Internal problem ID [1061]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page
91
Problem number: 1(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y+\left (2 x +\frac {1}{y}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 37
dsolve(y(x)+(2*x+1/y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-1+\sqrt {4 x c_{1}+1}}{2 x} \\ y \relax (x ) = -\frac {1+\sqrt {4 x c_{1}+1}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 54
DSolve[y[x]+(2*x+1/y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1+\sqrt {1+4 c_1 x}}{2 x} \\ y(x)\to \frac {-1+\sqrt {1+4 c_1 x}}{2 x} \\ y(x)\to 0 \\ \end{align*}