7.7.2 problem 2

Internal problem ID [180]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 2
Date solved : Friday, February 07, 2025 at 08:01:30 AM
CAS classification : [_separable]

\begin{align*} x y^{2}+3 y^{2}-y^{\prime } x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 18

dsolve(x*y(x)^2+3*y(x)^2-x^2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {x}{-\ln \left (x \right ) x +c_1 x +3} \]

✓ Solution by Mathematica

Time used: 0.144 (sec). Leaf size: 25

DSolve[x*y[x]^2+3*y[x]^2-x^2*D[y[x],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*}