Internal problem ID [1899]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}-2 x -8\right ) y^{\prime }-y^{2}-y+2=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.179 (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)
\[ y \relax (x ) = \frac {2 x +8-2 \sqrt {-2 x^{2}+4 x +16}}{3 x +4} \]
✓ Solution by Mathematica
Time used: 0.54 (sec). Leaf size: 34
DSolve[{(x^2-2*x-8)*y'[x]==y[x]^2+y[x]-2,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2 \sqrt {-2 x^2+4 x+16}+2 x+8}{3 x+4} \\ \end{align*}