Internal problem ID [1970]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {x y^{3}+x^{2} y^{2} y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 74
dsolve((x*y(x)^3-1)+x^2*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}}}{2 x} \\ y \left (x \right ) &= -\frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y \left (x \right ) &= \frac {\left (12 x^{2}+8 c_{1} \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.208 (sec). Leaf size: 80
DSolve[(x*y[x]^3-1)+x^2*y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{3 x^2+2 c_1}}{x} \\ y(x)\to \frac {\sqrt [3]{\frac {3 x^2}{2}+c_1}}{x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{\frac {3 x^2}{2}+c_1}}{x} \\ \end{align*}