40.3.12 problem 24 (c)

Internal problem ID [6616]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 24 (c)
Date solved : Monday, January 27, 2025 at 02:15:58 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

dsolve((x^2+y(x)^2)+x*y(x)*diff(y(x),x)=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: 0.214 (sec). Leaf size: 46

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