2.3.170 Problems 16901 to 17000

Table 2.913: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16901	209	\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	2.554
16902	22180	\begin{align*} {\mathrm e}^{x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.554
16903	8261	\begin{align*} y^{\prime \prime }+9 y&=18 \\ \end{align*}	✓	✓	✓	✓	2.555
16904	167	\begin{align*} y^{\prime }+y^{2}&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✗	2.556
16905	805	\begin{align*} y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.556
16906	5698	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.556
16907	8229	\begin{align*} \left (y^{3}+1\right ) y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.557
16908	685	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	2.558
16909	4656	\begin{align*} y^{\prime }&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.558
16910	4955	\begin{align*} x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.558
16911	6399	\begin{align*} x^{2} y^{\prime \prime }&=\sqrt {b y^{2}+a \,x^{2} {y^{\prime }}^{2}} \\ \end{align*}	✗	✓	✗	✗	2.558
16912	23256	\begin{align*} 7 y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.558
16913	6954	\begin{align*} \frac {y x +1}{y}+\frac {\left (-x +2 y\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.559
16914	12389	\begin{align*} x y^{\prime \prime }-\left (2 a \,x^{2}+1\right ) y^{\prime }+b \,x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.559
16915	24984	\begin{align*} y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.559
16916	3436	\begin{align*} y^{\prime }&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.560
16917	8332	\begin{align*} y^{\prime }&=y \left (2-y\right ) \left (4-y\right ) \\ \end{align*}	✓	✓	✓	✓	2.560
16918	18873	\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (t -1\right )^{2} {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✗	2.560
16919	82	\begin{align*} 2 x y^{\prime }-3 y&=9 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.561
16920	1115	\begin{align*} 2 y+t y^{\prime }&=\sin \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.563
16921	26693	\begin{align*} y^{\prime \prime }-\lambda ^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= \frac {1}{\lambda } \\ \end{align*}	✓	✓	✓	✓	2.563
16922	7013	\begin{align*} y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	2.564
16923	12618	\begin{align*} y^{\prime \prime }&=-\frac {\left (x^{3}-1\right ) y^{\prime }}{x \left (x^{3}+1\right )}+\frac {x y}{x^{3}+1} \\ \end{align*}	✓	✓	✓	✗	2.564
16924	17190	\begin{align*} \frac {y}{2}+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	2.565
16925	25475	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.566
16926	16298	\begin{align*} 3 y^{\prime }&=-2+\sqrt {2 x +3 y+4} \\ \end{align*}	✓	✓	✓	✓	2.568
16927	4626	\begin{align*} y^{\prime }&=1-y \cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.569
16928	8875	\begin{align*} y^{\prime }+a y&=b \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.569
16929	23048	\begin{align*} y^{\prime \prime } {y^{\prime }}^{2}-x^{2}&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.569
16930	25456	\begin{align*} y^{\prime }&=y+{\mathrm e}^{t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.569
16931	25799	\begin{align*} y^{\prime }&=x +y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.570
16932	15780	\begin{align*} x^{\prime }&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	2.571
16933	17061	\begin{align*} t y^{\prime }+y&=t \sin \left (t \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.571
16934	21391	\begin{align*} y^{\prime }&=\frac {2 x y}{y^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✗	2.571
16935	998	\begin{align*} x_{1}^{\prime }&=9 x_{1}-7 x_{2}-5 x_{3} \\ x_{2}^{\prime }&=-12 x_{1}+7 x_{2}+11 x_{3}+9 x_{4} \\ x_{3}^{\prime }&=24 x_{1}-17 x_{2}-19 x_{3}-9 x_{4} \\ x_{4}^{\prime }&=-18 x_{1}+13 x_{2}+17 x_{3}+9 x_{4} \\ \end{align*}	✓	✓	✓	✓	2.572
16936	12432	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y-3 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.572
16937	25892	\begin{align*} y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	2.572
16938	3780	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+5 y&=0 \\ y \left (1\right ) &= \sqrt {2} \\ y^{\prime }\left (1\right ) &= 3 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	2.573
16939	4939	\begin{align*} x \left (1-x \right ) y^{\prime }+2-3 y x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.573
16940	10451	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.573
16941	7963	\begin{align*} 2 y&={y^{\prime }}^{2}+4 x y^{\prime } \\ \end{align*}	✓	✓	✓	✗	2.574
16942	23856	\begin{align*} y x +\ln \left (y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.575
16943	26880	\begin{align*} y^{\prime }+3 y&=5 \,{\mathrm e}^{2 x}-6 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.575
16944	1113	\begin{align*} \frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.576
16945	11599	\begin{align*} \left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.576
16946	17645	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=0 \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.576
16947	23161	\begin{align*} x y^{\prime }+y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	2.577
16948	7567	\begin{align*} y^{\prime }&=2 y^{{2}/{3}} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.578
16949	16223	\begin{align*} y^{\prime }&={\mathrm e}^{2 x -3 y} \\ \end{align*}	✓	✓	✓	✓	2.578
16950	26857	\begin{align*} y^{\prime }&=\frac {2 x y}{-x^{2}+2} \\ \end{align*}	✓	✓	✓	✓	2.578
16951	16381	\begin{align*} x^{2} y^{\prime }+3 y x&=6 \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.579
16952	16697	\begin{align*} x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✗	2.579
16953	4616	\begin{align*} y^{\prime }&=x \left ({\mathrm e}^{-x^{2}}+a y\right ) \\ \end{align*}	✓	✓	✓	✓	2.580
16954	7535	\begin{align*} y^{3}+4 y \,{\mathrm e}^{x}+\left (2 \,{\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.580
16955	8748	\begin{align*} y \left (1+\sqrt {x^{2} y^{4}-1}\right )+2 x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.580
16956	19105	\begin{align*} y^{\prime }&=2 y x -x^{3}+x \\ \end{align*}	✓	✓	✓	✓	2.580
16957	9482	\begin{align*} x^{\prime }&=x+2 y-4 t +1 \\ y^{\prime }&=-x+2 y+3 t +4 \\ \end{align*}	✓	✓	✓	✓	2.582
16958	15242	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=3 \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.582
16959	15866	\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✗	2.582
16960	16305	\begin{align*} y^{\prime }&=2 \sqrt {2 x +y-3}-2 \\ \end{align*}	✓	✓	✓	✓	2.582
16961	16602	\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=x \\ \end{align*}	✓	✓	✓	✓	2.582
16962	26077	\begin{align*} y^{\prime }&=\left (-1+y\right ) x \\ \end{align*}	✓	✓	✓	✓	2.582
16963	1569	\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.583
16964	5216	\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.583
16965	11441	\begin{align*} x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+a x +2&=0 \\ \end{align*}	✓	✓	✓	✗	2.583
16966	16338	\begin{align*} y^{\prime }&=x^{2}-2 y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	2.584
16967	4268	\begin{align*} x y^{\prime }-3 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.585
16968	4511	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \\ \end{align*}	✓	✓	✓	✗	2.585
16969	15930	\begin{align*} y^{\prime }&=y+4 \cos \left (t^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.585
16970	18009	\begin{align*} y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \\ \end{align*}	✓	✓	✓	✗	2.585
16971	702	\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.586
16972	16256	\begin{align*} x^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.586
16973	25829	\begin{align*} y^{\prime }&=-\frac {1}{2 y} \\ \end{align*}	✓	✓	✓	✓	2.586
16974	6168	\begin{align*} 4 \left (x^{2}+1\right ) y^{\prime \prime }&=x^{2}+4 x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.587
16975	14891	\begin{align*} x^{\prime }+p x&=q \\ \end{align*}	✓	✓	✓	✓	2.587
16976	24833	\begin{align*} 4 {y^{\prime }}^{2} x +4 y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.588
16977	11841	\begin{align*} \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.589
16978	18363	\begin{align*} y^{\prime \prime }+y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.589
16979	23957	\begin{align*} y x -x&=\left (x y^{2}+x -y^{2}-1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.589
16980	24288	\begin{align*} 1+4 y x -4 x^{2} y+\left (-x^{3}+x^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	2.590
16981	14180	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }&=2 \\ \end{align*}	✓	✓	✓	✓	2.592
16982	24945	\begin{align*} y^{\prime }&=y \left (t +y\right ) \\ \end{align*}	✓	✓	✓	✓	2.592
16983	6052	\begin{align*} a -x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.593
16984	6126	\begin{align*} -\left (x +2\right ) y-\left (-x^{2}-x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.593
16985	6228	\begin{align*} -6 y x +6 x^{2} y^{\prime }+\left (-2 x^{3}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.593
16986	12011	\begin{align*} y^{\prime }&=\frac {y \left (x -y\right )}{x \left (x -y^{3}\right )} \\ \end{align*}	✓	✓	✓	✗	2.593
16987	13722	\begin{align*} x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y&=0 \\ \end{align*}	✓	✓	✓	✓	2.593
16988	161	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \ln \left (y\right ) y \\ \end{align*}	✓	✓	✓	✗	2.595
16989	4984	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=2-4 x^{2} y \\ \end{align*}	✓	✓	✓	✓	2.595
16990	26475	\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=4 y^{2} \\ \end{align*}	✓	✓	✓	✗	2.595
16991	19084	\begin{align*} y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y}&=0 \\ \end{align*}	✓	✓	✓	✓	2.596
16992	25436	\begin{align*} y^{\prime }&=a \left (t \right ) y+q \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.596
16993	20567	\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.597
16994	27084	\begin{align*} y^{\prime }&=y \sin \left (x \right )-3 x^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.597
16995	1591	\begin{align*} y^{\prime }+2 x \left (y+1\right )&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.598
16996	3567	\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.598
16997	21323	\begin{align*} x^{\prime \prime }+4 x^{3}&=0 \\ x \left (0\right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.598
16998	213	\begin{align*} y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.600
16999	25461	\begin{align*} y^{\prime }&=t +2 y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.600
17000	14694	\begin{align*} x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y&=3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	2.601