Internal problem ID [1993]
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 14.23 (b) .
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {4 y^{2}}{x^{2}}+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)= 4*y(x)^2/x^2 - y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{c_{1} x +x^{2}+4} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 24
DSolve[y'[x]== 4*y[x]^2/x^2 - y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{x^2-c_1 x+4} \\ y(x)\to 0 \\ \end{align*}