12.6.28 problem 28(a)

Internal problem ID [1707]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 28(a)
Date solved : Monday, January 27, 2025 at 05:31:12 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

\begin{align*} x^{2}+y^{2}+2 x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 47

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

\begin{align*} y &= -\frac {\sqrt {3}\, \sqrt {-x \left (x^{3}-3 c_1 \right )}}{3 x} \\ y &= \frac {\sqrt {3}\, \sqrt {-x \left (x^{3}-3 c_1 \right )}}{3 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 60

DSolve[(x^2+y[x]^2)+(2*x*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ y(x)\to \frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ \end{align*}