7.7.6 problem 6

Internal problem ID [184]
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 : 6
Date solved : Friday, February 07, 2025 at 08:01:48 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.152 (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*}