2.3.138 Problems 13701 to 13800

Table 2.807: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13701	17140	\begin{align*} -y+y^{\prime }&=2 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.571
13702	25474	\begin{align*} y^{\prime }&=a y-b y^{n} \\ \end{align*}	✓	✓	✓	✓	2.571
13703	17185	\begin{align*} y^{\prime }+10 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.572
13704	376	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \\ \end{align*}	✓	✓	✓	✓	2.573
13705	13872	\begin{align*} x^{4} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	2.573
13706	14502	\begin{align*} 2 x \left (1+y\right )-\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	2.573
13707	22612	\begin{align*} y^{\prime }&=\frac {y^{2}}{x -1}-\frac {x y}{x -1}+1 \\ \end{align*}	✓	✓	✓	✓	2.574
13708	3531	\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.575
13709	22469	\begin{align*} x^{2} y+y^{3}-x +\left (x^{3}-y+x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.575
13710	3537	\begin{align*} t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.576
13711	3565	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.576
13712	16086	\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.576
13713	78	\begin{align*} y^{\prime } x +5 y&=7 x^{2} \\ y \left (2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.577
13714	7538	\begin{align*} y^{\prime }&=2-\sqrt {2 x -y+3} \\ \end{align*}	✓	✓	✓	✓	2.577
13715	15931	\begin{align*} y^{\prime }&=-{\mathrm e}^{-t^{2}} y+\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✗	2.577
13716	25196	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=2 t \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	2.577
13717	25614	\begin{align*} y^{\prime }-a y&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	2.578
13718	228	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\ y \left (2\right ) &= 10 \\ y^{\prime }\left (2\right ) &= 15 \\ \end{align*}	✓	✓	✓	✓	2.579
13719	685	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	2.579
13720	17836	\begin{align*} x^{\prime \prime }+x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.579
13721	23157	\begin{align*} y^{\prime }-\frac {3 y}{x -1}&=\left (x -1\right )^{4} \\ \end{align*}	✓	✓	✓	✓	2.579
13722	7162	\begin{align*} \cos \left (y\right ) \sin \left (x \right )&=\cos \left (x \right ) \sin \left (y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.580
13723	24237	\begin{align*} y^{\prime }&=\csc \left (x \right )-\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.580
13724	25595	\begin{align*} y^{\prime \prime }+3 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.581
13725	3530	\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.582
13726	15401	\begin{align*} y^{\prime \prime }&=a^{2} y \\ \end{align*}	✓	✓	✓	✓	2.582
13727	21373	\begin{align*} x \sin \left (y\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	2.582
13728	12966	\begin{align*} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.583
13729	15156	\begin{align*} y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y&=\tan \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	2.583
13730	16318	\begin{align*} 1+3 y^{2} x^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.583
13731	15884	\begin{align*} w^{\prime }&=\left (w^{2}-2\right ) \arctan \left (w\right ) \\ \end{align*}	✓	✓	✓	✓	2.584
13732	19346	\begin{align*} y-x +x y \cot \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.584
13733	25568	\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.585
13734	3698	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.586
13735	4674	\begin{align*} y^{\prime }&=1+a \left (x -y\right ) y \\ \end{align*}	✓	✓	✓	✗	2.586
13736	15545	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {15-x^{2}-y^{2}}} \\ \end{align*}	✗	✗	✗	✗	2.586
13737	23021	\begin{align*} 9 y^{\prime \prime }+49 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.586
13738	19085	\begin{align*} \left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.587
13739	23013	\begin{align*} y^{\prime \prime }-3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.587
13740	570	\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=\delta \left (t -\pi \right )+\delta \left (t -2 \pi \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.588
13741	7043	\begin{align*} 6 y^{\prime \prime }-11 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.588
13742	16994	\begin{align*} y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.588
13743	80	\begin{align*} y+3 y^{\prime } x&=12 x \\ \end{align*}	✓	✓	✓	✓	2.589
13744	3140	\begin{align*} 2 y^{\prime \prime }+y^{\prime }&=8 \sin \left (2 x \right )+{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.589
13745	10408	\begin{align*} y^{3} {y^{\prime \prime }}^{2}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.590
13746	24585	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	2.590
13747	25490	\begin{align*} y^{\prime }&=a \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.591
13748	3983	\begin{align*} y^{\prime \prime }+16 y&=4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.592
13749	8389	\begin{align*} y^{\prime }&=y-y^{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	2.592
13750	19726	\begin{align*} p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	2.592
13751	4720	\begin{align*} y^{\prime }&=\cot \left (x \right ) \cot \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.593
13752	13301	\begin{align*} y^{\prime }&=y^{2}+a x \,{\mathrm e}^{\lambda x} y+a \,{\mathrm e}^{\lambda x} \\ \end{align*}	✓	✓	✓	✗	2.594
13753	259	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	2.595
13754	13725	\begin{align*} y^{\prime \prime } x +a y^{\prime }+\left (b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.595
13755	833	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.596
13756	7050	\begin{align*} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.596
13757	8234	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (2\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.596
13758	20293	\begin{align*} \left (20 x^{2}+8 y x +4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+y x +y^{2}+y^{3}\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.596
13759	1584	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.597
13760	12032	\begin{align*} y^{\prime }&=\frac {\left (x^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\ \end{align*}	✓	✓	✓	✗	2.597
13761	2321	\begin{align*} \cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.598
13762	10945	\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.598
13763	22977	\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.598
13764	8302	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.599
13765	9084	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.600
13766	20469	\begin{align*} \left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	2.600
13767	19728	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	2.602
13768	25193	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.602
13769	238	\begin{align*} 2 y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.603
13770	5450	\begin{align*} x {y^{\prime }}^{2}+x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.605
13771	5459	\begin{align*} x {y^{\prime }}^{2}-y y^{\prime }+a x&=0 \\ \end{align*}	✓	✓	✓	✓	2.605
13772	21375	\begin{align*} y^{\prime }&=-\frac {{\mathrm e}^{y}}{x \,{\mathrm e}^{y}+2 y} \\ \end{align*}	✓	✓	✓	✓	2.605
13773	22137	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	2.605
13774	20618	\begin{align*} y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=x \\ \end{align*}	✓	✓	✓	✗	2.606
13775	11309	\begin{align*} y^{\prime }+\cos \left (x \right ) y-{\mathrm e}^{-\sin \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	2.607
13776	15968	\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}	✓	✓	✓	✓	2.607
13777	16470	\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*}	✓	✓	✓	✓	2.607
13778	5487	\begin{align*} 4 x {y^{\prime }}^{2}&=\left (a -3 x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.608
13779	6238	\begin{align*} -\left (2 x^{2}+1\right ) y+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.608
13780	12607	\begin{align*} y^{\prime \prime }&=-\frac {\left ({\mathrm e}^{\frac {2}{x}}-v^{2}\right ) y}{x^{4}} \\ \end{align*}	✗	✓	✓	✗	2.608
13781	7904	\begin{align*} 2 y-3 x y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.609
13782	11661	\begin{align*} {y^{\prime }}^{2}+y^{2}-a^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.609
13783	21402	\begin{align*} 1+3 x \sin \left (y\right )-x^{2} y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.610
13784	17178	\begin{align*} y+y^{\prime }&=5 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	2.611
13785	8106	\begin{align*} -y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.612
13786	8757	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.612
13787	16206	\begin{align*} y^{\prime }+\left (8-x \right ) y-y^{2}&=-8 x \\ \end{align*}	✓	✓	✓	✗	2.612
13788	18192	\begin{align*} y^{\prime \prime }+8 y^{\prime }&=8 x \\ \end{align*}	✓	✓	✓	✓	2.612
13789	5583	\begin{align*} \left (a^{2} x^{2}-y^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +x^{2} \left (a^{2}-1\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.613
13790	13882	\begin{align*} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.613
13791	7434	\begin{align*} y^{\prime }-\frac {y}{x}&=x \,{\mathrm e}^{x} \\ y \left (1\right ) &= {\mathrm e}-1 \\ \end{align*}	✓	✓	✓	✓	2.614
13792	183	\begin{align*} 3 y+x^{4} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	2.615
13793	8441	\begin{align*} p^{\prime }+2 t p&=p+4 t -2 \\ \end{align*}	✓	✓	✓	✓	2.615
13794	12368	\begin{align*} a \,x^{2} y+2 y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.615
13795	19332	\begin{align*} -y+y^{\prime } x&=2 x^{2}-3 \\ \end{align*}	✓	✓	✓	✓	2.615
13796	19849	\begin{align*} e y^{\prime \prime }&=-\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \\ \end{align*}	✓	✓	✓	✓	2.615
13797	19858	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	2.615
13798	134	\begin{align*} \left ({\mathrm e}^{y}+x \right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \\ \end{align*}	✓	✓	✓	✓	2.617
13799	23174	\begin{align*} \left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \\ y \left (-1\right ) &= 16 \\ \end{align*}	✓	✓	✓	✓	2.617
13800	12005	\begin{align*} y^{\prime }&=\frac {2 a}{y+2 a y^{4}-16 y^{2} a^{2} x +32 a^{3} x^{2}} \\ \end{align*}	✓	✓	✓	✗	2.618