12.7.1 problem 1(a)

Internal problem ID [1711]
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)
Date solved : Monday, January 27, 2025 at 05:32:05 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y+\left (2 x +\frac {1}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve(y(x)+(2*x+1/y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-1+\sqrt {4 c_1 x +1}}{2 x} \\ y &= \frac {-1-\sqrt {4 c_1 x +1}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.326 (sec). Leaf size: 54

DSolve[y[x]+(2*x+1/y[x])*D[y[x],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*}