	13810	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✓	4.703
19587	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*}	✓	✓	✓	✗	4.704
19588	8377	\begin{align*} y^{\prime }&=y^{2}-4 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	4.705
19589	19899	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.705
19590	13824	\begin{align*} \left (x^{2}+a \right ) y^{\prime \prime }+2 b x y^{\prime }+2 \left (b -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.706
19591	22487	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.707
19592	18377	\begin{align*} \ln \left (x \right ) y^{\prime \prime }-\sin \left (x \right ) y&=0 \\ y \left ({\mathrm e}\right ) &= {\mathrm e}^{-1} \\ y^{\prime }\left ({\mathrm e}\right ) &= 0 \\ \end{align*} Series expansion around \(x={\mathrm e}\).	✓	✓	✓	✓	4.708
19593	21349	\begin{align*} \cos \left (x \right ) x +\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.710
19594	26168	\begin{align*} y^{2} y^{\prime } x +y^{3}&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	4.712
19595	13960	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	4.713
19596	4936	\begin{align*} x \left (x +1\right ) y^{\prime }&=\left (1-2 x \right ) y \\ \end{align*}	✓	✓	✓	✓	4.714
19597	12103	\begin{align*} y^{\prime }&=\frac {y \left (y x +1\right )}{x \left (-y x -1+x^{3} y^{4}\right )} \\ \end{align*}	✓	✓	✓	✗	4.717
19598	15657	\begin{align*} \sqrt {1-x}\, y^{\prime \prime }-4 y&=\sin \left (x \right ) \\ y \left (-2\right ) &= 3 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✗	✓	✗	✗	4.717
19599	17095	\begin{align*} \frac {\sqrt {\ln \left (x \right )}}{x}&=\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \\ \end{align*}	✓	✓	✓	✓	4.718
19600	4812	\begin{align*} y^{\prime } x +\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.719