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: 75
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 \right ) &= {\left (\left (-x^{2}+3 \ln \left (x \right )+c_{1} \right ) x \right )}^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {{\left (\left (-x^{2}+3 \ln \left (x \right )+c_{1} \right ) x \right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {{\left (\left (-x^{2}+3 \ln \left (x \right )+c_{1} \right ) x \right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{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*}