Internal problem ID [5042]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 43.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y^{\prime } x^{2}-y^{3}-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 48
dsolve(2*x^2*diff(y(x),x)=y(x)^3+x*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-\left (\ln \relax (x )-c_{1}\right ) x}}{\ln \relax (x )-c_{1}} \\ y \relax (x ) = -\frac {\sqrt {-\left (\ln \relax (x )-c_{1}\right ) x}}{\ln \relax (x )-c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.161 (sec). Leaf size: 49
DSolve[2*x^2*y'[x]==y[x]^3+x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x}}{\sqrt {-\log (x)+c_1}} \\ y(x)\to \frac {\sqrt {x}}{\sqrt {-\log (x)+c_1}} \\ y(x)\to 0 \\ \end{align*}