Internal problem ID [126]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 x y^{2}+y^{\prime } x^{2}-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(2*x*y(x)^2+x^2*diff(y(x),x) = y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{1+2 x \ln \left (x \right )+c_{1} x} \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 26
DSolve[2*x*y[x]^2+x^2*y'[x] == y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{2 x \log (x)+c_1 (-x)+1} y(x)\to 0 \end{align*}