Internal problem ID [1019]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {3 y^{\prime } y^{2} x -y^{3}=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
dsolve(3*x*y(x)^2*diff(y(x),x)=y(x)^3+x,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (\left (\ln \left (x \right )+c_{1} \right ) x \right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (\left (\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 (\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: 0.196 (sec). Leaf size: 69
DSolve[3*x*y[x]^2*y'[x]==y[x]^3+x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{x} \sqrt [3]{\log (x)+c_1} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{x} \sqrt [3]{\log (x)+c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{x} \sqrt [3]{\log (x)+c_1} \\ \end{align*}