29.19.29 problem 542

Internal problem ID [5138]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 542
Date solved : Monday, January 27, 2025 at 10:13:54 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: 0.005 (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 \left (x \right ) &= -\frac {\sqrt {3}\, \sqrt {-x \left (x^{3}-3 c_{1} \right )}}{3 x} \\ y \left (x \right ) &= \frac {\sqrt {3}\, \sqrt {-x \left (x^{3}-3 c_{1} \right )}}{3 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.223 (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*}