Internal problem ID [134]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{3}-x^{2} y+y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve(x^3*diff(y(x),x) = x^2*y(x)-y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x}{\sqrt {2 \ln \relax (x )+c_{1}}} \\ y \relax (x ) = -\frac {x}{\sqrt {2 \ln \relax (x )+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.184 (sec). Leaf size: 41
DSolve[x^3*y'[x] == x^2*y[x]-y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\sqrt {2 \log (x)+c_1}} \\ y(x)\to \frac {x}{\sqrt {2 \log (x)+c_1}} \\ y(x)\to 0 \\ \end{align*}