8.6.6 problem 6

Internal problem ID [776]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 6
Date solved : Monday, January 27, 2025 at 03:04:45 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

\[ y = \frac {x}{1+2 x \ln \left (x \right )+c_1 x} \]

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 26

DSolve[2*x*y[x]^2+x^2*D[y[x],x] == y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x}{2 x \log (x)+c_1 (-x)+1} \\ y(x)\to 0 \\ \end{align*}