2.3.190 Problems 18901 to 19000

Table 2.953: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18901	14491	\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.564
18902	15802	\begin{align*} y^{\prime }&=t y^{2}+2 y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.564
18903	18531	\begin{align*} -y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	3.565
18904	21334	\begin{align*} x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.565
18905	25854	\begin{align*} 1-x^{2}+2 y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.566
18906	7683	\begin{align*} 3 x y^{\prime }+y+x^{2} y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	3.567
18907	13885	\begin{align*} \left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+2 a x \left (a \,x^{2}+b \right ) y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✗	3.567
18908	22519	\begin{align*} y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	3.569
18909	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*}	✓	✓	✓	✓	3.569
18910	25905	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \\ \end{align*}	✓	✓	✓	✓	3.570
18911	9811	\begin{align*} x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.571
18912	6161	\begin{align*} \left (x +3\right ) y-2 x \left (x +2\right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.572
18913	7974	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	3.572
18914	11974	\begin{align*} y^{\prime }&=\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{3}+x^{3}}{2 x} \\ \end{align*}	✓	✓	✓	✗	3.573
18915	19702	\begin{align*} x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 x y^{\prime }+4 y&=0 \\ \end{align*}	✗	✓	✓	✗	3.573
18916	22006	\begin{align*} y^{\prime }&=\frac {x \,{\mathrm e}^{x}}{2 y} \\ \end{align*}	✓	✓	✓	✓	3.573
18917	7352	\begin{align*} y^{\prime }+y x&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	3.575
18918	7864	\begin{align*} 1+2 y-\left (4-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.576
18919	14827	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right . \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.576
18920	15797	\begin{align*} y^{\prime }&=-y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.576
18921	14201	\begin{align*} x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\ \end{align*}	✓	✓	✓	✓	3.579
18922	15911	\begin{align*} y^{\prime }+2 y&=t^{2}+2 t +1+{\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	3.580
18923	17473	\begin{align*} y^{\prime }-4 y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	3.580
18924	12680	\begin{align*} y^{\prime \prime }&=-\frac {\left (\sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }}{\sin \left (x \right )}-y \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.581
18925	12556	\begin{align*} 50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.582
18926	18961	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=g \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.582
18927	8419	\begin{align*} y^{\prime }&=\frac {x \left (1-x \right )}{y \left (-2+y\right )} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.583
18928	9358	\begin{align*} y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.584
18929	21849	\begin{align*} 3 x^{2}-2 y x +\left (4 y^{3}-x^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	3.584
18930	26168	\begin{align*} x y^{2} y^{\prime }+y^{3}&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	3.584
18931	4843	\begin{align*} \left (x +a \right ) y^{\prime }+b \,x^{2}+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.585
18932	13938	\begin{align*} y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.587
18933	10216	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-8\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.588
18934	14054	\begin{align*} y&=-x y^{\prime }+x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	3.588
18935	5400	\begin{align*} {y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.589
18936	17945	\begin{align*} y^{\prime }-y&=-2 \,{\mathrm e}^{-x} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.589
18937	18346	\begin{align*} x^{\prime \prime }+{x^{\prime }}^{2}+x&=0 \\ \end{align*}	✓	✓	✓	✗	3.589
18938	24831	\begin{align*} 9 {y^{\prime }}^{2} x +3 y y^{\prime }+y^{8}&=0 \\ \end{align*}	✓	✓	✓	✓	3.589
18939	17155	\begin{align*} y^{\prime }+y x&=x^{3} \\ \end{align*}	✓	✓	✓	✓	3.590
18940	19959	\begin{align*} y^{\prime } \sqrt {a^{2}+x^{2}}+y&=\sqrt {a^{2}+x^{2}}-x \\ \end{align*}	✓	✓	✓	✓	3.590
18941	18351	\begin{align*} x^{\prime \prime }+\left (x+2\right ) x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.592
18942	21828	\begin{align*} y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.592
18943	26337	\begin{align*} x +y^{2}-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.592
18944	15853	\begin{align*} y^{\prime }&=y \left (-1+y\right ) \left (y-3\right ) \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	3.593
18945	19145	\begin{align*} y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✓	✓	3.593
18946	7693	\begin{align*} y^{\prime }+\frac {2 y}{x}-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.594
18947	11976	\begin{align*} y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x} \\ \end{align*}	✓	✓	✓	✗	3.594
18948	7222	\begin{align*} y^{\prime }&=\frac {2 x y^{2}+x}{x^{2} y-y} \\ y \left (\sqrt {2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.595
18949	25667	\begin{align*} p^{\prime }&=p \left (1-p\right ) \\ \end{align*}	✓	✓	✓	✓	3.595
18950	24851	\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}	✓	✓	✓	✗	3.596
18951	4603	\begin{align*} x y^{\prime \prime }-2 x y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.598
18952	4630	\begin{align*} y^{\prime }&={\mathrm e}^{x} \sin \left (x \right )+y \cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.599
18953	4658	\begin{align*} y^{\prime }&=2 x -\left (x^{2}+1\right ) y+y^{2} \\ \end{align*}	✓	✓	✓	✗	3.599
18954	15916	\begin{align*} y^{\prime }&=\frac {3 y}{t}+t^{5} \\ \end{align*}	✓	✓	✓	✓	3.599
18955	19301	\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.599
18956	19379	\begin{align*} \left ({\mathrm e}^{x}-3 x^{2} y^{2}\right ) y^{\prime }+y \,{\mathrm e}^{x}&=2 x y^{3} \\ \end{align*}	✓	✓	✓	✗	3.599
18957	7521	\begin{align*} y^{\prime }&=\frac {2 y}{x}+\cos \left (\frac {y}{x^{2}}\right ) \\ \end{align*}	✓	✓	✓	✗	3.601
18958	673	\begin{align*} y y^{\prime }&=x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.602
18959	19934	\begin{align*} 3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3}&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	3.602
18960	21047	\begin{align*} x^{\prime }&=x t -t^{3} \\ x \left (0\right ) &= a^{2} \\ \end{align*}	✓	✓	✓	✓	3.602
18961	27315	\begin{align*} \left (x^{3}+3 \ln \left (y\right )\right ) y&=x y^{\prime } \\ \end{align*}	✗	✓	✓	✓	3.602
18962	11306	\begin{align*} y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.603
18963	14214	\begin{align*} u^{\prime }&=\frac {1}{5-2 u} \\ \end{align*}	✓	✓	✓	✓	3.603
18964	3448	\begin{align*} t y^{\prime }&=y+t^{3} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.604
18965	7473	\begin{align*} 2 x +\frac {y}{x}+\left (y x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.604
18966	8455	\begin{align*} y^{\prime }+y \tan \left (x \right )&=\cos \left (x \right )^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.604
18967	14364	\begin{align*} x^{\prime \prime }+\pi ^{2} x&=\pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.604
18968	7156	\begin{align*} y^{\prime }&=a x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.605
18969	19678	\begin{align*} x^{\prime }+x \tan \left (t \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.606
18970	21829	\begin{align*} y^{\prime }+y \sin \left (x \right )&=2 x \,{\mathrm e}^{\cos \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	3.606
18971	26147	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\ \end{align*}	✓	✓	✓	✓	3.607
18972	7010	\begin{align*} x y^{\prime }-y^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	3.609
18973	7554	\begin{align*} x^{3}-y+x y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.609
18974	65	\begin{align*} x y^{\prime }-y&=2 x^{2} y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.611
18975	6543	\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }&=\left (-2 y+1\right ) {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.612
18976	9752	\begin{align*} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	3.613
18977	19328	\begin{align*} x y^{\prime }&=x^{5}+x^{3} y^{2}+y \\ \end{align*}	✓	✓	✓	✓	3.614
18978	4925	\begin{align*} \left (-x^{2}+4\right ) y^{\prime }+4 y&=\left (x +2\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.615
18979	14425	\begin{align*} 2 y+y^{\prime }&=6 \,{\mathrm e}^{x}+4 \,{\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	3.615
18980	15921	\begin{align*} y^{\prime }&=-\frac {y}{t +1}+2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.615
18981	19291	\begin{align*} 2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.615
18982	21101	\begin{align*} x&=t \left (1+x^{\prime }\right )+x^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.615
18983	8425	\begin{align*} y^{\prime }+2 y x&=x^{3} \\ \end{align*}	✓	✓	✓	✓	3.618
18984	4670	\begin{align*} y^{\prime }&=a \,x^{n -1}+b \,x^{2 n}+c y^{2} \\ \end{align*}	✓	✓	✓	✗	3.619
18985	23189	\begin{align*} 2 x -y \sin \left (y x \right )+\left (6 y^{2}-x \sin \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.619
18986	8672	\begin{align*} x +2 x^{3}+\left (2 y^{3}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.621
18987	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.	✓	✓	✓	✓	3.622
18988	2656	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	3.623
18989	3033	\begin{align*} \sec \left (y\right )^{2} y^{\prime }&=\tan \left (y\right )+2 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✗	✓	✗	3.624
18990	4817	\begin{align*} x y^{\prime }+y+2 x \sec \left (y x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.625
18991	20265	\begin{align*} y^{\prime }+y \cot \left (x \right )&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.625
18992	25792	\begin{align*} y^{\prime }&=\frac {x^{2}}{5}+y \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.625
18993	16208	\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.627
18994	19232	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.627
18995	1589	\begin{align*} \left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right )&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.628
18996	5389	\begin{align*} {y^{\prime }}^{2}+x y^{\prime }+x -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.628
18997	27502	\begin{align*} y^{\prime }-8 x \sqrt {y}&=\frac {4 x y}{x^{2}-1} \\ \end{align*}	✓	✓	✓	✓	3.628
18998	21267	\begin{align*} t x^{\prime \prime }&=x \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	3.629
18999	4073	\begin{align*} x^{2} y^{\prime \prime }-x \left (2-x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.630
19000	8868	\begin{align*} y^{\prime }-2 y&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	3.631