2.3.137 Problems 13601 to 13700

Table 2.847: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13601	9252	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\ \end{align*}	✓	✓	✓	✓	1.307
13602	16101	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=3 t +2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.307
13603	18082	\begin{align*} \left (x -1\right ) y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.307
13604	7603	\begin{align*} 5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.308
13605	9241	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.308
13606	10382	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+y&=0 \\ \end{align*}	✓	✓	✓	✗	1.308
13607	14944	\begin{align*} x^{\prime \prime }+4 x&=289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.308
13608	18965	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }&=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	1.308
13609	23339	\begin{align*} y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.308
13610	26917	\begin{align*} y^{\prime }&=\sin \left (y x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	1.308
13611	783	\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{4} \\ \end{align*}	✗	✗	✗	✗	1.309
13612	7982	\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.309
13613	18254	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.309
13614	16	\begin{align*} x^{\prime \prime }&=\frac {1}{\sqrt {t +4}} \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.310
13615	101	\begin{align*} y^{\prime }&=1+2 y x \\ \end{align*}	✓	✓	✓	✓	1.310
13616	12983	\begin{align*} x y y^{\prime \prime }+\left (\frac {a x}{\sqrt {b^{2}-x^{2}}}-x \right ) {y^{\prime }}^{2}-y y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.310
13617	14744	\begin{align*} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.310
13618	21567	\begin{align*} y^{\prime \prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.310
13619	20372	\begin{align*} y+y^{\prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.311
13620	24860	\begin{align*} {y^{\prime }}^{2} x^{2}-\left (1+2 y x \right ) y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.311
13621	924	\begin{align*} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }&=5 x-y-t^{2} \\ \end{align*}	✓	✓	✓	✓	1.312
13622	3217	\begin{align*} y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \sin \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	1.312
13623	13701	\begin{align*} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (a \,x^{3} b +a c \,x^{2}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.312
13624	13806	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +b \left (a \,x^{n}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.312
13625	6464	\begin{align*} 2 y^{\prime } \left (y^{\prime }+1\right )+\left (x -y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.313
13626	6956	\begin{align*} \left (2 x +y+1\right ) y-x \left (x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.313
13627	9571	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.313
13628	20554	\begin{align*} y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )}&=\frac {x^{2}}{a \left (a^{2}-x^{2}\right )} \\ \end{align*}	✓	✓	✓	✗	1.313
13629	2606	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=1+t^{2}+{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	1.314
13630	21381	\begin{align*} y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	1.314
13631	23926	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	1.314
13632	9405	\begin{align*} 4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.315
13633	11893	\begin{align*} y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right ) x^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	1.315
13634	14843	\begin{align*} f \left (t \right ) x^{\prime \prime }+x g \left (t \right )&=0 \\ \end{align*}	✗	✗	✗	✗	1.315
13635	20650	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✗	1.315
13636	24003	\begin{align*} y^{\prime \prime \prime }-y&=x^{n} \\ \end{align*}	✓	✓	✓	✓	1.315
13637	25766	\begin{align*} x y^{\prime \prime }+y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.315
13638	8030	\begin{align*} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=6 x \\ \end{align*}	✓	✓	✓	✗	1.316
13639	20862	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.317
13640	26997	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.317
13641	27079	\begin{align*} x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.317
13642	6515	\begin{align*} \left (x y^{\prime }-y\right )^{2}+x^{2} y y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.318
13643	26193	\begin{align*} y^{\prime }&=x^{2}+2 x -y \\ \end{align*}	✓	✓	✓	✓	1.318
13644	6305	\begin{align*} y^{\prime \prime }&=f \left (x \right )+g \left (x \right ) y+2 y^{3} \\ \end{align*}	✗	✗	✗	✗	1.319
13645	12429	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-v^{2}+x^{2}\right ) y-f \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.319
13646	17482	\begin{align*} y^{\prime \prime }+16 y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	1.319
13647	20165	\begin{align*} y^{\prime \prime }+y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.319
13648	9002	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.320
13649	9800	\begin{align*} {y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+x y^{\prime \prime }\right ) \\ \end{align*}	✓	✓	✗	✗	1.320
13650	14784	\begin{align*} 3 x^{\prime }+2 y^{\prime }-x+y&=t -1 \\ x^{\prime }+y^{\prime }-x&=t +2 \\ \end{align*}	✓	✓	✓	✓	1.320
13651	12431	\begin{align*} -y+\left (x +a \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.321
13652	19111	\begin{align*} {y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.321
13653	20507	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.321
13654	23977	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.321
13655	726	\begin{align*} x y^{\prime }+\left (2 x -3\right ) y&=4 x^{4} \\ \end{align*}	✓	✓	✓	✓	1.322
13656	5954	\begin{align*} x^{2} y^{\prime \prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	1.322
13657	9902	\begin{align*} x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.322
13658	10266	\begin{align*} y^{\prime }&=a x +b y \\ \end{align*}	✓	✓	✓	✓	1.322
13659	16628	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=20 \\ \end{align*}	✓	✓	✓	✓	1.322
13660	19973	\begin{align*} {y^{\prime }}^{3}&=a \,x^{4} \\ \end{align*}	✓	✓	✓	✓	1.323
13661	23112	\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	1.323
13662	2392	\begin{align*} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}	✓	✓	✓	✗	1.324
13663	4566	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }&=-x_{1}+2 x_{2}+3 x_{3} \\ \end{align*}	✓	✓	✓	✓	1.324
13664	18742	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.324
13665	23015	\begin{align*} 4 y^{\prime \prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.324
13666	9591	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.325
13667	14630	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \\ \end{align*}	✓	✓	✓	✓	1.325
13668	23753	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\pi \right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.325
13669	26877	\begin{align*} 2 y+y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	1.325
13670	5661	\begin{align*} y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.326
13671	5775	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=50 \cos \left (x \right ) \cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.326
13672	9174	\begin{align*} x +3 y^{2}+2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.326
13673	15762	\begin{align*} y_{1}^{\prime }&=2 y_{1}+y_{2} \\ y_{2}^{\prime }&=-y_{1}+2 y_{2} \\ y_{3}^{\prime }&=3 y_{3}-4 y_{4} \\ y_{4}^{\prime }&=4 y_{3}+3 y_{4} \\ \end{align*}	✓	✓	✓	✓	1.326
13674	18178	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=a \sin \left (n x +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	1.326
13675	19884	\begin{align*} y^{\prime }-3 y-2 z&=0 \\ z^{\prime }+y-2 z&=0 \\ \end{align*}	✓	✓	✓	✓	1.326
13676	25219	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.326
13677	27618	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.326
13678	13742	\begin{align*} x y^{\prime \prime }+\left (a \,x^{2}+b x +2\right ) y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✗	1.327
13679	5648	\begin{align*} x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.328
13680	5826	\begin{align*} 2 \left (2 x^{2}+1\right ) y+4 x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.328
13681	9966	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.328
13682	18218	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.328
13683	21674	\begin{align*} 4 x y^{\prime \prime }+2 y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.328
13684	12445	\begin{align*} \left (a^{2} x^{2}+2\right ) y-2 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.329
13685	14203	\begin{align*} x^{\prime }&=t \cos \left (t^{2}\right ) \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.329
13686	19358	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.329
13687	24949	\begin{align*} y y^{\prime }&=1-y \\ \end{align*}	✓	✓	✓	✓	1.329
13688	26144	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.329
13689	10315	\begin{align*} {y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \\ \end{align*}	✓	✓	✓	✓	1.330
13690	20647	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=-4 x^{3} \\ \end{align*}	✓	✓	✓	✗	1.330
13691	6463	\begin{align*} -y^{\prime }+{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.331
13692	9562	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.331
13693	17749	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=5 t^{2} \\ \end{align*}	✓	✓	✓	✓	1.331
13694	20986	\begin{align*} y^{\prime }&={\mathrm e}^{x}+x \cos \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.331
13695	27036	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=3 \delta \left (t -2\right )-4 \delta \left (t -5\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.331
13696	1330	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.332
13697	20436	\begin{align*} x^{2} \left (-x y^{\prime }+y\right )&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.332
13698	21956	\begin{align*} t^{2} s^{\prime \prime }-t s^{\prime }&=1-\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.332
13699	22482	\begin{align*} x^{2} y^{\prime \prime }&=x^{2}+1 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.333
13700	5582	\begin{align*} \left (a^{2}-y^{2}\right ) {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.334