2.3.167 Problems 16601 to 16700

Table 2.865: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16601	12293	\begin{align*} y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.644
16602	2072	\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (9-x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.645
16603	15679	\begin{align*} y^{\prime \prime }+\alpha y&=0 \\ \end{align*}	✓	✓	✓	✓	1.645
16604	12399	\begin{align*} \left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.647
16605	16358	\begin{align*} 1-\left (x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.647
16606	19696	\begin{align*} x^{\prime \prime }-x&=t^{2} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.647
16607	23132	\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.647
16608	24073	\begin{align*} y^{\prime \prime }-y^{\prime }-y&=\sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.647
16609	2096	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.648
16610	4283	\begin{align*} y^{\prime } x +y&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.648
16611	5240	\begin{align*} \left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	1.648
16612	5671	\begin{align*} {y^{\prime }}^{4}+y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✗	✗	1.648
16613	6202	\begin{align*} y a \,x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.648
16614	13289	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{k x} y^{2}+b \,{\mathrm e}^{s x} \\ \end{align*}	✓	✓	✓	✗	1.648
16615	16898	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.648
16616	20103	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.648
16617	23860	\begin{align*} 2 x^{3} y+\left (2 y^{2} x^{2}+2 y^{4}+\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	1.648
16618	9089	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.649
16619	23162	\begin{align*} y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	1.649
16620	748	\begin{align*} y^{2} y^{\prime }+2 x y^{3}&=6 x \\ \end{align*}	✓	✓	✓	✓	1.650
16621	6332	\begin{align*} y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.650
16622	2098	\begin{align*} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.651
16623	4753	\begin{align*} y^{\prime } x&=x^{3}-y \\ \end{align*}	✓	✓	✓	✓	1.651
16624	23538	\begin{align*} 5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	1.651
16625	2071	\begin{align*} x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.652
16626	14521	\begin{align*} x^{2}-2 y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.652
16627	2303	\begin{align*} t^{2} y+y^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	1.653
16628	10454	\begin{align*} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.653
16629	3905	\begin{align*} x_{1}^{\prime }&=-16 x_{1}+30 x_{2}-18 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+8 x_{2}+16 x_{3} \\ x_{3}^{\prime }&=8 x_{1}-15 x_{2}+9 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.654
16630	4094	\begin{align*} {\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.654
16631	7481	\begin{align*} x^{4}-x +y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.654
16632	9389	\begin{align*} y^{\prime \prime } x +y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.654
16633	5163	\begin{align*} 2 x y^{\prime } y+x^{2} \left (a \,x^{3}+1\right )&=6 y^{2} \\ \end{align*}	✓	✓	✓	✓	1.655
16634	6344	\begin{align*} f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.655
16635	8828	\begin{align*} a y^{\prime \prime } y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.655
16636	12444	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✗	1.655
16637	14251	\begin{align*} t x^{\prime }&=-x+t^{2} \\ \end{align*}	✓	✓	✓	✓	1.655
16638	10424	\begin{align*} 10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \\ \end{align*}	✗	✓	✓	✗	1.657
16639	15115	\begin{align*} y^{\prime }&=y \,{\mathrm e}^{x +y} \left (x^{2}+1\right ) \\ \end{align*}	✓	✓	✓	✓	1.657
16640	22514	\begin{align*} s^{2} t s^{\prime }+t^{2}+4&=0 \\ \end{align*}	✓	✓	✓	✓	1.657
16641	1228	\begin{align*} x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.658
16642	2343	\begin{align*} 3 t^{2}+4 t y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.658
16643	2374	\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*}	✓	✓	✓	✓	1.658
16644	2965	\begin{align*} 1&=\left ({\mathrm e}^{y}+x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.658
16645	22511	\begin{align*} y^{\prime }+\frac {2 y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.658
16646	23629	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ z^{\prime }&=x+y-5 z \\ u^{\prime }&=5 z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ u \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.658
16647	15376	\begin{align*} \left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.659
16648	22308	\begin{align*} y^{\prime \prime }&=12 x \left (4-x \right ) \\ y \left (0\right ) &= 7 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.659
16649	18274	\begin{align*} y^{\prime \prime }-y^{\prime }&=-5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\ y \left (0\right ) &= -4 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.661
16650	18595	\begin{align*} \left (1+y^{4}\right ) y^{\prime }&=x^{4}+1 \\ \end{align*}	✓	✓	✓	✓	1.661
16651	19875	\begin{align*} x&=y^{\prime \prime }+y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.661
16652	23048	\begin{align*} y^{\prime \prime } {y^{\prime }}^{2}-x^{2}&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.661
16653	89	\begin{align*} \left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.662
16654	12468	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.662
16655	21977	\begin{align*} y^{\prime }&=\frac {y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	1.662
16656	6056	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.663
16657	2518	\begin{align*} y^{\prime }&=2 t \left (1+y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.664
16658	16214	\begin{align*} y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.664
16659	16300	\begin{align*} y^{\prime }&=4+\frac {1}{\sin \left (4 x -y\right )} \\ \end{align*}	✓	✓	✓	✓	1.664
16660	22070	\begin{align*} y^{\prime }+6 y x&=0 \\ y \left (\pi \right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.664
16661	23550	\begin{align*} -3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\ y \left (\frac {1}{4}\right ) &= 0 \\ y^{\prime }\left (\frac {1}{4}\right ) &= {\frac {14}{9}} \\ \end{align*}	✓	✓	✓	✓	1.664
16662	13763	\begin{align*} y^{\prime \prime } x +\left (a b \,x^{n}+b \,x^{n -1}+a x -1\right ) y^{\prime }+a^{2} b \,x^{n} y&=0 \\ \end{align*}	✗	✗	✗	✗	1.665
16663	17930	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.665
16664	22975	\begin{align*} y^{\prime }&=\frac {x +y+2}{x +1} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.665
16665	1545	\begin{align*} y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.666
16666	14711	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=4 x -6 \\ \end{align*}	✓	✓	✓	✓	1.666
16667	22042	\begin{align*} y+1-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.666
16668	1124	\begin{align*} \frac {y}{2}+y^{\prime }&=2 \cos \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.668
16669	2978	\begin{align*} 2 y-y x -3+y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.668
16670	4727	\begin{align*} y^{\prime }&=\cos \left (x \right ) \sec \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.668
16671	5180	\begin{align*} \left (1-x^{2} y\right ) y^{\prime }+1-x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.668
16672	6388	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+2 y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.668
16673	8146	\begin{align*} \sin \left (x \right ) y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.668
16674	8431	\begin{align*} \left (x +1\right ) y^{\prime }-y x&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	1.668
16675	5091	\begin{align*} \left (x^{3}+2 y\right ) y^{\prime }&=3 x \left (2-y x \right ) \\ \end{align*}	✓	✓	✓	✗	1.669
16676	25431	\begin{align*} y^{\prime }-a \left (t \right ) y&=q \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.669
16677	3272	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.671
16678	12490	\begin{align*} y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.671
16679	15045	\begin{align*} x^{\prime }+5 x&=10 t +2 \\ x \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.671
16680	17796	\begin{align*} 4 x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.671
16681	23290	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +y&=2 \\ y \left (\frac {3 \pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {3 \pi }{4}\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	1.671
16682	16994	\begin{align*} y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.672
16683	19874	\begin{align*} y^{\prime \prime } x +3 y^{\prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	1.672
16684	25018	\begin{align*} 2 y y^{\prime }&=y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	1.672
16685	16921	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.673
16686	805	\begin{align*} y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	1.674
16687	1127	\begin{align*} -y+y^{\prime }&=1+3 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.674
16688	11325	\begin{align*} y^{\prime }+a y^{2}-b&=0 \\ \end{align*}	✓	✓	✓	✓	1.674
16689	11808	\begin{align*} {y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	1.674
16690	1667	\begin{align*} y^{\prime }&=\frac {2 x +y+1}{x +2 y-4} \\ \end{align*}	✓	✓	✓	✗	1.675
16691	2309	\begin{align*} y+y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.675
16692	21562	\begin{align*} y-\frac {y^{\prime } x}{2}-\frac {x}{2 y^{\prime }}&=0 \\ \end{align*}	✓	✓	✓	✓	1.676
16693	176	\begin{align*} x^{\prime }&=3 x \left (5-x\right ) \\ x \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.677
16694	1135	\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x} \\ \end{align*}	✗	✗	✗	✗	1.677
16695	22048	\begin{align*} 1-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	1.677
16696	5991	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	1.678
16697	13293	\begin{align*} y^{\prime }&={\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y+a \lambda \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\ \end{align*}	✓	✓	✓	✗	1.678
16698	14516	\begin{align*} y^{\prime }&=-y^{2}+y x +1 \\ \end{align*}	✓	✓	✓	✗	1.678
16699	14970	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=0 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.678
16700	21792	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.678