6.5 problem 5

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]]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {-1-2 y x -y^{2}}{x^{2}+2 y x}=0} \end {gather*}

Solution by Maple

Time used: 0.005 (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 \relax (x ) = \frac {-x^{2}+\sqrt {x^{4}-4 x c_{1}-4 x^{2}}}{2 x} \\ y \relax (x ) = -\frac {x^{2}+\sqrt {x^{4}-4 x c_{1}-4 x^{2}}}{2 x} \\ \end{align*}

Solution by Mathematica

Time used: 0.321 (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*}