Internal problem ID [12149]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {3 y}{x}+y^{2} x^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x)-3*y(x)/x+x^3*y(x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {7 x^{3}}{x^{7}+7 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.238 (sec). Leaf size: 25
DSolve[y'[x]-3*y[x]/x+x^3*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {7 x^3}{x^7+7 c_1} \\ y(x)\to 0 \\ \end{align*}