2.3.181 Problems 18001 to 18100

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

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18001	16392	\begin{align*} y^{\prime \prime } x -{y^{\prime }}^{2}&=6 x^{5} \\ \end{align*}	✓	✓	✓	✗	2.555
18002	17539	\begin{align*} \left (-t \cos \left (t \right )+\sin \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=t \\ y \left (\frac {\pi }{4}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.555
18003	15383	\begin{align*} 6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.556
18004	19987	\begin{align*} x^{2} \left (y-y^{\prime } x \right )&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.556
18005	21440	\begin{align*} y^{\prime }+\frac {\left (2 x +1\right ) y}{x}&={\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	2.556
18006	18957	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.557
18007	17952	\begin{align*} \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y&=-\sin \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.559
18008	23912	\begin{align*} y^{\prime }-\frac {y}{-x^{2}+1}&=3 \\ \end{align*}	✓	✓	✓	✓	2.559
18009	4787	\begin{align*} y^{\prime } x +b x +\left (2+a x y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.560
18010	18010	\begin{align*} y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	2.560
18011	26200	\begin{align*} y^{\prime }&=y+x^{2} \\ \end{align*}	✓	✓	✓	✓	2.560
18012	4719	\begin{align*} y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.561
18013	6349	\begin{align*} 2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.561
18014	2972	\begin{align*} \cos \left (\theta \right ) r^{\prime }&=2+2 r \sin \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	2.562
18015	15015	\begin{align*} \tan \left (y\right )-\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.562
18016	20670	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x&=m^{2} y \\ \end{align*}	✓	✓	✓	✗	2.562
18017	21729	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 4 \\ y \left (\pi \right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	2.562
18018	21986	\begin{align*} y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	2.562
18019	25090	\begin{align*} y^{\prime } t +y&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.562
18020	4924	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.563
18021	5928	\begin{align*} x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	2.563
18022	16264	\begin{align*} y^{\prime }+4 y&=y^{3} \\ \end{align*}	✓	✓	✓	✓	2.563
18023	8878	\begin{align*} y^{\prime }+{\mathrm e}^{x} y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.566
18024	19198	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \\ \end{align*}	✓	✓	✓	✓	2.566
18025	21064	\begin{align*} x^{\prime }&=\sqrt {1-x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.567
18026	1584	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.568
18027	4760	\begin{align*} y^{\prime } x&=a y \\ \end{align*}	✓	✓	✓	✓	2.569
18028	4867	\begin{align*} x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.569
18029	12913	\begin{align*} \left (-y+y^{\prime } x \right )^{3}+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.569
18030	19891	\begin{align*} y^{\prime }-2 y-2 z&={\mathrm e}^{3 x} \\ z^{\prime }+5 y-2 z&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	2.569
18031	8237	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	2.570
18032	10318	\begin{align*} y^{\prime }&=\sqrt {1+6 x +y} \\ \end{align*}	✓	✓	✓	✓	2.570
18033	12391	\begin{align*} y^{\prime \prime } x +\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	2.570
18034	15598	\begin{align*} y^{\prime }&=\frac {y}{x -1}+x^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.570
18035	5424	\begin{align*} {y^{\prime }}^{2}-y y^{\prime } x +y^{2} \ln \left (a y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.571
18036	24292	\begin{align*} a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.571
18037	5296	\begin{align*} 2 y^{3} y^{\prime }&=x^{3}-x y^{2} \\ \end{align*}	✓	✓	✓	✗	2.572
18038	24980	\begin{align*} \cos \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=1 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.573
18039	19080	\begin{align*} y^{\prime }&=2 y x -x^{3}+x \\ \end{align*}	✓	✓	✓	✓	2.574
18040	7956	\begin{align*} y {y^{\prime }}^{2}-y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.575
18041	17986	\begin{align*} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.575
18042	25441	\begin{align*} y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.575
18043	26152	\begin{align*} -y+y^{\prime } x&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.575
18044	15543	\begin{align*} y^{\prime }&=\ln \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	2.576
18045	14430	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\ y \left (-1\right ) &= {\mathrm e}+3 \\ \end{align*}	✓	✓	✓	✓	2.577
18046	5665	\begin{align*} y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	2.579
18047	11469	\begin{align*} x^{3} y^{\prime }-y^{2}-x^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.579
18048	14482	\begin{align*} x^{4} y^{\prime }+2 x^{3} y&=1 \\ \end{align*}	✓	✓	✓	✓	2.579
18049	14518	\begin{align*} 6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.579
18050	18523	\begin{align*} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.579
18051	21432	\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \\ y \left (\textit {x\_0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	2.579
18052	6882	\begin{align*} y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	2.580
18053	25018	\begin{align*} 2 y y^{\prime }&=y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	2.580
18054	8782	\begin{align*} {\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.581
18055	24293	\begin{align*} y-\sin \left (x \right )^{2}+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.581
18056	4980	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=\left (-x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.582
18057	3560	\begin{align*} y^{\prime }&=-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.583
18058	15794	\begin{align*} y^{\prime }&=\sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.584
18059	2472	\begin{align*} \sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.585
18060	4281	\begin{align*} \left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+{\mathrm e}^{x} y&=2 x y^{3} \\ \end{align*}	✓	✓	✓	✗	2.585
18061	4869	\begin{align*} x^{2} y^{\prime }&=\left (b x +a \right ) y \\ \end{align*}	✓	✓	✓	✓	2.585
18062	12306	\begin{align*} y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.585
18063	22634	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.585
18064	27469	\begin{align*} 2 y^{\prime } x -y&=\sin \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	2.585
18065	8749	\begin{align*} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.586
18066	10072	\begin{align*} y^{\prime }&=2 y \left (x \sqrt {y}-1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.586
18067	19434	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.586
18068	6350	\begin{align*} a {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.587
18069	19735	\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.587
18070	11456	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+a \left (1-2 y x +y^{2}\right )&=0 \\ \end{align*}	✗	✓	✓	✗	2.589
18071	17939	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.589
18072	18512	\begin{align*} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.589
18073	131	\begin{align*} 3 y^{2} y^{\prime } x&=3 x^{4}+y^{3} \\ \end{align*}	✓	✓	✓	✓	2.592
18074	5372	\begin{align*} {y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.592
18075	14884	\begin{align*} x^{\prime }&=-x \left (1-x\right ) \left (2-x\right ) \\ \end{align*}	✓	✓	✓	✓	2.592
18076	21422	\begin{align*} y^{\prime }&=\frac {-y x +\ln \left (x^{2}\right )}{x^{2}+x \,{\mathrm e}^{y}} \\ \end{align*}	✓	✓	✓	✗	2.592
18077	21815	\begin{align*} x^{2}+y \,{\mathrm e}^{2 y}+\left (2 y x +x \right ) {\mathrm e}^{2 y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.592
18078	23972	\begin{align*} y^{\prime }-y x&=-x^{5}+4 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.592
18079	4636	\begin{align*} y^{\prime }&=y \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.593
18080	24991	\begin{align*} y^{\prime }-\frac {2 y}{1+t}&=\left (1+t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.593
18081	16700	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=\frac {10}{x} \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= -15 \\ \end{align*}	✓	✓	✓	✓	2.594
18082	789	\begin{align*} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.595
18083	18606	\begin{align*} y^{\prime } t +y&=t^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	2.595
18084	11689	\begin{align*} 2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	2.596
18085	11711	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.596
18086	2538	\begin{align*} y^{\prime }&=1-t +y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.598
18087	13488	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+g^{\prime }\left (x \right ) y+a f \left (x \right ) {\mathrm e}^{2 g \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	2.598
18088	11325	\begin{align*} y^{\prime }+a y^{2}-b&=0 \\ \end{align*}	✓	✓	✓	✓	2.599
18089	15567	\begin{align*} y^{\prime }&=\cot \left (x \right ) y+\csc \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.600
18090	21821	\begin{align*} x^{3} y^{\prime }-x^{2} y&=y x^{5} \\ \end{align*}	✓	✓	✓	✓	2.600
18091	146	\begin{align*} \frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.601
18092	16372	\begin{align*} 2 y+y^{\prime }&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.601
18093	17134	\begin{align*} y^{\prime }&=y^{2}-y \\ \end{align*}	✓	✓	✓	✓	2.601
18094	6466	\begin{align*} \left (x -y\right ) y^{\prime \prime }&=f \left (y^{\prime }\right ) \\ \end{align*}	✗	✓	✓	✗	2.602
18095	21363	\begin{align*} {\mathrm e}^{-y} \left (1+y^{\prime }\right )&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.602
18096	15335	\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.603
18097	5875	\begin{align*} {\mathrm e}^{2 x} y-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.604
18098	16419	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.604
18099	33	\begin{align*} y y^{\prime }&=x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.605
18100	10131	\begin{align*} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	2.605