29.18.29 problem 507

Internal problem ID [5103]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 507
Date solved : Monday, January 27, 2025 at 10:11:23 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 39

dsolve(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 {-2 x^{4}+4 c_{1}}}{2 x} \\ y \left (x \right ) &= \frac {\sqrt {-2 x^{4}+4 c_{1}}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 46

DSolve[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 {-\frac {x^4}{2}+c_1}}{x} \\ y(x)\to \frac {\sqrt {-\frac {x^4}{2}+c_1}}{x} \\ \end{align*}