Internal problem ID [1898]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+x +1\right ) y^{\prime }-y^{2}-2 y-5=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.479 (sec). Leaf size: 35
dsolve([(x^2+x+1)*diff(y(x),x)=y(x)^2+2*y(x)+5,y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = -1+2 \cot \left (\frac {4 \pi \sqrt {3}}{9}-\frac {4 \sqrt {3}\, \arctan \left (\frac {\left (1+2 x \right ) \sqrt {3}}{3}\right )}{3}+\frac {\pi }{4}\right ) \]
✓ Solution by Mathematica
Time used: 1.007 (sec). Leaf size: 44
DSolve[{(x^2+x+1)*y'[x]==y[x]^2+2*y[x]+5,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \tan \left (\frac {4 \text {ArcTan}\left (\frac {2 x+1}{\sqrt {3}}\right )}{\sqrt {3}}+\frac {1}{36} \left (9-16 \sqrt {3}\right ) \pi \right )-1 \\ \end{align*}