7.7.8 problem 8

Internal problem ID [186]
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 : 8
Date solved : Friday, February 07, 2025 at 08:01:54 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

\[ y = \frac {3 x}{3 c_1 \,x^{3}+1} \]

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 24

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

\begin{align*} y(x)\to \frac {3 x}{1+3 c_1 x^3} \\ y(x)\to 0 \\ \end{align*}