Internal problem ID [572]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{\prime }-\frac {-1-2 y x -y^{2}}{x^{2}+2 y x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 57
dsolve(diff(y(x),x) = (-1-2*x*y(x)-y(x)^2)/(x^2+2*x*y(x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {-x^{2}+\sqrt {x^{4}-4 c_{1} x -4 x^{2}}}{2 x} \\ y \left (x \right ) = -\frac {x^{2}+\sqrt {x^{4}-4 c_{1} x -4 x^{2}}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.437 (sec). Leaf size: 67
DSolve[y'[x] == (-1-2*x*y[x]-y[x]^2)/(x^2+2*x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2+\sqrt {x \left (x^3-4 x+4 c_1\right )}}{2 x} \\ y(x)\to \frac {-x^2+\sqrt {x \left (x^3-4 x+4 c_1\right )}}{2 x} \\ \end{align*}