2.3.167 Problems 16601 to 16700

Table 2.907: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16601	4935	\begin{align*} x \left (1-x \right ) y^{\prime }&=2 y x -2 \\ \end{align*}	✓	✓	✓	✓	2.414
16602	6246	\begin{align*} \left (-x^{2}+1\right ) y-x \left (-x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.414
16603	8082	\begin{align*} x y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.414
16604	16574	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.414
16605	20654	\begin{align*} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a}&=0 \\ \end{align*}	✓	✓	✓	✗	2.414
16606	21305	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{4} \\ x_{2}^{\prime }&=-x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}+x_{3} \\ x_{4}^{\prime }&=x_{1}-x_{4} \\ \end{align*}	✓	✓	✓	✓	2.414
16607	23132	\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.414
16608	5626	\begin{align*} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	2.415
16609	8176	\begin{align*} 2 x y^{\prime }-y&=2 x \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.415
16610	13743	\begin{align*} x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (2 a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.415
16611	20302	\begin{align*} \ln \left (y\right ) y+x y^{\prime }&=y x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.415
16612	26303	\begin{align*} y^{\prime }-y \tan \left (x \right )&=\sec \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.415
16613	4912	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=a +4 y x \\ \end{align*}	✓	✓	✓	✓	2.417
16614	16994	\begin{align*} y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.417
16615	9142	\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.418
16616	20497	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.418
16617	20864	\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.418
16618	17805	\begin{align*} 10 x^{\prime \prime }+\frac {x}{10}&=0 \\ x \left (0\right ) &= -5 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.419
16619	20184	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=x^{5} \\ \end{align*}	✓	✓	✓	✗	2.421
16620	25908	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.421
16621	17665	\begin{align*} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=\arctan \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.422
16622	12338	\begin{align*} y^{\prime \prime }-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y \,{\mathrm e}^{2 x}-{\mathrm e}^{3 x}&=0 \\ \end{align*}	✓	✓	✓	✗	2.423
16623	1128	\begin{align*} -\frac {3 y}{2}+y^{\prime }&=2 \,{\mathrm e}^{t}+3 t \\ \end{align*}	✓	✓	✓	✓	2.424
16624	1521	\begin{align*} y^{\prime }+2 y x&=x \\ \end{align*}	✓	✓	✓	✓	2.424
16625	6552	\begin{align*} x^{2} y^{2} y^{\prime \prime }&=\left (x^{2}+y^{2}\right ) \left (x y^{\prime }-y\right ) \\ \end{align*}	✗	✓	✓	✗	2.424
16626	24687	\begin{align*} y^{\left (6\right )}-y&=x^{10} \\ \end{align*}	✓	✓	✓	✓	2.424
16627	3971	\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.425
16628	4979	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=a -x^{2} y \\ \end{align*}	✓	✓	✓	✓	2.425
16629	25581	\begin{align*} r^{\prime \prime }+r&=1 \\ r \left (0\right ) &= 0 \\ r^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.425
16630	5963	\begin{align*} -\left (n \left (n +1\right )+a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.426
16631	1238	\begin{align*} \frac {-4+6 y x +2 y^{2}}{3 x^{2}+4 y x +3 y^{2}}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.427
16632	16415	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }-2\right ) \\ \end{align*}	✓	✓	✓	✓	2.427
16633	21612	\begin{align*} \left (x +2\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	2.427
16634	23142	\begin{align*} y^{\prime }&=x -y x -y+1 \\ \end{align*}	✓	✓	✓	✓	2.427
16635	26465	\begin{align*} 2 y^{2} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✗	2.427
16636	20426	\begin{align*} {y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y^{2}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.428
16637	25861	\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.428
16638	21794	\begin{align*} y^{\prime }+y&=2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	2.429
16639	2409	\begin{align*} y^{\prime \prime }+\frac {t^{2} y}{4}&=f \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✗	2.431
16640	6020	\begin{align*} \left (\operatorname {b2} \,x^{2}+\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.431
16641	17105	\begin{align*} y^{\prime }&=y^{3}-y \\ \end{align*}	✓	✓	✓	✓	2.431
16642	20957	\begin{align*} y^{\prime }&=y-\mu y^{2} \\ \end{align*}	✓	✓	✓	✓	2.432
16643	801	\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	2.433
16644	8888	\begin{align*} 3 y^{\prime \prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.433
16645	10112	\begin{align*} y^{\prime \prime }-y x -x^{6}-x^{3}+42&=0 \\ \end{align*}	✓	✓	✓	✓	2.433
16646	5888	\begin{align*} x y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.434
16647	25812	\begin{align*} y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.434
16648	8431	\begin{align*} \left (x +1\right ) y^{\prime }-y x&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	2.435
16649	18295	\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.436
16650	14300	\begin{align*} x^{\prime \prime }+x^{\prime }+x&={\mathrm e}^{2 t} \cos \left (t \right )+t^{2} \\ \end{align*}	✓	✓	✓	✓	2.437
16651	19345	\begin{align*} 2 y-x^{3}&=x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.437
16652	22113	\begin{align*} y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.437
16653	11726	\begin{align*} {y^{\prime }}^{2} x^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.438
16654	22714	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) {\mathrm e}^{-x}+2 x \\ \end{align*}	✓	✓	✓	✓	2.438
16655	1542	\begin{align*} y^{\prime }+\frac {\left (x +1\right ) y}{x}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.440
16656	12824	\begin{align*} y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.440
16657	16575	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y&=0 \\ y \left (1\right ) &= 9 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.440
16658	23968	\begin{align*} y^{\prime }-2 y&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	2.440
16659	6924	\begin{align*} \frac {1+2 y x}{y}+\frac {\left (-x +y\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.441
16660	15441	\begin{align*} y^{\prime \prime }+n^{2} y&=h \sin \left (r x \right ) \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= c \\ \end{align*}	✓	✓	✓	✓	2.441
16661	15910	\begin{align*} y^{\prime }+2 y&=3 t^{2}+2 t -1 \\ \end{align*}	✓	✓	✓	✓	2.441
16662	17388	\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.441
16663	2438	\begin{align*} t^{2} y^{\prime \prime }-t y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.442
16664	7780	\begin{align*} \frac {x^{\prime \prime }}{2}&=-48 x \\ x \left (0\right ) &= {\frac {1}{6}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.442
16665	9754	\begin{align*} 2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.442
16666	12364	\begin{align*} x y^{\prime \prime }-y^{\prime }-a \,x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.442
16667	15791	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{t} y}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.442
16668	24809	\begin{align*} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	2.442
16669	2090	\begin{align*} x y^{\prime \prime }-5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.444
16670	18740	\begin{align*} y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.444
16671	21834	\begin{align*} 2+3 x -5 y+7 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.444
16672	27272	\begin{align*} \left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✗	2.444
16673	4894	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-1&=y x \\ \end{align*}	✓	✓	✓	✓	2.445
16674	4904	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.445
16675	7463	\begin{align*} 2 x +\frac {y}{1+x^{2} y^{2}}+\left (\frac {x}{1+x^{2} y^{2}}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.445
16676	18778	\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.445
16677	23894	\begin{align*} y^{3}+2 x y^{3}+1+3 x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.445
16678	25710	\begin{align*} y^{\prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	2.445
16679	7423	\begin{align*} 3 r&=r^{\prime }-\theta ^{3} \\ \end{align*}	✓	✓	✓	✓	2.446
16680	17355	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.446
16681	11404	\begin{align*} x y^{\prime }+a x y^{2}+2 y+b x&=0 \\ \end{align*}	✓	✓	✓	✗	2.447
16682	6416	\begin{align*} f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right )^{2} y^{\prime \prime }&=g \left (y, f \left (x \right ) y^{\prime }\right ) \\ \end{align*}	✗	✗	✗	✗	2.448
16683	6946	\begin{align*} x^{2}+y^{2}+x +x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.448
16684	19338	\begin{align*} y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.449
16685	25733	\begin{align*} 2 y+y^{\prime }&=3 x -6 \\ y \left (x_{0} \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.450
16686	720	\begin{align*} \left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.451
16687	8145	\begin{align*} x y^{\prime \prime }+x^{5} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.451
16688	23168	\begin{align*} x y^{\prime }-\frac {y}{2 \ln \left (x \right )}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.451
16689	12300	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 x}+b \,{\mathrm e}^{x}+c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.453
16690	15634	\begin{align*} y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.453
16691	20859	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.453
16692	13770	\begin{align*} \left (x +\gamma \right ) y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a n \,x^{n -1}+b m \,x^{m -1}\right ) y&=0 \\ \end{align*}	✓	✓	✗	✗	2.454
16693	17139	\begin{align*} -y+y^{\prime }&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.454
16694	19134	\begin{align*} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	2.454
16695	1568	\begin{align*} x y^{\prime }-2 y&=-x^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.455
16696	3008	\begin{align*} 2 y x -2 x y^{3}+x^{3}+\left (x^{2}+y^{2}-3 x^{2} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.455
16697	3317	\begin{align*} y&=y^{\prime } x \left (y^{\prime }+1\right ) \\ \end{align*}	✓	✓	✓	✓	2.455
16698	5714	\begin{align*} y^{\prime \prime }&=\operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x} \\ \end{align*}	✓	✓	✓	✓	2.455
16699	5961	\begin{align*} -\left (a^{2} x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.455
16700	22710	\begin{align*} y^{\prime \prime }+y&=x \,{\mathrm e}^{-x}+3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.455