Internal problem ID [5263]
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: 23 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]
\[ \boxed {y^{2}+2 x y y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve((x^2+y(x)^2)+2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = -\frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 c_{1} \right )}}{3 x} y = \frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 c_{1} \right )}}{3 x} \end{align*}
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 60
DSolve[(x^2+y[x]^2)+2*x*y[x]*y'[x]==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*}