2.3.166 Problems 16501 to 16600

Table 2.863: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16501	19711	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.055
16502	23910	\begin{align*} y^{\prime }+\frac {y}{x}&=\ln \left (x \right )-2 \\ \end{align*}	✓	✓	✓	✓	4.055
16503	1134	\begin{align*} y^{\prime } x&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.056
16504	12301	\begin{align*} y^{\prime \prime }+\left (a \cosh \left (x \right )^{2}+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.056
16505	14432	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✗	✗	✗	4.056
16506	3003	\begin{align*} \left (1-x \right ) y^{\prime }-1-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.058
16507	12589	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x +1}-\frac {y}{x \left (x +1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.059
16508	14833	\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x&=0 \\ \end{align*}	✓	✓	✓	✓	4.059
16509	15486	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.059
16510	19352	\begin{align*} y^{\prime } x +y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	4.060
16511	20800	\begin{align*} y^{\prime \prime } x +\left (x -1\right ) y^{\prime }-y&=x^{2} \\ \end{align*}	✓	✓	✓	✗	4.061
16512	11616	\begin{align*} \left (10 x^{2} y^{3}-3 y^{2}-2\right ) y^{\prime }+5 y^{4} x +x&=0 \\ \end{align*}	✓	✓	✓	✓	4.062
16513	23130	\begin{align*} y^{\prime } x +y^{2}&=1 \\ y \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.064
16514	23891	\begin{align*} 2 x^{2} y-y^{2}+6 x^{3} y^{3}+\left (2 y^{2} x^{4}-x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.064
16515	4676	\begin{align*} y^{\prime }&=x y \left (3+y\right ) \\ \end{align*}	✓	✓	✓	✓	4.065
16516	16310	\begin{align*} y^{\prime }+2 x&=2 \sqrt {y+x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.065
16517	23667	\begin{align*} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.065
16518	4347	\begin{align*} y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.066
16519	5160	\begin{align*} x^{2}+y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.068
16520	20859	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.068
16521	11618	\begin{align*} \left (2 x^{3} y^{3}-x \right ) y^{\prime }+2 x^{3} y^{3}-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.069
16522	15184	\begin{align*} y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}}&=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \\ \end{align*}	✗	✗	✗	✗	4.069
16523	1269	\begin{align*} y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.070
16524	24145	\begin{align*} r^{\prime }&=-2 r t \\ r \left (0\right ) &= r_{0} \\ \end{align*}	✓	✓	✓	✓	4.070
16525	11421	\begin{align*} y^{\prime } x +\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.071
16526	25008	\begin{align*} y^{\prime }&=\frac {t^{2}+y^{2}}{t y} \\ y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✓	4.071
16527	1604	\begin{align*} y^{\prime }+y&=\frac {2 x \,{\mathrm e}^{-x}}{1+{\mathrm e}^{x} y} \\ \end{align*}	✓	✓	✓	✗	4.072
16528	11320	\begin{align*} y^{\prime }-y^{2}-y x -x +1&=0 \\ \end{align*}	✓	✓	✓	✗	4.073
16529	19918	\begin{align*} 2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.074
16530	21482	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.076
16531	25029	\begin{align*} y-t +\left (t +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.076
16532	4115	\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.077
16533	5338	\begin{align*} \left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	4.077
16534	20663	\begin{align*} y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=\left (x -2\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	4.077
16535	11426	\begin{align*} y^{\prime } x -y f \left (x^{a} y^{b}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.078
16536	21799	\begin{align*} r^{\prime } \sin \left (t \right )+r \cos \left (t \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.078
16537	20642	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.079
16538	1539	\begin{align*} y^{\prime } x +y \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.080
16539	20545	\begin{align*} y^{\prime \prime }-a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.082
16540	4677	\begin{align*} y^{\prime }&=1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \\ \end{align*}	✓	✓	✓	✓	4.084
16541	9200	\begin{align*} -y+y^{\prime } x&=2 x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.084
16542	1243	\begin{align*} y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\ \end{align*}	✓	✓	✓	✗	4.085
16543	19379	\begin{align*} \left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+{\mathrm e}^{x} y&=2 x y^{3} \\ \end{align*}	✓	✓	✓	✗	4.085
16544	755	\begin{align*} 3 y^{\prime } y^{2} x&=3 x^{4}+y^{3} \\ \end{align*}	✓	✓	✓	✓	4.086
16545	3467	\begin{align*} y^{\prime }&=\frac {1}{x +2 y+1} \\ \end{align*}	✓	✓	✓	✓	4.086
16546	16800	\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.087
16547	6908	\begin{align*} y x -y^{2}-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.088
16548	21844	\begin{align*} 4 x^{2} y^{2} y^{\prime }-3 x y^{3}&=x^{2} y^{3}+2 x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.089
16549	22681	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.089
16550	25537	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.090
16551	12379	\begin{align*} y^{\prime \prime } x +\left (b -x \right ) y^{\prime }-a y&=0 \\ \end{align*}	✗	✓	✓	✗	4.091
16552	14144	\begin{align*} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	4.092
16553	10125	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	4.093
16554	14558	\begin{align*} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	4.095
16555	11636	\begin{align*} \left (\ln \left (y\right )+x \right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	4.096
16556	21631	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	4.097
16557	15381	\begin{align*} \left (y^{3}-x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	4.098
16558	21072	\begin{align*} x +\sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= \pi \\ \end{align*}	✓	✓	✗	✓	4.098
16559	19473	\begin{align*} 2 y^{\prime \prime }+y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.100
16560	9160	\begin{align*} 2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.101
16561	18302	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=-\frac {16 \ln \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	4.101
16562	227	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.102
16563	11893	\begin{align*} y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right ) x^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	4.102
16564	14163	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	4.102
16565	19872	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	4.102
16566	23271	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.102
16567	7254	\begin{align*} y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	4.103
16568	21730	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	4.103
16569	22620	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	4.104
16570	13303	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+b n \,x^{n -1}-a \,b^{2} {\mathrm e}^{\lambda x} x^{2 n} \\ \end{align*}	✓	✗	✗	✗	4.105
16571	22099	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.105
16572	18054	\begin{align*} y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right )&=\cos \left (\frac {x}{2}-\frac {y}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.107
16573	20920	\begin{align*} y^{\prime \prime }+6 y^{\prime }+18 y&=2 \operatorname {Heaviside}\left (\pi -t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.107
16574	25403	\begin{align*} y^{\prime }&=5 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.108
16575	7497	\begin{align*} y x +y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.109
16576	24201	\begin{align*} 2 x y \cos \left (x^{2}\right )-2 y x +1+\left (\sin \left (x^{2}\right )-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.109
16577	5051	\begin{align*} \left (1+y\right ) y^{\prime }&=x^{2} \left (1-y\right ) \\ \end{align*}	✓	✓	✓	✓	4.112
16578	20096	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	4.112
16579	757	\begin{align*} 2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=4 x^{2}+\sin \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.113
16580	5042	\begin{align*} y y^{\prime }&=a x +b y^{2} \\ \end{align*}	✓	✓	✓	✓	4.113
16581	7218	\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	4.114
16582	20266	\begin{align*} \cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.114
16583	17782	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.115
16584	9161	\begin{align*} y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	4.116
16585	23337	\begin{align*} y^{\prime \prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.116
16586	21118	\begin{align*} x^{\prime \prime }+5 x^{\prime }+6 x&=0 \\ \end{align*}	✓	✓	✓	✓	4.117
16587	23385	\begin{align*} x^{2} y^{\prime \prime }+\frac {7 y^{\prime } x}{2}-\frac {3 y}{2}&=0 \\ y \left (-4\right ) &= 1 \\ y^{\prime }\left (-4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.117
16588	23860	\begin{align*} 2 x^{3} y+\left (2 y^{2} x^{2}+2 y^{4}+\ln \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	4.117
16589	24975	\begin{align*} y^{\prime }&=\frac {\cot \left (y\right )}{t} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	4.118
16590	25275	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +y&=t \\ \end{align*}	✓	✓	✓	✓	4.118
16591	5613	\begin{align*} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.119
16592	16475	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.119
16593	22017	\begin{align*} y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✓	4.119
16594	25576	\begin{align*} y^{\prime \prime }+b y^{\prime }+y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.119
16595	11474	\begin{align*} x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	4.120
16596	12231	\begin{align*} y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{2}+a x y+\frac {x^{4}}{16}+\frac {a \,x^{3}}{4}+\frac {a^{2} x^{2}}{4}+y^{3}+\frac {3 y^{2} x^{2}}{4}+\frac {3 a x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 y a \,x^{3}}{4}+\frac {3 y a^{2} x^{2}}{4}+\frac {x^{6}}{64}+\frac {3 x^{5} a}{32}+\frac {3 a^{2} x^{4}}{16}+\frac {a^{3} x^{3}}{8} \\ \end{align*}	✓	✓	✓	✗	4.123
16597	5673	\begin{align*} {y^{\prime }}^{4}+4 y {y^{\prime }}^{3}+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y&=0 \\ \end{align*}	✓	✗	✓	✓	4.125
16598	22773	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x -2 \\ \end{align*}	✓	✓	✓	✓	4.125
16599	162	\begin{align*} y^{\prime } x -4 x^{2} y+2 y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.126
16600	12553	\begin{align*} -\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.127