Internal problem ID [576]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-1-2 y x}{x^{2}+2 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 47
dsolve(diff(y(x),x) = (-1-2*x*y(x))/(x^2+2*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{2}}{2}-\frac {\sqrt {x^{4}-4 c_{1}-4 x}}{2} \\ y \relax (x ) = -\frac {x^{2}}{2}+\frac {\sqrt {x^{4}-4 c_{1}-4 x}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 61
DSolve[y'[x]== (-1-2*x*y[x])/(x^2+2*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-x^2-\sqrt {x^4-4 x+4 c_1}\right ) \\ y(x)\to \frac {1}{2} \left (-x^2+\sqrt {x^4-4 x+4 c_1}\right ) \\ \end{align*}