2.3.157 Problems 15601 to 15700

Table 2.857: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15601	25700	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\ x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	2.084
15602	1821	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=8 x^{5} \\ \end{align*}	✓	✓	✓	✗	2.085
15603	10415	\begin{align*} y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	2.085
15604	16573	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.086
15605	18069	\begin{align*} x -y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.086
15606	21344	\begin{align*} y^{\prime }&=\frac {x +1}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.087
15607	21669	\begin{align*} x^{4} \left (x^{2}+1\right ) \left (x -1\right )^{2} y^{\prime \prime }+4 x^{3} \left (x -1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	2.087
15608	5817	\begin{align*} -y+y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.088
15609	19134	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.088
15610	19677	\begin{align*} x^{\prime }+2 x&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.088
15611	24794	\begin{align*} 3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.088
15612	22086	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +y&=4 x y^{2} \\ \end{align*}	✗	✗	✗	✗	2.089
15613	25432	\begin{align*} y^{\prime }-a \left (t \right ) y&=q \\ \end{align*}	✓	✓	✓	✓	2.089
15614	12334	\begin{align*} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.090
15615	19367	\begin{align*} y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	2.090
15616	12372	\begin{align*} y^{\prime \prime } x +a y^{\prime }+b \,x^{\operatorname {a1}} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.091
15617	134	\begin{align*} \left ({\mathrm e}^{y}+x \right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \\ \end{align*}	✓	✓	✓	✓	2.092
15618	9737	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.092
15619	12342	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.092
15620	14047	\begin{align*} \left (2 y^{\prime } x -y\right )^{2}&=8 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.092
15621	15636	\begin{align*} y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✗	2.092
15622	79	\begin{align*} 2 y^{\prime } x +y&=10 \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	2.093
15623	24810	\begin{align*} 3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.094
15624	17357	\begin{align*} t^{2} y^{\prime \prime }+7 y^{\prime } t -7 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -22 \\ \end{align*}	✓	✓	✓	✓	2.095
15625	24999	\begin{align*} -y+y^{\prime }&={\mathrm e}^{2 t} t \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	2.095
15626	15354	\begin{align*} t -s+t s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.096
15627	13697	\begin{align*} y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+a \,x^{2}+b +2 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.097
15628	22565	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.097
15629	23680	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y p&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.097
15630	6982	\begin{align*} y^{\prime }-y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.098
15631	25674	\begin{align*} y^{\prime }+2 y x&=1 \\ \end{align*}	✓	✓	✓	✓	2.098
15632	748	\begin{align*} y^{2} y^{\prime }+2 x y^{3}&=6 x \\ \end{align*}	✓	✓	✓	✓	2.099
15633	1107	\begin{align*} -y+y^{\prime } t&={\mathrm e}^{-t} t^{2} \\ \end{align*}	✓	✓	✓	✓	2.099
15634	13744	\begin{align*} y^{\prime \prime } x +\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (c -1\right ) \left (a x +b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.100
15635	85	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.101
15636	7687	\begin{align*} y^{\prime \prime } x +\frac {y^{\prime }}{2}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.101
15637	17031	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.101
15638	11329	\begin{align*} y^{\prime }+a y \left (-x +y\right )-1&=0 \\ \end{align*}	✓	✓	✓	✗	2.102
15639	17593	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=\sec \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.102
15640	18539	\begin{align*} -y+y^{\prime }&=1+3 \sin \left (t \right ) \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	2.102
15641	25859	\begin{align*} x^{3}+y^{4} x +2 y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.102
15642	15535	\begin{align*} y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	2.103
15643	19153	\begin{align*} x^{2} y^{2} y^{\prime \prime }-3 y^{2} y^{\prime } x +4 y^{3}+x^{6}&=0 \\ \end{align*}	✗	✓	✓	✗	2.103
15644	24979	\begin{align*} 3 y+y^{\prime }&={\mathrm e}^{t} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.103
15645	18086	\begin{align*} y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	2.104
15646	2473	\begin{align*} \frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.105
15647	1563	\begin{align*} y^{\prime } x +3 y&=\frac {2}{x \left (x^{2}+1\right )} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.106
15648	12694	\begin{align*} y^{\prime \prime }&=\frac {\cos \left (2 x \right ) y^{\prime }}{\sin \left (2 x \right )}-2 y \\ \end{align*}	✓	✓	✓	✗	2.106
15649	54	\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	2.108
15650	11671	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	2.108
15651	14652	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.108
15652	3445	\begin{align*} y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right )^{3} \\ \end{align*}	✓	✓	✓	✓	2.109
15653	14693	\begin{align*} x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=x^{3} \\ \end{align*}	✓	✓	✓	✗	2.109
15654	16958	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.109
15655	18527	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.109
15656	20691	\begin{align*} a^{2}-2 y x -y^{2}-\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.109
15657	23144	\begin{align*} \cos \left (x \right ) \sin \left (y\right ) y^{\prime }-\cos \left (x \right ) \cos \left (y\right )-\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.109
15658	15506	\begin{align*} y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.110
15659	18570	\begin{align*} 2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.110
15660	23098	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.110
15661	7731	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=y^{3} \sec \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	2.111
15662	22180	\begin{align*} {\mathrm e}^{x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.111
15663	13903	\begin{align*} x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y&=0 \\ \end{align*}	✓	✓	✗	✗	2.112
15664	193	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	2.113
15665	6476	\begin{align*} 2 y y^{\prime \prime }&=3 y^{4}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.113
15666	7603	\begin{align*} 5 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.113
15667	15071	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=2 \\ \end{align*}	✓	✓	✓	✓	2.113
15668	19983	\begin{align*} y^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.114
15669	13702	\begin{align*} y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a \,x^{3} b -a \,x^{2}+b^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.115
15670	13873	\begin{align*} x^{4} y^{\prime \prime }-\left (a +b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) x +a b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.115
15671	16378	\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}	✓	✓	✓	✓	2.115
15672	5503	\begin{align*} x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.116
15673	14670	\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right )^{2}-\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.117
15674	22807	\begin{align*} y^{\prime \prime }&=f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.117
15675	7595	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.118
15676	14759	\begin{align*} y^{\prime \prime } x -\left (x^{2}+2\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.118
15677	3474	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=1 \\ y \left (\frac {\pi }{4}\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.119
15678	6007	\begin{align*} -5 y-3 y^{\prime } x +x^{2} y^{\prime \prime }&=\ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	2.119
15679	9482	\begin{align*} x^{\prime }&=x+2 y-4 t +1 \\ y^{\prime }&=-x+2 y+3 t +4 \\ \end{align*}	✓	✓	✓	✓	2.120
15680	13669	\begin{align*} y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.120
15681	14314	\begin{align*} x^{\prime \prime }-b x^{\prime }+x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.120
15682	21966	\begin{align*} y^{\prime }+y&=0 \\ y \left (3\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.120
15683	22369	\begin{align*} i^{\prime }+5 i&=10 \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.120
15684	9745	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.121
15685	10308	\begin{align*} {y^{\prime }}^{2}&=x +y \\ \end{align*}	✓	✓	✓	✓	2.121
15686	21014	\begin{align*} x^{\prime }&=-t^{2} x \\ \end{align*}	✓	✓	✓	✓	2.121
15687	8236	\begin{align*} y^{\prime } x&=y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.122
15688	14953	\begin{align*} \left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right )&=0 \\ \end{align*}	✗	✗	✗	✗	2.122
15689	24130	\begin{align*} x^{2}+y \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.122
15690	24950	\begin{align*} t^{2} y^{\prime }&=1-2 t y \\ \end{align*}	✓	✓	✓	✓	2.122
15691	5592	\begin{align*} 4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.124
15692	21382	\begin{align*} \left (x +y^{2}\right ) y^{\prime }-x^{2}+y&=0 \\ \end{align*}	✓	✓	✓	✗	2.124
15693	8199	\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.125
15694	11469	\begin{align*} x^{3} y^{\prime }-y^{2}-x^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.125
15695	19135	\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.125
15696	496	\begin{align*} x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.126
15697	15531	\begin{align*} y^{\prime }&=-y x \\ \end{align*}	✓	✓	✓	✓	2.126
15698	15824	\begin{align*} y^{\prime }&=y^{2}+y \\ \end{align*}	✓	✓	✓	✓	2.127
15699	21450	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.127
15700	11752	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x -9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.128