Internal problem ID [1979]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.2 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+x y^{2}-4 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x)+x*y(x)^2=4*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{4+x \ln \relax (x )+x c_{1}} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 24
DSolve[y'[x]+x*y[x]^2==4*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{(x-8) x-2 c_1} \\ y(x)\to 0 \\ \end{align*}