Internal problem ID [97]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y x +y^{\prime } x^{2}-5 y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(2*x*y(x)+x^2*diff(y(x),x) = 5*y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (x^{5} c_{1}+2\right ) x}}{x^{5} c_{1}+2} \\ y \relax (x ) = -\frac {\sqrt {\left (x^{5} c_{1}+2\right ) x}}{x^{5} c_{1}+2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.388 (sec). Leaf size: 51
DSolve[2*x*y[x]+x^2*y'[x] == 5*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x}}{\sqrt {2+c_1 x^5}} \\ y(x)\to \frac {\sqrt {x}}{\sqrt {2+c_1 x^5}} \\ y(x)\to 0 \\ \end{align*}