Internal problem ID [11584]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number: 2(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]
\[ \boxed {2 x y y^{\prime }+y^{2}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 49
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: 0.377 (sec). Leaf size: 60
DSolve[2*x*y[x]*y'[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*}