Internal problem ID [12160]
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 63.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]
\[ \boxed {3 x y^{2} y^{\prime }+y^{3}=2 x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 73
dsolve(3*x*y(x)^2*diff(y(x),x)+y(x)^3-2*x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {{\left (\left (x^{2}+c_{1} \right ) x^{2}\right )}^{\frac {1}{3}}}{x} \\ y \left (x \right ) &= -\frac {{\left (\left (x^{2}+c_{1} \right ) x^{2}\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2 x} \\ y \left (x \right ) &= \frac {{\left (\left (x^{2}+c_{1} \right ) x^{2}\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.352 (sec). Leaf size: 72
DSolve[3*x*y[x]^2*y'[x]+y[x]^3-2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ \end{align*}