Internal problem ID [2051]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {-y^{3}+3 y^{\prime } y^{2} x=-2 x^{3}+3 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 108
dsolve((2*x^3-y(x)^3-3*x)+(3*x*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \left (-x^{3}+3 x \ln \left (x \right )+c_{1} x \right )^{\frac {1}{3}} y = -\frac {\left (-x^{3}+3 x \ln \left (x \right )+c_{1} x \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (-x^{3}+3 x \ln \left (x \right )+c_{1} x \right )^{\frac {1}{3}}}{2} y = -\frac {\left (-x^{3}+3 x \ln \left (x \right )+c_{1} x \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (-x^{3}+3 x \ln \left (x \right )+c_{1} x \right )^{\frac {1}{3}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.354 (sec). Leaf size: 80
DSolve[(2*x^3-y[x]^3-3*x)+(3*x*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{x \left (-x^2+3 \log (x)+c_1\right )} y(x)\to -\sqrt [3]{-1} \sqrt [3]{x \left (-x^2+3 \log (x)+c_1\right )} y(x)\to (-1)^{2/3} \sqrt [3]{x \left (-x^2+3 \log (x)+c_1\right )} \end{align*}