18.1.17 problem Problem 14.23 (b)

Internal problem ID [3473]
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)
Date solved : Monday, January 27, 2025 at 07:38:18 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 0.162 (sec). Leaf size: 24

DSolve[D[y[x],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*}