64.1.5 problem 2(a)

Internal problem ID [13250]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 2(a)
Date solved : Tuesday, January 28, 2025 at 05:13:05 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 47

dsolve(2*x*y(x)*diff(y(x),x)+x^2+y(x)^2=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: 0.248 (sec). Leaf size: 60

DSolve[2*x*y[x]*D[y[x],x]+x^2+y[x]^2==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*}