Internal problem ID [5273]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}+x y y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.198 (sec). Leaf size: 46
DSolve[(x^2+y[x]^2)+x*y[x]*y'[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*}