Internal problem ID [3009]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan,
1960
Section: Exercises, page 14
Problem number: 1(h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{3}-y^{\prime } y^{2} x=-x^{3}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 74
dsolve((x^3+y(x)^3)-x*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}} x y \left (x \right ) = \left (-\frac {\left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}\right ) x y \left (x \right ) = \left (-\frac {\left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (3 \ln \left (x \right )+c_{1} \right )^{\frac {1}{3}}}{2}\right ) x \end{align*}
✓ Solution by Mathematica
Time used: 0.193 (sec). Leaf size: 63
DSolve[(x^3+y[x]^3)-x*y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \sqrt [3]{3 \log (x)+c_1} y(x)\to -\sqrt [3]{-1} x \sqrt [3]{3 \log (x)+c_1} y(x)\to (-1)^{2/3} x \sqrt [3]{3 \log (x)+c_1} \end{align*}