2.3.115 Problems 11401 to 11500

Table 2.761: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
11401	15946	\begin{align*} y^{\prime }&=t y \\ \end{align*}	✓	✓	✓	✓	1.706
11402	23195	\begin{align*} x^{2}-2 y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.707
11403	23453	\begin{align*} \left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.708
11404	4218	\begin{align*} y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	1.709
11405	23758	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.709
11406	14645	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 x \,{\mathrm e}^{-3 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.710
11407	16566	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.710
11408	65	\begin{align*} -y+y^{\prime } x&=2 x^{2} y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.711
11409	7312	\begin{align*} 2 y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.711
11410	8394	\begin{align*} y^{\prime }&=\frac {1}{-3+y} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.711
11411	15872	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ \end{align*}	✓	✓	✓	✓	1.711
11412	25455	\begin{align*} y^{\prime }&=t^{2}+y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.711
11413	1115	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.712
11414	22208	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.712
11415	2308	\begin{align*} t y+y^{\prime }&=1+t \\ y \left (\frac {3}{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.713
11416	13355	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b \\ \end{align*}	✓	✗	✗	✗	1.713
11417	24860	\begin{align*} x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.713
11418	25018	\begin{align*} 2 y y^{\prime }&=y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	1.713
11419	25024	\begin{align*} 2 y y^{\prime }&=y^{2}+t -1 \\ \end{align*}	✓	✓	✓	✓	1.713
11420	8334	\begin{align*} y^{\prime }&=\left ({\mathrm e}^{y} y-9 y\right ) {\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	1.714
11421	15393	\begin{align*} y&=y^{\prime } x +\sqrt {1-{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.714
11422	22588	\begin{align*} y^{\prime }&=y \left (x +y\right ) \\ \end{align*}	✓	✓	✗	✓	1.714
11423	23905	\begin{align*} y^{\prime }+3 y&=x +1 \\ \end{align*}	✓	✓	✓	✓	1.714
11424	2961	\begin{align*} x^{\prime }+x&={\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	1.715
11425	19424	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=6 \\ \end{align*}	✓	✓	✓	✓	1.715
11426	24798	\begin{align*} 4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.715
11427	17302	\begin{align*} 1+2 y-2 y^{\prime } t&=\frac {1}{{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	1.716
11428	1229	\begin{align*} y^{\prime }+y&=\frac {1}{{\mathrm e}^{x}+1} \\ \end{align*}	✓	✓	✓	✓	1.717
11429	4752	\begin{align*} y^{\prime } x +x^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.717
11430	18933	\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ 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.	✓	✓	✓	✓	1.717
11431	19850	\begin{align*} e y^{\prime \prime }&=-P \left (L -x \right ) \\ \end{align*}	✓	✓	✓	✓	1.717
11432	1212	\begin{align*} 1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.718
11433	7226	\begin{align*} y^{\prime }-y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.718
11434	24863	\begin{align*} \left (1+y^{\prime }\right )^{2} \left (-y^{\prime } x +y\right )&=1 \\ \end{align*}	✓	✓	✓	✗	1.718
11435	1514	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.719
11436	2693	\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.719
11437	1102	\begin{align*} -2 y+y^{\prime }&=3 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	1.720
11438	11858	\begin{align*} f \left (x {y^{\prime }}^{2}\right )+2 y^{\prime } x -y&=0 \\ \end{align*}	✗	✓	✓	✗	1.720
11439	16721	\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.720
11440	885	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.721
11441	8868	\begin{align*} y^{\prime }-2 y&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	1.721
11442	263	\begin{align*} y^{\prime \prime }-2 y^{\prime }-5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.722
11443	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*}	✓	✓	✓	✓	1.722
11444	20423	\begin{align*} 4 y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.722
11445	668	\begin{align*} y^{\prime }&=x^{2}-y-2 \\ \end{align*}	✓	✓	✓	✓	1.724
11446	9532	\begin{align*} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.724
11447	12946	\begin{align*} \left (x -y\right ) y^{\prime \prime }-h \left (y^{\prime }\right )&=0 \\ \end{align*}	✗	✓	✓	✗	1.724
11448	18361	\begin{align*} y^{\prime \prime }+\alpha y^{\prime }&=0 \\ y \left (0\right ) &= {\mathrm e}^{\alpha } \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.724
11449	22101	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.724
11450	845	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.725
11451	4296	\begin{align*} \ln \left (x \right ) y^{\prime }+\frac {x +y}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.725
11452	15934	\begin{align*} y^{\prime }&=t^{r} y+4 \\ \end{align*}	✓	✓	✓	✗	1.725
11453	811	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.726
11454	10118	\begin{align*} y^{\prime \prime }-x^{3} y-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	1.726
11455	17132	\begin{align*} y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	1.726
11456	20865	\begin{align*} 4 x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.726
11457	24974	\begin{align*} 2 t y+y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.726
11458	25546	\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.726
11459	1113	\begin{align*} \frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.727
11460	7016	\begin{align*} y^{\prime } x +a y+b \,x^{n}&=0 \\ \end{align*}	✓	✓	✓	✓	1.727
11461	20875	\begin{align*} x^{\prime \prime }+x&=5 t^{2} \\ x \left (0\right ) &= 4 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.727
11462	21264	\begin{align*} x^{\prime \prime }-x+3 x^{2}&=0 \\ x \left (0\right ) &= {\frac {1}{4}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.727
11463	3439	\begin{align*} y^{\prime }&=2 y+{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	1.728
11464	7159	\begin{align*} \frac {x}{1+y}&=\frac {y y^{\prime }}{x +1} \\ \end{align*}	✓	✓	✓	✗	1.728
11465	15335	\begin{align*} -y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.728
11466	15907	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.728
11467	19678	\begin{align*} x^{\prime }+x \tan \left (t \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.728
11468	3807	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.730
11469	3974	\begin{align*} y^{\prime }+4 y&=3 \delta \left (t -1\right ) \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.730
11470	14326	\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.730
11471	15948	\begin{align*} y^{\prime }&=\frac {t y}{t^{2}+1} \\ \end{align*}	✓	✓	✓	✓	1.731
11472	23169	\begin{align*} y^{\prime }-y x&=\left (-x^{2}+1\right ) {\mathrm e}^{\frac {x^{2}}{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.731
11473	19730	\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	1.733
11474	25518	\begin{align*} y^{\prime \prime }&=-9 y \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.733
11475	2062	\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.734
11476	4193	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.734
11477	6491	\begin{align*} 5 y y^{\prime \prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	1.734
11478	9623	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.734
11479	12292	\begin{align*} y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.734
11480	9418	\begin{align*} \left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.735
11481	18948	\begin{align*} y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ 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.	✓	✓	✓	✓	1.735
11482	7960	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.736
11483	11758	\begin{align*} y {y^{\prime }}^{2}-\left (-x +y\right ) y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	1.736
11484	20424	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.736
11485	3272	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.737
11486	4792	\begin{align*} y^{\prime } x&=a \,x^{m}-b y-c \,x^{n} y^{2} \\ \end{align*}	✓	✓	✓	✗	1.737
11487	19676	\begin{align*} 2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✗	1.737
11488	14367	\begin{align*} x^{\prime }+3 x&=\delta \left (t -1\right )+\operatorname {Heaviside}\left (t -4\right ) \\ x \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.738
11489	16399	\begin{align*} y^{\prime \prime \prime }&=2 \sqrt {y^{\prime \prime }} \\ \end{align*}	✓	✓	✓	✓	1.739
11490	22630	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.739
11491	4007	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.740
11492	14311	\begin{align*} x^{\prime \prime }+x&=9 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.740
11493	22069	\begin{align*} y^{\prime }+\frac {2 y}{x}&=x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.740
11494	23201	\begin{align*} 2 x^{2}+2 y^{2}+x +\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.740
11495	3715	\begin{align*} y^{\prime \prime }+y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.741
11496	23924	\begin{align*} 3 y y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.741
11497	5210	\begin{align*} \left (x +y^{2}\right ) y^{\prime }+y&=b x +a \\ \end{align*}	✓	✓	✓	✗	1.742
11498	7799	\begin{align*} y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.742
11499	14905	\begin{align*} x^{\prime }+\left (a +\frac {1}{t}\right ) x&=b \\ x \left (1\right ) &= x_{0} \\ \end{align*}	✓	✓	✓	✗	1.743
11500	15022	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	1.743