8.6.2 problem 2

Internal problem ID [772]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:04:38 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 25

DSolve[3*y[x]^2+x*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*}