2.3.169 Problems 16801 to 16900

Table 2.887: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16801	17413	\begin{align*} 3 t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.743
16802	19753	\begin{align*} r^{\prime \prime }-a^{2} r&=0 \\ \end{align*}	✓	✓	✓	✓	2.744
16803	24565	\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.744
16804	5965	\begin{align*} \left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.745
16805	15323	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.747
16806	16226	\begin{align*} y y^{\prime }&=x y^{2}+x \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.747
16807	20464	\begin{align*} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.747
16808	90	\begin{align*} y^{\prime } x&=2 y+\cos \left (x \right ) x^{3} \\ \end{align*}	✓	✓	✓	✓	2.748
16809	5542	\begin{align*} y {y^{\prime }}^{2}&=a \\ \end{align*}	✓	✓	✓	✓	2.749
16810	11671	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	2.749
16811	11699	\begin{align*} x {y^{\prime }}^{2}+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.749
16812	26393	\begin{align*} \left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.749
16813	7367	\begin{align*} y^{\prime \prime }&=-4 y \\ \end{align*}	✓	✓	✓	✓	2.750
16814	15370	\begin{align*} y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\ \end{align*}	✓	✓	✓	✗	2.750
16815	12963	\begin{align*} 2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	2.752
16816	16235	\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}	✓	✓	✓	✓	2.752
16817	26145	\begin{align*} y^{\prime } x +y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.752
16818	22422	\begin{align*} y^{\prime }&=\frac {2 x -\sin \left (y\right )}{x \cos \left (y\right )} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.753
16819	26223	\begin{align*} y^{\prime }&=a x +b y+c \\ \end{align*}	✓	✓	✓	✓	2.753
16820	26339	\begin{align*} x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.753
16821	12836	\begin{align*} y^{\prime \prime }-6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.754
16822	15094	\begin{align*} m x^{\prime \prime }&=f \left (x\right ) \\ \end{align*}	✓	✓	✓	✗	2.754
16823	24563	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=-18 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.754
16824	6154	\begin{align*} \left (4 x k -4 p^{2}-x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.755
16825	15903	\begin{align*} y^{\prime }&=3 y-4 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	2.755
16826	54	\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	2.757
16827	202	\begin{align*} 9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.757
16828	8214	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	2.757
16829	18799	\begin{align*} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✓	2.757
16830	797	\begin{align*} 3 y+x^{3} y^{4}+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.758
16831	17643	\begin{align*} 3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.759
16832	15520	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (2\right ) &= -12 \\ \end{align*}	✓	✓	✓	✓	2.760
16833	20858	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.760
16834	14118	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	2.761
16835	5223	\begin{align*} y \left (1+y\right ) y^{\prime }&=x \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✗	2.763
16836	10324	\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}	✓	✓	✓	✓	2.763
16837	22022	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.763
16838	10216	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.764
16839	23268	\begin{align*} y^{\prime \prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.764
16840	5975	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.766
16841	14723	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= -8 \\ \end{align*}	✓	✓	✓	✓	2.766
16842	16317	\begin{align*} 2-2 x +3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.766
16843	19669	\begin{align*} x^{\prime }&=2 \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.766
16844	11618	\begin{align*} \left (2 x^{3} y^{3}-x \right ) y^{\prime }+2 x^{3} y^{3}-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.767
16845	14504	\begin{align*} x^{\prime }-x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.767
16846	18338	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (x -1\right )^{2} {\mathrm e}^{x} \\ y \left (-\infty \right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	2.768
16847	13989	\begin{align*} y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	2.769
16848	14511	\begin{align*} a y^{\prime }+b y&=k \,{\mathrm e}^{-\lambda x} \\ \end{align*}	✓	✓	✓	✓	2.769
16849	15292	\begin{align*} x^{\prime }&=2 x+y-z+5 \sin \left (t \right ) \\ y^{\prime }&=y+z-10 \cos \left (t \right ) \\ z^{\prime }&=x+z+2 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.769
16850	16263	\begin{align*} y^{\prime }&=\sin \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.769
16851	188	\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	2.770
16852	24939	\begin{align*} y^{\prime }&=y-t \\ \end{align*}	✓	✓	✓	✓	2.770
16853	2471	\begin{align*} y \cos \left (t \right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.772
16854	4279	\begin{align*} y^{\prime } x +y&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	2.773
16855	18026	\begin{align*} {y^{\prime }}^{2}-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.773
16856	22505	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	2.773
16857	12703	\begin{align*} y^{\prime \prime }&=-\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )} \\ \end{align*}	✗	✗	✗	✗	2.774
16858	26384	\begin{align*} 3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.774
16859	13987	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.776
16860	15604	\begin{align*} y^{\prime } x +x^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.776
16861	17189	\begin{align*} y+y^{\prime }&=2 \cos \left (t \right )+t \\ \end{align*}	✓	✓	✓	✓	2.776
16862	17240	\begin{align*} y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.777
16863	17639	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=8 \\ \end{align*}	✓	✓	✓	✓	2.780
16864	7440	\begin{align*} y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}}&=x \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.781
16865	2978	\begin{align*} 2 y-y x -3+y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.782
16866	5740	\begin{align*} y^{\prime \prime }+a^{2} y&=\cot \left (a x \right ) \\ \end{align*}	✓	✓	✓	✓	2.782
16867	15230	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.782
16868	16251	\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.783
16869	26191	\begin{align*} y^{\prime }&=\cos \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	2.783
16870	1111	\begin{align*} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.784
16871	7445	\begin{align*} u^{\prime }&=\alpha \left (1-u\right )-\beta u \\ \end{align*}	✓	✓	✓	✓	2.786
16872	25043	\begin{align*} y^{\prime }&=t -y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.786
16873	9009	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{{\mathrm e}^{x}+1} \\ \end{align*}	✓	✓	✓	✓	2.787
16874	2518	\begin{align*} y^{\prime }&=2 t \left (1+y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.788
16875	8218	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.788
16876	10286	\begin{align*} y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	2.788
16877	18954	\begin{align*} y^{\prime \prime }+w^{2} y&=g \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.788
16878	1642	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ \end{align*}	✓	✓	✓	✓	2.789
16879	22598	\begin{align*} y^{\prime }&=\tan \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	2.789
16880	14254	\begin{align*} x^{\prime }+\frac {5 x}{t}&=1+t \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.790
16881	23346	\begin{align*} y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \sqrt {3} \\ \end{align*}	✓	✓	✓	✓	2.790
16882	1609	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}+y}{x^{2}+y^{2}} \\ \end{align*}	✗	✗	✗	✗	2.792
16883	25090	\begin{align*} y^{\prime } t +y&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.792
16884	15837	\begin{align*} v^{\prime }&=2 V \left (t \right )-2 v \\ \end{align*}	✓	✓	✓	✓	2.793
16885	22469	\begin{align*} x^{2} y+y^{3}-x +\left (x^{3}-y+x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.793
16886	7425	\begin{align*} y^{\prime }&=\frac {y}{x}+2 x +1 \\ \end{align*}	✓	✓	✓	✓	2.794
16887	16345	\begin{align*} 2+2 x^{2}-2 y x +\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.796
16888	1213	\begin{align*} y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.798
16889	17029	\begin{align*} 2 y+y^{\prime }&=x^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.798
16890	1209	\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.799
16891	6101	\begin{align*} y-\left (x +1\right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.799
16892	11785	\begin{align*} \left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.799
16893	1667	\begin{align*} y^{\prime }&=\frac {2 x +y+1}{x +2 y-4} \\ \end{align*}	✓	✓	✓	✗	2.800
16894	12887	\begin{align*} 9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.800
16895	22427	\begin{align*} \cos \left (x \right ) y^{\prime }-2 \sin \left (x \right ) y+3&=0 \\ \end{align*}	✓	✓	✓	✓	2.800
16896	5189	\begin{align*} \left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.801
16897	11309	\begin{align*} y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{-\sin \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	2.801
16898	19348	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.802
16899	8736	\begin{align*} 2 x \left (x -y^{2}\right ) y^{\prime }+y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.803
16900	20431	\begin{align*} 4 x {y^{\prime }}^{2}+4 y y^{\prime }&=y^{4} \\ \end{align*}	✓	✓	✓	✓	2.803