Internal problem ID [1898]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 5, page 21
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x^{2}+x +1\right ) y^{\prime }-y^{2}-2 y=5} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.141 (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)
\[ y \left (x \right ) = -1+2 \cot \left (\frac {4 \sqrt {3}\, \pi }{9}-\frac {4 \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \left (2 x +1\right )}{3}\right )}{3}+\frac {\pi }{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.905 (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]
\[ y(x)\to 2 \tan \left (\frac {4 \arctan \left (\frac {2 x+1}{\sqrt {3}}\right )}{\sqrt {3}}+\frac {1}{36} \left (9-16 \sqrt {3}\right ) \pi \right )-1 \]