Internal problem ID [122]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {3 y^{2}+x y^{2}-y^{\prime } x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(3*y(x)^2+x*y(x)^2-x^2*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{x \ln \left (x \right )-c_{1} x -3} \]
✓ Solution by Mathematica
Time used: 0.13 (sec). Leaf size: 25
DSolve[3*y[x]^2+x*y[x]^2-x^2*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{x \log (x)+c_1 x-3} y(x)\to 0 \end{align*}