6.8 problem 8

Internal problem ID [128]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 8.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]

Solve \begin {gather*} \boxed {2 y x +y^{\prime } x^{2}-y^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

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

\[ y \relax (x ) = \frac {3 x}{3 x^{3} c_{1}+1} \]

Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 24

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