Internal problem ID [138]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y x^{2}-y^{\prime } x^{3}-y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 30
dsolve(2*x^2*y(x)-x^3*diff(y(x),x) = y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2}}{\sqrt {x^{2}+c_{1}}} \\ y \relax (x ) = -\frac {x^{2}}{\sqrt {x^{2}+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 43
DSolve[2*x^2*y[x]-x^3*y'[x] == y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{\sqrt {x^2+c_1}} \\ y(x)\to \frac {x^2}{\sqrt {x^2+c_1}} \\ y(x)\to 0 \\ \end{align*}