2.3.168 Problems 16701 to 16800

Table 2.909: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16701	8177	\begin{align*} y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.456
16702	4934	\begin{align*} x \left (1-x \right ) y^{\prime }&=2 y x +2 \\ \end{align*}	✓	✓	✓	✓	2.457
16703	15942	\begin{align*} y^{\prime }&=\sin \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.457
16704	19129	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	2.457
16705	19340	\begin{align*} x y^{\prime }-3 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	2.457
16706	19396	\begin{align*} y^{\prime }&=1+3 y \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.457
16707	24310	\begin{align*} x^{2}-1+2 y+\left (-x^{2}+1\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.457
16708	26295	\begin{align*} y^{\prime }&=\frac {3 x^{2}}{1+x^{3}+y} \\ \end{align*}	✓	✓	✓	✓	2.457
16709	3523	\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+32 \\ \end{align*}	✓	✓	✓	✗	2.459
16710	689	\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	2.460
16711	5984	\begin{align*} -\left (-a^{2} x^{2}+p^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.460
16712	13801	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}+\left (a b -1\right ) x +b \right ) y^{\prime }+y a^{2} b x&=0 \\ \end{align*}	✓	✓	✓	✗	2.460
16713	17168	\begin{align*} t y^{\prime }+y&=2 \,{\mathrm e}^{t} t \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.460
16714	20919	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.460
16715	25481	\begin{align*} y^{\prime }&=2 \left (1-y\right ) \left (1-{\mathrm e}^{y}\right ) \\ \end{align*}	✓	✓	✓	✓	2.460
16716	27223	\begin{align*} x x^{\prime }+t&=1 \\ \end{align*}	✓	✓	✓	✓	2.460
16717	91	\begin{align*} y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.461
16718	717	\begin{align*} x y^{\prime }-3 y&=x^{3} \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.461
16719	8140	\begin{align*} x y^{\prime \prime }+x^{3} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.461
16720	15830	\begin{align*} y^{\prime }&=t +y t \\ \end{align*}	✓	✓	✓	✓	2.461
16721	17185	\begin{align*} y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.461
16722	12341	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.462
16723	19708	\begin{align*} v^{\prime }+u^{2} v&=\sin \left (u \right ) \\ \end{align*}	✓	✓	✓	✓	2.462
16724	20029	\begin{align*} y&=x y^{\prime }+\sqrt {b^{2}+a^{2} y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	2.463
16725	8275	\begin{align*} y^{\prime }+y \sin \left (x \right )&=x \\ \end{align*}	✓	✓	✓	✓	2.464
16726	19988	\begin{align*} y&=x y^{\prime }+\arcsin \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	2.464
16727	24999	\begin{align*} -y+y^{\prime }&={\mathrm e}^{2 t} t \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	2.464
16728	20842	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.465
16729	25808	\begin{align*} y^{\prime }&=y^{2} \left (4-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.465
16730	4893	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+1&=y x \\ \end{align*}	✓	✓	✓	✓	2.467
16731	17140	\begin{align*} -y+y^{\prime }&=2 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.467
16732	27340	\begin{align*} y^{\prime }&=3 y^{{2}/{3}}+1 \\ \end{align*}	✓	✓	✓	✓	2.467
16733	11600	\begin{align*} \left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.468
16734	16239	\begin{align*} y^{\prime }&=\frac {6 x^{2}+4}{3 y^{2}-4 y} \\ \end{align*}	✓	✓	✓	✗	2.468
16735	19146	\begin{align*} 2 \left (2 a -y\right ) y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.468
16736	98	\begin{align*} \frac {1-4 x y^{2}}{x^{\prime }}&=y^{3} \\ \end{align*}	✓	✓	✓	✓	2.469
16737	21979	\begin{align*} y^{\prime }&=\frac {x^{2}+y}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	2.469
16738	23200	\begin{align*} x^{2}-y^{2}+x +2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.469
16739	1179	\begin{align*} y^{\prime }&=y \left (3-y t \right ) \\ \end{align*}	✓	✓	✓	✓	2.470
16740	1609	\begin{align*} y^{\prime }&=\frac {y+{\mathrm e}^{x}}{x^{2}+y^{2}} \\ \end{align*}	✗	✗	✗	✗	2.470
16741	7477	\begin{align*} x^{2} \sin \left (x \right )+4 y+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.470
16742	7539	\begin{align*} y^{\prime }+y \tan \left (x \right )+\sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.470
16743	17178	\begin{align*} y+y^{\prime }&=5 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	2.470
16744	24237	\begin{align*} y^{\prime }&=\csc \left (x \right )-y \cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.470
16745	22296	\begin{align*} y^{\prime \prime }+y x&=\sin \left (y^{\prime \prime }\right ) \\ \end{align*}	✗	✗	✗	✗	2.471
16746	3258	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.472
16747	8883	\begin{align*} 2 y+y^{\prime }&=b \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.472
16748	13738	\begin{align*} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.472
16749	6155	\begin{align*} \left (4 a^{2} x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.473
16750	15908	\begin{align*} 3 y+y^{\prime }&=\cos \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.473
16751	21080	\begin{align*} 2 y+x +\left (x^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.473
16752	20135	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	2.474
16753	20446	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }&=3 x y^{2}-x^{2} \\ \end{align*}	✓	✓	✓	✗	2.474
16754	24111	\begin{align*} x^{2} y^{\prime \prime }+2 x^{4} y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.474
16755	13204	\begin{align*} g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{0} \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.475
16756	15163	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=1-2 x \\ \end{align*}	✓	✓	✓	✗	2.475
16757	17146	\begin{align*} x y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	2.476
16758	25427	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.477
16759	7711	\begin{align*} x^{2} \left (y+1\right )+y^{2} \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.478
16760	11569	\begin{align*} \left (x^{2}+y^{2}+x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.478
16761	1683	\begin{align*} 2 x -2 y^{2}+\left (12 y^{2}-4 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.480
16762	5897	\begin{align*} x y^{\prime \prime }+2 y^{\prime }-y x&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	2.480
16763	10264	\begin{align*} y^{\prime }&=a x y \\ \end{align*}	✓	✓	✓	✓	2.480
16764	14136	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=\left (1-x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.480
16765	17799	\begin{align*} x^{\prime \prime }+100 x&=0 \\ x \left (0\right ) &= -{\frac {1}{4}} \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.480
16766	12176	\begin{align*} y^{\prime }&=\frac {x +1+y^{4}-2 x^{2} y^{2}+x^{4}+y^{6}-3 x^{2} y^{4}+3 y^{2} x^{4}-x^{6}}{y} \\ \end{align*}	✓	✓	✓	✗	2.481
16767	14305	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=t^{3}+1-4 \cos \left (t \right ) t \\ \end{align*}	✓	✓	✓	✓	2.481
16768	26331	\begin{align*} y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.482
16769	4976	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \\ \end{align*}	✓	✓	✓	✓	2.484
16770	7570	\begin{align*} m y^{\prime \prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	2.484
16771	9625	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.484
16772	13230	\begin{align*} y^{\prime }&=y^{2}+a \,x^{n} y+b \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	2.484
16773	14362	\begin{align*} x^{\prime }&=x-2 \operatorname {Heaviside}\left (t -1\right ) \\ x \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.484
16774	1216	\begin{align*} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.485
16775	7446	\begin{align*} x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.485
16776	11322	\begin{align*} y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x&=0 \\ \end{align*}	✓	✓	✓	✗	2.485
16777	16960	\begin{align*} x^{\prime \prime }+2 \sin \left (x\right )&=\sin \left (2 t \right ) \\ \end{align*}	✗	✗	✗	✗	2.485
16778	26384	\begin{align*} 3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.485
16779	4933	\begin{align*} x \left (1-x \right ) y^{\prime }&=a +\left (x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.486
16780	25674	\begin{align*} y^{\prime }+2 y x&=1 \\ \end{align*}	✓	✓	✓	✓	2.486
16781	800	\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	2.487
16782	8242	\begin{align*} y^{\prime }&=y^{2} \\ y \left (3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.487
16783	18016	\begin{align*} y&=x y^{\prime }+\frac {a}{{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	2.487
16784	18084	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.487
16785	21119	\begin{align*} x^{\prime \prime }+p x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.487
16786	20980	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.488
16787	1116	\begin{align*} 4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.490
16788	17332	\begin{align*} t r^{\prime }+r&=\cos \left (t \right ) t \\ \end{align*}	✓	✓	✓	✓	2.490
16789	18808	\begin{align*} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.491
16790	31	\begin{align*} y^{\prime }&=\sqrt {x -y} \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	2.493
16791	6141	\begin{align*} -y+\left (x +1\right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.493
16792	19376	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}-2 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.493
16793	23337	\begin{align*} y^{\prime \prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.493
16794	3535	\begin{align*} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.494
16795	5503	\begin{align*} {y^{\prime }}^{2} x^{2}-\left (1+2 y x \right ) y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.494
16796	8914	\begin{align*} y^{\prime \prime }+\omega ^{2} y&=A \cos \left (\omega x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.494
16797	21987	\begin{align*} y^{\prime }&=y x +1 \\ \end{align*}	✓	✓	✓	✓	2.494
16798	17798	\begin{align*} x^{\prime \prime }+64 x&=0 \\ x \left (0\right ) &= {\frac {3}{4}} \\ x^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.495
16799	2309	\begin{align*} y+y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.496
16800	20328	\begin{align*} y^{\prime \prime }-n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.496