Internal problem ID [13105]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {4 y^{2}-y^{2} x^{2}+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(4*y(x)^2-x^2*y(x)^2+diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {3}{-x^{3}+3 c_{1} +12 x} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 25
DSolve[4*y[x]^2-x^2*y[x]^2+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3}{x^3-12 x+3 c_1} y(x)\to 0 \end{align*}