Internal problem ID [1899]
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: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x^{2}-2 x -8\right ) y^{\prime }-y^{2}-y=-2} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 31
dsolve([(x^2-2*x-8)*diff(y(x),x)=y(x)^2+y(x)-2,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 x +8-2 \sqrt {-2 x^{2}+4 x +16}}{3 x +4} \]
✓ Solution by Mathematica
Time used: 3.813 (sec). Leaf size: 48
DSolve[{(x^2-2*x-8)*y'[x]==y[x]^2+y[x]-2,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4 \sqrt {x+2}-2 \sqrt {8-2 x}}{\sqrt {8-2 x}+4 \sqrt {x+2}} \]