60.1.231 problem 232

Internal problem ID [10245]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 232
Date solved : Monday, January 27, 2025 at 06:41:25 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 0.221 (sec). Leaf size: 46

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